In essence, the diagonals are employed to usurp the grid.
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Hondros, whose prints are rectangular, favored longer sightlines and sharper diagonals.
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It's here that Cruel Diagonals really intersects with Megan Mitchell the archivist.
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He began incorporating intrusive diagonals and forging higher, wider and skewed horizons.
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The stems and diagonals on most letters are slab-thick or hairline-thin.
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In both cases, the paintings travel far from the geometric diagonals of the 1970s.
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The other dancers follow, locking into diagonals, lines and circles while the rhythms change.
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To make the web, pipe four intersecting lines of fudge: horizontal,vertical and two diagonals.
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By ordering the complexity of these distinct, intersecting color diagonals, the artist paradoxically unifies them.
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His compositions are deliberately unbalanced, with forms that surge from one side or along forward diagonals.
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She corrected details of floor patterns: Diamonds should keep recurring in terms of diagonals and edges.
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On diagonals and round edges, the diamond pattern makes for a more natural curve without stair-stepping.
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The letters never spell out words, so we are left appreciating their geometric verticals, horizontals, and diagonals.
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A few well-placed diagonals are all it takes to check the canvas from its own internal chaos.
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James rammed his way down the lane, pulled up for jumpers, and flung passes on 40-foot diagonals.
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Disambiguation, her debut album as Cruel Diagonals (premiering below), is a captivatingly eerie wash of experimental electronic music.
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The diagonals, like rods of rebar, reinforce their immutability as they conjure up a welter of unsettling associations.
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Here we see the process of rotating a square counterclockwise about its center point (the intersection of its diagonals).
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TJ Dillashaw likes to move on diagonals and show different stances every engagement, dancing around the cage in between.
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And although Lego has perfected the right angle, she said, it could diversify its offerings of diagonals and curves.
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The sun was high and Fran hiked briskly, ducking the blue-green diagonals of fir trees, her hair wild behind her.
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Two dark rivers intersect at diagonals in this nightscape with roofed houses proliferating against forest and mountains in the far distance.
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While horizontals and verticals are resolutely flat, diagonals and ellipses can be simultaneously flat or indicate the receding edge of perspectival space.
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The general idea was to stretch a cat's cradle of diagonals — along with streets like 5th and one-half Avenue — across the grid.
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And young Sally Marx, a student from Flushing, Queens, apparently focused on aesthetics over symbolism, building a rhythmic design based on bold diagonals.
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"It has an incredible force that combines vertical, horizontal, diagonals and round shapes, carrying almost the entire DNA of an uppercase family," he says.
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Highly graphic in bold outlines of the forms, the severe diagonals animated the space, thereby attracting small children wanting to play in the booth.
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The verticals and diagonals formed by the house frame serve to section off the watercolor, effectively establishing discrete zones of different shapes and sizes.
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Later, she used the computer to draw airier compositions with diagonals; wobbly, concentric squares; and arrays of black bands that gently rise and fall.
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Each glass bead contained DNA with slightly different information that gave a computer clues about the hypothetical rows, columns, and diagonals of the puzzle.
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John E. Bennett: I tend to like crossword puzzles that use the diagonals in the grid as part of the theme and solving process.
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There is something smart and quietly witty about rendering Judd's work as diagonals, given how strictly his world is dominated by x and y axes.
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The outer room, with its large diagonals of color, struck me as the conscious mind, the public persona that one might safely show the world.
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Think: mod black-and-white flared trousers, bell-sleeve sweaters with one single statement stripe, and elegant wrap dresses swept up in dramatically different diagonals.
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Strong vertical and horizontal bands are offset by shorter, thinner diagonals, as in "Marfa Window" (2018), where the top edges of Judd boxes become diagonal lines.
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Even the daunting 1970s Alexandra Road Estate with its diagonals of balconies, and the 1960s Balfron Tower with its suspended corridors, folded together with some patience.
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For example, among the eight corners of the three-dimensional cube, the four points (0,0,2003), (1,1,0), (1,0,1) and (0,1,1) all sit across diagonals from one another.
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"The subtle softening of corners and diagonals adds a sense of optimism," the reader is told, although it isn't specified what we're to be optimistic about.
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If you, like me, have taken an art history class, you might remember the ways in which paintings are coldly dissected into diagonals and paths of light.
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The diagonals so familiar in his work do not always move the eye in a particular direction now, as they did at the outset of his career.
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Larsen makes no attempt to hide their internal mechanics: the prismatic reduction of forms, the sweeping arcs tethered by radial lines, the thrusting diagonals and pacing parallels.
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In the following years, 1971 and 1972, he introduced bold, repetitive diagonals, nearly but never quite alluding to Pop — given his penchant for Classicism, this would have been anathema.
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The adjusted to fit abstractions lay bare the classical elegance undergirding Lawler's compositions, accentuating the importance of horizontal and vertical alignments and the disorienting effects of diagonals and curves.
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She outputted these thickets of oscillating, stuttering strokes to a plotter, whose pen could move only along X and Y axes; look closely and you can see the janky diagonals.
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The last room of the exhibition is occupied by the magnificent "Ttéia" (1976–2004), where clusters of copper wires extend in diagonals from floor to ceiling like beams of sunlight.
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In the earliest painting here, "B/W V" (1967–68), each horizontal or vertical black line that dominates the painting intersects with at most two diagonals, and there are no curves.
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Scenes are almost obnoxiously symmetrical, often structured by a face-on shot of a building, or prettily off-center and enlivened by diagonals and organic forms (a wayward path, a flower).
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Above a field of orange and blue diagonals, "Zonk Out" juxtaposes a line of four yellow jagged shapes that resemble mop heads, shag throw pillows or Blondie (Dagwood's wife) on drugs.
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The revised design aims to strike a balance to include vendors, planters and benches while also maximizing views of the Noguchi Cube from directly across Broadway and on diagonals through each corner.
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Those circled squares on the down diagonals are examples of triple-checks — letters that form three different entries in three different directions, a very daunting endeavor that definitely requires some engineering chops.
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G. Cutting a new street between Seventh and Eighth Avenues, from Penn Station to 53rd Street, was one of many proposals for additional avenues and diagonals, all designed to relieve traffic congestion in Manhattan.
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Some, citing the photograph's thrusting diagonals, see the influence of Baroque masters such as Rubens and Caravaggio, painters who rejected the symmetry of the Renaissance in favour of off-kilter compositions filled with dynamic tension.
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But his adaptation of sharp diagonals — an attribute of form mostly foreign to Color Field painters, other than Kenneth Noland's Chevrons (1963–64) — offered Odita the potential to grapple with emotional content through formal conflict.
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I really liked the idea, but the construction, which needed to place the diagonals within the strictures of a symmetrical grid while including a large number of triple-checked letters, was very hard to manage.
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This is very difficult given the immense power of the queen; the player must ensure that each queen is placed on its own column, but such that no queen threatens another along other diagonals and rows.
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More paradoxically, even though we are conditioned to read the convergent diagonals of the painting's setting as indicating deep space, we are not exclusively pulled into a fictive distance by the rippling slashes in the sand.
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Indeed, I was taken by several paintings I had never seen before, including the "Untitled" diagonals from the mid-1970s as well as the heroically poured and squeegeed paintings "Oh Ed #2" and "Montirr Aix" (both 1999).
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" He drew on Polaroid pictures he had taken of his dining table to rethink it as "an interior with a complexity of horizontals and verticals and diagonals," he said, "so that it would be like being in a jungle of legs.
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Its construction is similar to the "Dyer's Shop": thrusting diagonals reaching way beyond the edges of the canvas; paper-thin geometric planes laid one on top of another; and a bright, white shape that both pulls you forward and opens beyond.
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In "Jesús 'Chuy' Torres, Poet/Performer" (1997), Torres's shadow extends over the gravel in the street, and cuts across and defies the prescribed diagonals of a nearby fence; they act as anchors, or legs almost, planting this immigrant identity as one to stay.
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But unlike Arbus, who abstracted and softened her scenery so it resembles stage flats, Hujar employed in his square-format pictures all the tricks of Henri Cartier-Bresson: strong diagonals (of slides, swings and supporting rails); inventively off-kilter angles; and asymmetric groupings.
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Paper place mats create a network of parallel diagonals, compounded by a fork and knife, disrupted by a misplaced spoon, and traversed by the butter on the pancakes, which has melted from left to right to create the image's only orthogonal line.
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Letter of Recommendation As if through a sieve, the kind you might use to dust confectioners' sugar on a cake, the snow began to fall one Sunday afternoon in January — white diagonals obscuring the view just outside my mother's living-room window.
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" She added, "Most of the dances achieved their impact through the structure of their group patterns, such as circles and diagonals, and the inherent value of the movements themselves — which mixed deliberate simplicity with an occasional leap or step from the ballet classroom.
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"The Raising of Lazarus" and "The Adoration of the Shepherds," hanging on adjacent walls in their own darkened gallery in Messina's Museo Regionale, are both exercises in diagonals, one ascending and the other descending, but both ostensibly terminating in signs of hope.
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For example, it can be rotated by 90 degrees counterclockwise, so that the arrangement of the labeled corners, starting from the lower right, ends up as (D, A, B, C). Or it can be rotated 180, 270 or 360 degrees, or flipped across either of its diagonals.
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Soldevilla cites Malevich in "Sin Titulo" (21950), in which the spatial effects of overlapping color are dramatized in contrasts of scale and shape: along opposing diagonals, the green triangle flies downward and the white rectangle recedes; the brown circle echoes the curving edge of the black ground.
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The most striking is "Untitled (P-1714)" (2017), with its vertical, zigzagging orange dashes coupled with a diagonal set of straight and looping purple lines that thrust the orange strokes forward in space, while a barely discernible gray field hovers like a geometric shadow behind the purple diagonals .
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Lindsey Jones has an insistent string of rapid steps (emboîtés), with legs turned out, scarcely advancing, like a witty drill; Mr. Collins bobs backward in shimmering jumps that trace diagonals across the stage; Mr. Lozano, in profile to us, does an accelerating run on the spot of gathering force.
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Here the veteran Rasheed Araeen, who emigrated from Karachi, Pakistan to London in 21966, is displaying several new tessellated abstract paintings, though even stronger are his wall-mounted wooden sculptures, formed of repeated squares and diagonals and painted solid colors that sometimes parallel and sometimes interrupt the armature.
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Driven by Hokusai's series Thirty-Six Views of Mt Fuji (1830-18903), he experiments with parallel and incongruent diagonals in "Seascape near Les Saintes-Maries-de-la-Mer" (1888), in which the horizon buckles as if bending under the weight of the serene, subtly gradated color fields across the expansive sky.
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All around the MDI, the slanted roof recalls the high modern architecture of Alvar Aalto or Marcel Breuer — but once inside the main axis of the building, called the "Living Room," the diagonals meet in a pitched gable roof that pays homage to the gray, post-war bungalows in the neighborhood.
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Mehta learned from Picasso and Barnett Newman when he painted simplified, stylized lovers whose bodies were slashed by bold diagonals; he drew just as much inspiration from Rajasthani miniatures, like the 16th-century example here whose depiction of Krishna at war also makes use of flattened figures in solid color.
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Suits made with Savile Row-quality wools and silks were cut on the bias, the lines of the wool's window panes running at distorted diagonals, while extravagant feathers dotted collars and hemlines and a leather cape with rows of hand-cut incisions was made to look like the peck of a bird's beak.
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The contrast between the downward-pointing verticals, horizontals, and diagonals of the "yellow" house and the diagonal planes formed by the outlines of the shadows may be purely factual, but they elicit so much more: the house's angles, pointing downward, seem suspended and about to plummet; the shadow's shapes become collapsed forms, a cardboard box in the process of being unfolded and flattened.
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In her large, multi-media works, vivid spray-painted, translucent atmospheres are contrasted with opaque, hand-painted geometric areas reminiscent of pointillism or pixelation, a juxtaposition that creates significant spatial depth Recent works such as "Gray Matter" (2017) inhabit an intersection between the theatrical baroque and the graphic specificity of stained glass, which is accentuated a dynamic sense of movement, swirling spirals, upward diagonals, and heavy impasto.
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We went back and forth a few times about the best way to hide the two names (Easter egg #1, you might call it); I had mentioned that the least constrained way was to just include a message in the first letters of the clues, but breaking up the names into chunks (as we ended up doing) or hiding them along diagonals could also possibly work.
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The JoyCon D-pad is completely unsuited for fighting games where special moves are executed using smooth arcs from forward to down to halfway back again; and while the Pro Controller fares better, when the Switch is in TV mode, there's still areas of uncertainty, of inconsistency, in the button presses, where diagonals can be picked up as horizontal moves, and thus a retaliatory attack fails and you receive a kick in the chops.
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Each of the 22001 oil-on-wood-panel paintings in Don Voisine: X/V, a 21978-year (22-22017) survey of the Maine-born, Brooklyn-based painter currently on view at the Center for Contemporary Maine Art, presents a seemingly uncomplicated format, often consisting of broad, black, hard-edged central forms, sometimes X-shaped, sometimes diagonals, with triangular notches of different sizes along the edge and stripes and bands of color at top and bottom or on the sides.
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Then, a striking pairing of LeWitt's "Double Wall Piece" (111503) and an untitled work by Hesse (1964) crystallizes the divergence of their paths: LeWitt embraces the Minimalist grid, moving into three dimensions and eliminating all colors except black and white in the process; Hesse — who would soon move into three dimensions, too, and strip away most color — nods to the grid by structuring her piece with a border of small rectangles, but uses collage elements and looser, almost figurative forms set on diagonals to interrupt it.
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If the violence in a painting like "Interrogation I" feels timeless, with its jackbooted guards pummeling the above-mentioned naked victim with a steel pipe as he hangs by his feet like Titian's Marsyas or Rembrandt's slaughtered ox, his face obscured by foreshortening, his scrotum beaten to jelly, that impression is derived as much from the inventiveness of the composition — a controlled explosion of diagonals (steel pipe, holster strap, nude legs, rope ends) beside a vertical column of inexplicably untouched canvas — as from the shape-shifting nature of barbarity itself.
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A polyhedron (a solid object in three-dimensional space, bounded by two- dimensional faces) may have two different types of diagonals: face diagonals on the various faces, connecting non-adjacent vertices on the same face; and space diagonals, entirely in the interior of the polyhedron (except for the endpoints on the vertices). Just as a triangle has no diagonals, so also a tetrahedron (with four triangular faces) has no face diagonals and no space diagonals. A cuboid has two diagonals on each of the six faces and four space diagonals.
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A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and space diagonals. In 2009, dozens of perfect parallelepipeds were shown to exist,. answering an open question of Richard Guy. One example has edges 271, 106, and 103, minor face diagonals 101, 266, and 255, major face diagonals 183, 312, and 323, and space diagonals 374, 300, 278, and 272.
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For, in the Bilinski dodecahedron, the long body diagonal is parallel to the short diagonals of two faces, and to the long diagonals of two other faces. In the rhombic dodecahedron, the corresponding body diagonal is parallel to four short face diagonals, and in any affine transformation of the rhombic dodecahedron this body diagonal would remain parallel to four equal-length face diagonals. Another difference between the two dodecahedra is that, in the rhombic dodecahedron, all the body diagonals connecting opposite degree-4 vertices are parallel to face diagonals, while in the Bilinski dodecahedron the shorter body diagonals of this type have no parallel face diagonals.
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The smallest perfect parallelepiped has edges 271, 106, and 103; short face diagonals 101, 266, and 255; long face diagonals 183, 312, and 323; and body diagonals 374, 300, 278, and 272.
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The chessboard diagonals represent optional constraints, as some diagonals may not be occupied. If a diagonal is occupied, it can be occupied only once.
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Therefore, :AE = CE :BE = DE. Since the diagonals AC and BD divide each other into segments of equal length, the diagonals bisect each other. Separately, since the diagonals AC and BD bisect each other at point E, point E is the midpoint of each diagonal.
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Thus each face diagonal of a cube with side length a is a\sqrt 2.. A regular dodecahedron has 60 face diagonals (and 100 space diagonals)..
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If a line segment connecting the diagonals of a quadrilateral bisects both diagonals, then this line segment (the Newton Line) is itself bisected by the vertex centroid.
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The diagonals next to the edge diagonals contain the positive integers in order, but with each integer stated twice . Moving inwards, the next pair of diagonals contain the "quarter-squares" (), or the square numbers and pronic numbers interleaved. The next pair of diagonals contain the alkane numbers l(6, n) (). And the next pair of diagonals contain the alkane numbers l(7, n) (), while the next pair has the alkane numbers l(8, n) (), then alkane numbers l(9, n) (), then l(10, n) (), l(11, n) (), l(12, n) (), etc.
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Star diagonals are available in 0.965", 1.25" and 2" diameters. The 2" diagonals allow larger longer focal length low power 2 inch barrel eyepieces for a greater field of view. Star diagonals come in all price ranges, from as low as a few dollars up to hundreds of dollars.
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If no three diagonals of a convex polygon are concurrent at a point in the interior, the number of interior intersections of diagonals is given by \binom n4.Poonen, Bjorn; Rubinstein, Michael. "The number of intersection points made by the diagonals of a regular polygon". SIAM J. Discrete Math.
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Another isosceles trapezoid. The diagonals of an isosceles trapezoid have the same length; that is, every isosceles trapezoid is an equidiagonal quadrilateral. Moreover, the diagonals divide each other in the same proportions. As pictured, the diagonals AC and BD have the same length () and divide each other into segments of the same length ( and ).
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The tetrahedron and the Császár polyhedron have no diagonals at all: every pair of vertices in these polyhedra forms an edge. It remains an open question whether there are any other polyhedra (with manifold boundary) without diagonals , although there exist non-manifold surfaces with no diagonals and any number of vertices greater than five .
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More precisely, clusters are in one-to-one correspondence with triangulations and the distinguished elements are in one-to-one correspondence with diagonals (line segments joining two vertices of the polygon). One can distinguish between diagonals in the boundary, which belong to every cluster, and diagonals in the interior. This corresponds to a general distinction between coefficient variables and cluster variables.
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This allows them to carry more load. The Ashtabula Bridge diagonals, however, were only loosely fitted to the angle blocks. Prestressing brought the diagonals into a relatively close fit with the angle blocks, but did not put the diagonals in compression. The problem was worsened because shims were used to fill the space between the diagonal bearings and the angle blocks.
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Poor construction of the bridge's diagonals worsened the stresses placed on the lugs on the angle blocks. Howe trusses rely on prestressing of braces and counter-braces to improve the way the bridge carries load. Tightening the nuts on the vertical posts (prestressing) puts the verticals in tension (stretches them). If the diagonals are already closely fitted to the angle blocks, prestressing compresses the diagonals.
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Several more characterizations are known in the four subtriangles formed by the diagonals.
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Buchholz and MacDougall also showed that, in every Robbins pentagon, either all five of the internal diagonals are rational numbers or none of them are. If the five diagonals are rational (the case called a Brahmagupta pentagon by ), then the radius of its circumscribed circle must also be rational, and the pentagon may be partitioned into three Heron triangles by cutting it along any two non-crossing diagonals, or into five Heron triangles by cutting it along the five radii from the circle center to its vertices. Buchholz and MacDougall performed computational searches for Robbins pentagons with irrational diagonals but were unable to find any. On the basis of this negative result they suggested that Robbins pentagons with irrational diagonals may not exist.
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These diagonals (often called Star diagonals) use a mirror set at a 45° angle inside the diagonal to turn the telescope's image at a 90° angle to the rear cell. Mirror diagonals produce an image in the eyepiece that is correctly oriented vertically, but is reversed left-to-right horizontally. This causes image reversal, the view in the eyepiece is flipped left-right. The major advantage to mirror diagonals is that they cost less to produce to a high degree of optical accuracy compared to a prism and that they do not introduce any color errors to the image.
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In Reversed Mosaic stitch alternate cells run in opposite diagonals to form a chequerboard effect.
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The remaining three edges form diagonals of the polyhedron, but lie entirely outside the polyhedron.
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Animation of a net of a regular (pentagonal) dodecahedron being folded 3D model of a regular dodecahedron A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals).. It is represented by the Schläfli symbol {5,3}.
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How many diagonals are needed to divide a heptagon, a nonagon, and an undecagon into triangles?
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This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2_D square; broken oblique squares are 2-D in a 3-D cube. # The table shows the minimum lines or squares required for each class (i.e. Proper).
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The Pratt truss was invented in 1844 by Thomas and Caleb Pratt. A Pratt truss has vertical members and diagonals that slope down towards the center. The interior diagonals are under tension, and the vertical elements are under compression. The Pennsylvania truss is a variation on the Pratt truss.
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The Varignon parallelogram is a rhombus if and only if the two diagonals of the quadrilateral have equal length, that is, if the quadrilateral is an equidiagonal quadrilateral.. The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. If a crossing quadrilateral is formed from either pair of opposite parallel sides and the diagonals of a parallelogram, the Varignon parallelogram is a line segment traversed twice.
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But two of these diagonals are the same as the diagonals of the tangential quadrilateral, and the third diagonal of the hexagon is the line through two opposite points of tangency. Repeating this same argument with the other two points of tangency completes the proof of the result. If the extensions of opposite sides in a tangential quadrilateral intersect at J and K, and the diagonals intersect at P, then JK is perpendicular to the extension of IP where I is the incenter.
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"Horwitz bishops", a configuration in which two bishops are aggressively placed on adjacent diagonals, are named after Horwitz.
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To create a 3 in-a-row of one's pieces either horizontally or vertically. Diagonals do not count.
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It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon.
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In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.Michael John Bradley (2006). The Birth of Mathematics: Ancient Times to 1300. Publisher Infobase Publishing. .
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They are supplemented by additional diagonals at the ends and four wooden buttresses along the exterior on either side.
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A Pratt truss Gatton Railway Bridge showing the Pratt truss design A Pratt truss includes vertical members and diagonals that slope down towards the center, the opposite of the Howe truss. The interior diagonals are under tension under balanced loading and vertical elements under compression. If pure tension elements are used in the diagonals (such as eyebars) then crossing elements may be needed near the center to accept concentrated live loads as they traverse the span. It can be subdivided, creating Y- and K-shaped patterns.
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An equidiagonal quadrilateral, showing its equal diagonals, Varignon rhombus, and perpendicular bimedians In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics, where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types..
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In any convex quadrilateral ABCD, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of the line segment connecting the midpoints of the diagonals. Thus : a^2 + b^2 + c^2 + d^2 = p^2 + q^2 + 4x^2 where x is the distance between the midpoints of the diagonals. This is sometimes known as Euler's quadrilateral theorem and is a generalization of the parallelogram law. The German mathematician Carl Anton Bretschneider derived in 1842 the following generalization of Ptolemy's theorem, regarding the product of the diagonals in a convex quadrilateralAndreescu, Titu & Andrica, Dorian, Complex Numbers from A to...Z, Birkhäuser, 2006, pp. 207–209.
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The Grünbaum–Rigby configuration can be constructed from the seven points of a regular heptagon and its 14 interior diagonals. To complete the 21 points and lines of the configuration, these must be augmented by 14 more points and seven more lines. The remaining 14 points of the configuration are the points where pairs of equal-length diagonals of the heptagon cross each other. These form two smaller heptagons, one for each of the two lengths of diagonal; the sides of these smaller heptagons are the diagonals of the outer heptagon.
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Every kite is orthodiagonal, meaning that its two diagonals are at right angles to each other. Moreover, one of the two diagonals (the symmetry axis) is the perpendicular bisector of the other, and is also the angle bisector of the two angles it meets. One of the two diagonals of a convex kite divides it into two isosceles triangles; the other (the axis of symmetry) divides the kite into two congruent triangles. The two interior angles of a kite that are on opposite sides of the symmetry axis are equal.
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A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and body diagonals, but not necessarily with all right angles; a perfect cuboid is a special case of a perfect parallelepiped. In 2009, dozens of perfect parallelepipeds were shown to exist,. answering an open question of Richard Guy. Some of these perfect parallelepipeds have two rectangular faces.
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The painting contains only diagonal lines. The lack of horizontal and vertical lines throughout the painting along with the deep colors, create tension. This tension further highlights the chaos and violence of the animal's lives. These diagonals are emphasized in three primary ways: composition order, diagonal posture of the animals, and “the animal’s position in conformity with the diagonals.
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All the centers of inellipses of a given quadrilateral fall on the line segment connecting the midpoints of the diagonals of the quadrilateral.
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For a convex quadrilateral with sides a, b, c, d, diagonals e and f, and g being the line segment connecting the midpoints of the two diagonals, the following equations holds: :a^2+b^2+c^2+d^2=e^2+f^2+4g^2 If the quadrilateral is a parallelogram, then the midpoints of the diagonals coincide so that the connecting line segment g has length 0. In addition the parallel sides are of equal length, hence Euler's theorem reduces to :2a^2+2b^2=e^2+f^2 which is the parallelogram law. If the quadrilateral is rectangle, then equation simplifies further since now the two diagonals are of equal length as well: :2a^2+2b^2=2e^2 Dividing by 2 yields the Euler–Pythagoras theorem: :a^2+b^2=e^2 In other words, in the case of a rectangle the relation of the quadrilateral's sides and its diagonals is described by the Pythagorean theorem.Lokenath Debnath: The Legacy of Leonhard Euler: A Tricentennial Tribute.
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The Császár polyhedron is named after Hungarian topologist Ákos Császár, who discovered it in 1949. The dual to the Császár polyhedron, the Szilassi polyhedron, was discovered later, in 1977, by Lajos Szilassi; it has 14 vertices, 21 edges, and seven hexagonal faces, each sharing an edge with every other face. Like the Császár polyhedron, the Szilassi polyhedron has the topology of a torus. There are other known polyhedra such as the Schönhardt polyhedron for which there are no interior diagonals (that is, all diagonals are outside the polyhedron) as well as non-manifold surfaces with no diagonals .
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The N queens problem is an example of a generalized exact cover problem. The problem involves four kinds of constraints: : Rank: For each of the N ranks, there must be exactly one queen. : File: For each of the N files, there must be exactly one queen. : Diagonals: For each of the 2N − 1 diagonals, there must be at most one queen.
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From seemingly passive play, it often springs to life from three diagonals, frequently switching between them. Those diagonals are the b1–h7 diagonal, the a2–g8 diagonal, and the a4–e8 diagonal. White's usually maneuvers Nd2–f1–g3. Alternatively, it could be maneuvered Nd2–f1–e3, preventing a pin against the knight on f3, and threatening to jump into d5.
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1\. P-76 P-34, 2. P-26 P-54, 3. P-25. The opening starts with a position that with both players' bishop diagonals open looks similar to White's Cheerful Central Rook (which hadn't been invented yet). Both bishop diagonals are open, Black has chosen a Static Rook position, and White has pushed their central pawn. 3...P-55.
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A parallelogram. The sides are shown in blue and the diagonals in red. In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.
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The Pratt truss bridge was invented in 1844 by Thomas and Caleb Pratt. A Pratt truss has vertical members and diagonals that slope down towards the center. The interior diagonals are under tension, and the vertical elements are under compression. Pratt truss bridges were the preferred design for medium-span vehicular bridges during the late nineteenth and early twentieth centuries.
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A sufficient condition for similarity of polygons is that corresponding sides and diagonals are proportional. For given n, all regular n-gons are similar.
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The two diagonals and the two tangency chords are concurrent.Yiu, Paul, Euclidean Geometry, , 1998, pp. 156–157.Grinberg, Darij, Circumscribed quadrilaterals revisited, 2008 One way to see this is as a limiting case of Brianchon's theorem, which states that a hexagon all of whose sides are tangent to a single conic section has three diagonals that meet at a point. From a tangential quadrilateral, one can form a hexagon with two 180° angles, by placing two new vertices at two opposite points of tangency; all six of the sides of this hexagon lie on lines tangent to the inscribed circle, so its diagonals meet at a point.
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In a regular pentagon the ratio of a diagonal to a side is the golden ratio, while intersecting diagonals section each other in the golden ratio.
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In addition to appearing as the edges and diagonals of polygons and polyhedra, line segments also appear in numerous other locations relative to other geometric shapes.
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A magic square in which the broken diagonals have the same sum as the rows, columns, and diagonals is called a pandiagonal magic square... Examples of broken diagonals from the number square in the image are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4. 111x121px The fact that this square is a pandiagonal magic square can be verified by checking that all of its broken diagonals add up to the same constant: : 3+12+14+5=34 : 10+1+7+16=34 : 10+13+7+4=34 One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original: 111x121px111x121px The set of numbers {3, 12, 14, 5} of a broken diagonal, wrapped around the original square, can be seen starting with the first square of the ghost image and moving down to the left.
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For drawings in which the outer face may be freely chosen, the area lower bound of may not be tight. showed that this graph, and any graph formed by adding diagonals to its quadrilaterals, can be drawn within a box of dimensions n/3 × 2n/3. When no extra diagonals are added the nested triangles graph itself can be drawn in even smaller area, approximately n/3 × n/2, as shown.
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The Double Wing Attack is one of the most traditional openings dating back to over 250 years ago. Double Wing openings have two general variations. The first one has both bishop diagonals open (that is, P-76 and P-34) while the second type has bishop diagonals closed. The open bishop diagonal variations were most common historically being played from the 1700s and throughout the first part of the twentieth century.
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Since the area of the diagonals of the square is 0, the probability that the dart will land exactly on a diagonal is 0. That is, the dart will almost never land on a diagonal (equivalently, it will almost surely not land on a diagonal), even though the set of points on the diagonals is not empty, and a point on a diagonal is no less possible than any other point.
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A prototypical flip graph is that of a convex n-gon \pi. The vertices of this graph are the triangulations of \pi, and two triangulations are adjacent in it whenever they differ by a single interior edge. In this case, the flip operation consists in exchanging the diagonals of a convex quadrilateral. These diagonals are the interior edges by which two triangulations adjacent in the flip graph differ.
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Similar to the ordinary complex plane, a point not on the diagonals has a polar decomposition using the parametrization of the unit hyperbola and the alternative radial length.
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Side Pawn Capture has the same form as a Double Wing Attack opening with both players' bishop diagonals open. (Double Wing Attack with open bishop diagonals was more commonly played before the twentieth century while in modern times it usually keeps the bishop diagonals closed initially.) However, it deviates from Double Wing Attack when one player (usually Black) or both players capture the opponent's side pawn with their rook in a gambit move. The side pawns referred to are the pawns that are advanced in order to open both players' bishop diagonal (on 44 for White and 76 for Black). The games often have a different character compared with Double Wing Attack and can often feature very dynamic play.
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The bottoms of the diagonals tend to protrude below the sheathing. The Brown truss is noted for economy of materials as it can be built with very little metal.
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For all convex pentagons, the sum of the squares of the diagonals is less than 3 times the sum of the squares of the sides.Inequalities proposed in “Crux Mathematicorum”, .
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Image:CubeAndStel.svg Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices. New edges of a faceted polyhedron may be created along face diagonals or internal space diagonals. A faceted polyhedron will have two faces on each edge and creates new polyhedra or compounds of polyhedra. Faceting is the reciprocal or dual process to stellation.
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Proof without words of Varignon's theorem: 1\. An arbitrary quadrilateral and its diagonals. 2\. Bases of similar triangles are parallel to the blue diagonal. 3\. Ditto for the red diagonal. 4\.
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For n = 4, the area of an arbitrary quadrilateral is given by the formula S = pq sin(θ)/2 where p and q are the two diagonals of the quadrilateral and θ is either of the angles they form with each other. In order for the diameter to be at most 1, both p and q must themselves be at most 1. Therefore, the quadrilateral has largest area when the three factors in the area formula are individually maximized, with p = q = 1 and sin(θ) = 1\. The condition that p = q means that the quadrilateral is an equidiagonal quadrilateral (its diagonals have equal length), and the condition that sin(θ) = 1 means that it is an orthodiagonal quadrilateral (its diagonals cross at right angles).
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The Hesse configuration has the same incidence relations as the lines and points of the affine plane over the field of 3 elements. That is, the points of the Hesse configuration may be identified with ordered pairs of numbers modulo 3, and the lines of the configuration may correspondingly be identified with the triples of points satisfying a linear equation . Alternatively, the points of the configuration may be identified by the squares of a tic-tac-toe board, and the lines may be identified with the lines and broken diagonals of the board. Each point belongs to four lines: in the tic tac toe interpretation of the configuration, one line is horizontal, one vertical, and two are diagonals or broken diagonals.
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The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter, the square has the largest area. The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle. The Japanese theorem for cyclic quadrilateralsCyclic Quadrilateral Incentre-Rectangle with interactive animation illustrating a rectangle that becomes a 'crossed rectangle', making a good case for regarding a 'crossed rectangle' as a type of rectangle.
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The Pratt truss form, invented in 1844 by Thomas and Caleb Pratt, is the most common truss form in California and the United States. This form first appeared as a "combination truss" built in wood and iron with wooden vertical members, chords, and endposts, and iron tension diagonals. The basic form changed to all-metal construction by the 1880s. It retained the light metal diagonals but substituted heavier metal beams, posts, and chords for the wooden members.
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For a given span, a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.
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1\. P-77 P-34, 2. P-26. Open bishop diagonals. Black plays Static Rook. 2\. ...P-54. White pushes the central pawn, the signature move of Cheerful Central Rook. 3\. P-25.
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Each of the two smaller heptagons has 14 diagonals, seven of which are shared with the other smaller heptagon. The seven shared diagonals are the remaining seven lines of the configuration. The original construction of the Grünbaum–Rigby configuration by Klein viewed its points and lines as belonging to the complex projective plane, rather than the Euclidean plane. In this space, the points and lines form the perspective centers and axes of the perspective transformations of the Klein quartic.. See transl. p. 297.
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It simplified the 9×9 magic square puzzle so that each row, column, and broken diagonals contained only the numbers 1–9, but did not mark the subsquares. Although they are unmarked, each 3×3 subsquare does indeed comprise the numbers 1–9 and the additional constraint on the broken diagonals leads to only one solution. These weekly puzzles were a feature of French newspapers such as L'Écho de Paris for about a decade, but disappeared about the time of World War I.
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Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In the latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral: Brahmagupta's theorem: If a cyclic quadrilateral has diagonals that are perpendicular to each other, then the perpendicular line drawn from the point of intersection of the diagonals to any side of the quadrilateral always bisects the opposite side. Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalization of Heron's formula), as well as a complete description of rational triangles (i.e. triangles with rational sides and rational areas).
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Active continuous connection was not used on the bridge: The members of the chords were connected to angle blocks at only every other panel, the five beams making up each chord did not have a continuous interconnection between them, and the none of the parallel I-beams making up the diagonals were continuously interconnected. Åkesson points out that construction errors probably made the diagonals even less effective as thin members were placed where thicker ones should have gone and vice versa. The braces and counter-braces in a Howe truss must be the same size for the truss system to be robust and redundant. Making a brace stronger relative to a counter-brace, for example, actually reduces robustness and redundancy by changing the relative distribution of forces on the diagonals.
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In mathematics, particularly matrix theory, a band matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
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If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions. It is the sum of the sums of the divisors of the first 16 positive integers.
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This method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a pentadiagonal system of equations obtained while solving an elliptic partial differential equation in a two-dimensional space by a finite difference method. The LU approximate decomposition was looked in the same pentadiagonal form as the original matrix (three diagonals for L and three diagonals for U) as the best match of the seven possible equations for the five unknowns for each row of the matrix.
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It has also been reported that triangular lattices yield more accurate structures than other lattice shapes when compared to crystallographic data. To combat the parity problem, several researchers have suggested using triangular lattices when possible, as well as a square matrix with diagonals for theoretical applications where the square matrix may be more appropriate. Hexagonal lattices were introduced to alleviate sharp turns of adjacent residues in triangular lattices. Hexagonal lattices with diagonals have also been suggested as a way to combat the parity problem.
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Optionally, the minor improvements of marching tetrahedrons may be used to correct the aforementioned ambiguity in some configurations. In marching tetrahedra, each cube is split into six irregular tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the cube, we now have nineteen edges: the original twelve, six face diagonals, and the main diagonal.
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As well as defining rotation distance, asked for the computational complexity of computing the rotation distance between two given trees. The existence of short rotation sequences between any two trees implies that testing whether the rotation distance is at most belongs to the complexity class NP, but it is not known to be NP-complete, nor is it known to be solvable in polynomial time. The rotation distance between any two trees can be lower bounded, in the equivalent view of polygon triangulations, by the number of diagonals that need to be removed from one triangulation and replaced by other diagonals to produce the other triangulation. It can also be upper bounded by twice this number, by partitioning the problem into subproblems along any diagonals shared between both triangulations and then applying the method of to each subproblem.
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In Boden's mate two attacking bishops on criss-crossing diagonals deliver mate to a king obstructed by friendly pieces, usually a rook and a pawn.Renaud and Kahn (1962), p. 89.R. Schulder vs. Samuel Boden (London, 1853).
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The verticals and diagonals he uses, especially in Alone in Green (1973) and Battlefield #31 (1974), bring stress and energy to his paintings, trying to evoke the feeling that what is going on in Brazil is wrong.
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This is done by two techniques namely smoothing and flipping. In mesh smoothing the location of mesh vertices are adjusted. While in Flipping the diagonals of triangulated quadrilateral are exchanged. Flipping improves the quality measure of triangles.
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Verdier duality gives another link between them: morally speaking, it exchanges "∗" and "!", i.e. in the synopsis above it exchanges functors along the diagonals. For example the direct image is dual to the direct image with compact support.
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In mathematics, a semiperfect magic cube is a magic cube that is not a perfect magic cube, i.e., a magic cube for which the cross section diagonals do not necessarily sum up to the cube's magic constant.
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For every orthodiagonal quadrilateral, we can inscribe two infinite sets of rectangles: :(i) a set of rectangles whose sides are parallel to the diagonals of the quadrilateral :(ii) a set of rectangles defined by Pascal-points circles..
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Support piers consist of timber piles under the approach spans and four pairs of cast iron cylinders 1.83m diameter braced with wrought iron crossed rods. The ten panel Pratt trusses are simply supported and have horizontally positioned I-sections for the upper chords and sloping end diagonals, but flat metal strips for the tension bottom chords and for the tension diagonals. There are metal stringers on metal cross girders, the whole being located at about the mid depth of the main trusses. The piers are twin metal cylinders.
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Using diagonals to align subjects and the reciprocal diagonals associated to the size of the frame, one would be able to create a highly intricate work of fine art. For example, world renowned portrait photographer Annie Liebovitz used this method to create an image, among many others, for Vanity Fair Magazine. The image correctly posed each of the models to intersect the subject with a corresponding diagonal to draw the viewer to the main idea of the photograph. This powerful process was used regularly by French painter turned film photographer: Henri Cartier-Bresson.
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In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions. In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic.
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This assumption means that members of the truss (chords, verticals and diagonals) will act only in tension or compression. A more complex analysis is required where rigid joints impose significant bending loads upon the elements, as in a Vierendeel truss. In the bridge illustrated in the infobox at the top, vertical members are in tension, lower horizontal members in tension, shear, and bending, outer diagonal and top members are in compression, while the inner diagonals are in tension. The central vertical member stabilizes the upper compression member, preventing it from buckling.
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P lies on the Newton line EF In Euclidean geometry Newton's theorem states that in every tangential quadrilateral other than a rhombus, the center of the incircle lies on the Newton line. Let ABCD be a tangential quadrilateral with at most one pair of parallel sides. Furthermore, let E and F the midpoints of its diagonals AC and BD and P be the center of its incircle. Given such a configuration the point P is located on the Newton line, that is line EF connecting the midpoints of the diagonals.
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The history of the bridge indicates that some of these shims had come loose over time and fallen away. The loss of shims induced uneven loading, as the more tightly-connected diagonals absorbed load before the loose ones did. Åkesson points out that the shims themselves may even have created unequal pressure points between I-beams and the lugs, subjecting the lugs to bending forces as well as shear forces. With the diagonals not carrying the load they were intended to carry, extra stress was placed on the chords.
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The chord, diagonals, angle blocks, and vertical posts of the Ashtabula Bridge, as drawn from original plans by Charles MacDonald in 1877 Gasparini and Fields claim that the exact design of the angle blocks and the ends (the "bearings") of the diagonals are lost to history. Civil engineer Charles MacDonald, who inspected the bridge's original plans in 1877, described and made drawings of part of the angle blocks. He noted that the vertical posts were made of iron pipe in diameter with a wall thick. Inside the pipe ran an iron rod thick.
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Polygonometry was a significant part of Lexell's work. He used the trigonometric approach using the advance in trigonometry made mainly by Euler and presented a general method of solving simple polygons in two articles "On solving rectilinear polygons". Lexell discussed two separate groups of problems: the first had the polygon defined by its sides and angles, the second with its diagonals and angles between diagonals and sides. For the problems of the first group Lexell derived two general formulas giving n equations allowing to solve a polygon with n sides.
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Diagonals are connected only loosely to the joints, and rely on prestressing to perform correctly. Moreover, diagonals in tension can only withstand stress below the prestressing level. (The size of the member does not matter due to the loose fitting of the diagonal to the joint.) Proper prestressing is during construction is therefore critical in the correct performance of the bridge. Maximum stress is placed on the center of the chords when a live load reaches the center of the bridge, or when the live load extends the length of the bridge.
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It is a usual application when constructing earthquake-safe buildings.Reinforce Building With Cross Bracing, Earthquake Handbook, FEMA Hazard Mitigation Handbook Series, Federal Emergency Management Agency, 2002. Cross bracing may employ full diagonals, or corner bracing or knee bracing.
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In addition to the sides and diagonals of a quadrilateral, some important segments are the two bimedians (connecting the midpoints of opposite sides) and the four maltitudes (each perpendicularly connecting one side to the midpoint of the opposite side).
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A pentaprism provides the same inverted image orientation as viewing without a diagonal would. A simple 90-degree angle prism provides the same "flipped" or mirror reversed image as a mirror diagonal. Pentaprism diagonals are extremely difficult to find.
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Brianchon's theorem In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. It is named after Charles Julien Brianchon (1783–1864).
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Interactive Csaszar polyhedron model with vertices representing nodes. In the SVG image, move the mouse to rotate it.Ákos Császár, A Polyhedron Without Diagonals. , Bolyai Institute, University of Szeged, 1949 A complete graph with nodes represents the edges of an -simplex.
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A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant. A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an n \times n pandiagonal magic square can be regarded as having 8n^2 orientations.
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Below the juvenile's wing linings are light rufous to warm buff like the body colour. Usually juveniles appear with darker tips to greater coverts forming wing-diagonals (sometimes lacking or confined to carpal area) and a small but distinct area of white on primaries against the blackish tips. Until the 3rd year, the young eagles appear more like a 1st year juvenile than an adult, but begin developing more streaks below and darker greater underwing coverts. By the 4th year, the subadult Bonelli's are increasingly similar to the adult, with an increasing subterminal band, a whiter underbody and fairly prominent underwing-diagonals.
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The sums of the areas of opposing triangles are equal, that is Area(BCL) + Area(DAL) = Area(LAB) + Area(DLC) Anne's theorem, named after the French mathematician Pierre-Leon Anne (1806–1850), is a statement from Euclidean geometry, which describes an equality of certain areas within a convex quadrilateral. Specifically, it states: :Let ABCD be a convex quadrilateral with diagonals AC and BD, that is not a parallelogram. Furthermore let E and F be the midpoints of the diagonals and L be an arbitrary point in the interior of ABCD. L forms four triangles with the edges of ABCD.
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To correct this problem, Stone added more iron I-beams to the diagonals to strengthen them. The placement, size, and number of beams added is not clear, but Stone likely added two I-beams to the brace in the end panel, two I-beams to the brace in the first panel from the end, and one I-beam to the second panel from the end. This worsened the bridge's dead load problem. Collins, Congdon, Rogers, and Stone all later testified that the I-beams making up the diagonals were now turned 90 degrees, so that the flanges were horizontal.
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The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is cyclic (inscribed in a circle), these maltitudes are concurrent at (all meet at) a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. The perpendicular bisector construction forms a quadrilateral from the perpendicular bisectors of the sides of another quadrilateral.
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The colors of the painting are rich, dense, and festive. The composition is organized with three main diagonals: the angle of the boy's tilted back and head, the angle of the deep-green curtain behind the boy, and the long angle of the seat and table rising from the lower left. These three angles are countered by the angles of the boy's thighs and arms, creating a tightly articulated structure of intersecting diagonals. This painting was acquired from Cézanne by art dealer Ambroise Vollard, probably in 1895, and successively acquired by art collectors Marcell Nemes in 1909 and Gottlieb Reber in 1913.
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The bridge consists of six Warren Truss panels on each side. All the interior verticals are paired laced angles, diagonals were made from pairs of angles. The heaviest are located in the outer panels. Verticals and diagonal members have riveted stay plates.
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1\. P-76 P-34. The most common first two moves in shogi: bishop diagonals are opened. 2\. R-68. Black swings their rook to the sixth file on their second turn. This is the characteristic of Bishop Exchange Fourth File Rook.
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Additionally, earlier Fortress openings in the first part of the 20th century did not follow from the standard 1. P-76 P-84 opening used today and instead developed from mutual opening of the bishop diagonals with 1. P-76 P-34.
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The end posts and upper chord are made up of six flanged cast elements riveted together. The intermediate verticals and lateral struts have four apiece. The diagonals and lower chord have rectangular eyebars wide. Round bars are used for the counters and sway braces.
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The face angles of these rhombi are approximately 70.528° and 109.471°. The thirty slim rhombic faces have face vertex angles of 41.810° and 138.189°; the diagonals are in ratio of 1 to φ2. It is also called a rhombic enenicontahedron in Lloyd Kahn's Domebook 2.
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Upper and lower chords are composed of I beams. Where upper or lower chords meet the verticals and diagonals, joins are gussets, which are bolted to all members. The roadbed is created by heavy wooden decking with an overlay of asphalt. The original guardrail remains.
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Assuming a given polygon is y-monotone, the greedy algorithm begins by walking on one chain of the polygon from top to bottom while adding diagonals whenever it is possible. It is easy to see that the algorithm can be applied to any monotone polygon.
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If the two sums of areas of opposite triangles are equal ( Area(BCL) + Area(DAL) = Area(LAB) + Area(DLC) ), then the point L is located on the Newton line, that is the line which connects E and F. For a parallelogram the Newton line does not exist since both midpoints of the diagonals coincide with point of intersection of the diagonals. Moreover the area identity of the theorem holds in this case for any inner point of the quadrilateral. The converse of Anne's theorem is true as well, that is for any point on the Newton line which is an inner point of the quadrilateral, the area identity holds.
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Its distinctive feature is the diagonals connected to the lower chord by pins, which eliminated the need for vertical members on longer bridges. It remained popular through the American Civil War, making the Beaverkill bridge one of the last of its kind. A major deviation from Town's design are the additional diagonals at the ends, which distribute the load over a smaller area and eliminates the need for long abutment seats of bolster beams. A patent was granted in 1863 for a similar variation on Town's design, so it is quite likely that this technique was not developed by the builder of the Beaverkill bridge.
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The Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral that is not a parallelogram. The line segments connecting the midpoints of opposite sides of a convex quadrilateral intersect in a point that lies on the Newton line.
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Mosaic stitch. Mosaic stitch is the simplest diagonal stitch used in needlepoint. It is built up of cells of three stitches two short stitches flanking one long one. It is similar to Cushion stitch (or Scotch stitch) but has only 3 diagonals per group rather than five.
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The bandwidth ceilings are bandwidth diagonals placed below the idealized peak bandwidth diagonal. Their existence is due to the lack of some kind of memory related architectural optimization, such as cache coherence, or software optimization, such as poor exposure of concurrency (that in turn limit bandwidth usage).
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In the case of the three-dimensional cube, it is usual to consider the entire cube as a single eight-note scale, the octany - the cross-sections then are 1, 3 (triad), 3 (another triad), 1, taken along any of the four main diagonals of the cube.
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This opening is fairly sharp since both of the major pieces (rook and bishop) are being activated from the start before any castle construction is attempted. Although Side Pawn Capture is most common, a Double Wing Attack opening with mutually open bishop diagonals is another possibility.
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The midpoint polygon of a quadrilateral is a parallelogram called its Varignon parallelogram. If the quadrilateral is simple, the area of the parallelogram is one half the area of the original quadrilateral. The perimeter of the parallelogram equals the sum of the diagonals of the original quadrilateral.
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The bridge carried a single-track railway on an open deck (with transomes). It spans were , , three at , and . The four shorter approach spans were timber girders. The three spans were timber trusses of the Howe-type with timber compression diagonals, vertical tension rods and six bays.
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The assertion that quadrilateral A2 is a square is equivalent to the assertion that the diagonals of A1 are equal and perpendicular to each other. The latter assertion is the content of van Aubel's theorem. Thus van Aubel's theorem is a special case of the PDN-theorem.
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The quadrilaterals of this type include the square with unit-length diagonals, which has area 1/2. However, infinitely many other orthodiagonal and equidiagonal quadrilaterals also have diameter 1 and have the same area as the square, so in this case the solution is not unique.. As cited by .
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The Ulam spiral arranges the natural numbers in a two-dimensional grid, spiraling in concentric squares surrounding the origin with the prime numbers highlighted. Visually, the primes appear to cluster on certain diagonals and not others, suggesting that some quadratic polynomials take prime values more often than others.
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3-simplex (3D) The K4 complete graph is often drawn as a square with all 6 possible edges connected, hence appearing as a square with both diagonals drawn. This graph also represents an orthographic projection of the 4 vertices and 6 edges of the regular 3-simplex (tetrahedron).
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A Howe truss is a truss bridge consisting of chords, verticals, and diagonals whose vertical members are in tension and whose diagonal members are in compression. The Howe truss was invented by William Howe in 1840, and was widely used as a bridge in the mid to late 1800s.
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General matrix diagonals can be specified by an index k measured relative to the main diagonal: the main diagonal has k = 0; the superdiagonal has k = 1; the subdiagonal has k = -1; and in general, the k-diagonal consists of the entries A_{ij} with j = i+k.
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A rider posts to one "diagonal" or the other at the trot; when the rider is on the correct diagonal, the rider sits as the horse's inside hind leg and outside foreleg are on the ground and rises as the outside hind leg and inside foreleg are on the ground. Diagonals are used in the posting trot help to keep the horse balanced, and are also useful for timing certain riding aids, such as those for the canter. A rider can learn to recognize diagonals by feel. However, less-experienced riders can check for the correct diagonal by a quick glance at the horse's shoulder, sitting when the outside foreleg is on the ground and the shoulder is back.
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The Moser spindle embedded as a unit distance graph in the plane, together with a seven-coloring of the plane. As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other. The eleven edges of the graph are the eight rhombus sides, the two short diagonals of the rhombi, and the edge between the unit-distance pair of acute-angled vertices.
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Pythagoras's theorem: "manifestum est": Copernicus More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d2, the right hand side of Ptolemy's relation is the sum a2 + b2. Copernicus – who used Ptolemy's theorem extensively in his trigonometrical work – refers to this result as a 'Porism' or self-evident corollary: :Furthermore it is clear (manifestum est) that when the chord subtending an arc has been given, that chord too can be found which subtends the rest of the semicircle.
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One way of constructing the Perles configuration is to start with a regular pentagon and its five diagonals, which form the sides of a smaller regular pentagon within the initial one. The nine points of the configuration consist of four out of the five vertices of each pentagon and the shared center of the two pentagons; the two missing pentagon vertices are chosen to be collinear with the center. The nine lines of the configuration consist of the five lines that are diagonals of the outer pentagon and sides of the inner pentagon, and the four lines that pass through the center and through corresponding pairs of vertices from the two pentagons.
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1\. Players decide what colors to play, and who starts first. 2\. The 28 soldiers or peasants are initially set up on each player's half of the board, on each intersection of the gridlines of the first 5 ranks (including the intersections of the diagonals in between the "main" orthogonal grid). The Sami Prince is placed on the sixth rank, on the intersection of diagonals to that player's farthest right. The Sami King is placed on the seventh rank, at the right edge of the board (please refer to the image above and the first external link below for a visual description of the initial setup for both Sami tribe and landowner party).
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The bridges in Fulton County exhibit two types of steel truss bridge construction, Pratt bridge and Parker, which were the most common early types of steel truss bridges. Due to variation within each type of bridge, the collection in Fulton County offered a unique opportunity to view the evolution of late 19th and early 20th century steel truss bridge construction. For example, the now- demolished London Mills Bridge, a Pratt built in 1883, features pinned connection and double eyebars for the lower chord and for the diagonals. This is compared to the also destroyed Indian Ford Bridge, a Pratt bridge built in 1917, which used riveted connections and I-beam construction for its lower chords and diagonals.
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When the grids are filled, the players score the six rows, six column, and two diagonals. When a player has spelled a word that is at least three letters long that player receives points for that scoring line. Longer words are worth more points. The player with the most points wins.
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Rather than ordering new I-beams, Rogers used shims to close the space between the bearings and the lugs. When the falsework was removed a second time, the bridge buckled where the vertical posts connected to the deck. Several diagonals also buckled. Once more, the falsework went back in place.
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1\. P-77. Black opens their bishop diagonal. This is the most flexible first move. 1\. ...P-34. White responds by opening their bishop diagonal as well. This variation of Double Wing with both players' bishop diagonals open from the start is a much less common way to play Double Wing.
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It is claimed to lie at the "geometrical centre" of Poland, although it is not the true geographical centre – it is the centre determined as the intersection of the great circle diagonals of a rectangle formed by lines of latitude and longitude passing through the four extreme points of Poland.
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This is a method of determining the center of mass of an L-shaped object. CG of L-shaped object #Divide the shape into two rectangles, as shown in fig 2. Find the center of masses of these two rectangles by drawing the diagonals. Draw a line joining the centers of mass.
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The seven shorter ones equal each other, and the seven longer ones equal each other. The reciprocal of the side equals the sum of the reciprocals of a short and a long diagonal. In any regular n-gon with n even, the long diagonals all intersect each other at the polygon's center.
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Holzman has designed many important civic and academic structures throughout the United States, especially libraries, museums and performing arts venues. His collagist plans with rotated grids, diagonals and eclectic sensibilities, quickly established him as a pioneer.Andres, Glenn M. Hardy Holzman Pfeiffer Associates: Concepts and Buildings. Middlebury, Vermont: Middlebury College Museum of Art, 1993.
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The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is cyclic (inscribed in a circle), these maltitudes all meet at a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always goes through the midpoint of the opposite side. Varignon's theorem states that the midpoints of the sides of an arbitrary quadrilateral form the vertices of a parallelogram, and if the quadrilateral is not self-intersecting then the area of the parallelogram is half the area of the quadrilateral.
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The leftmost and rightmost diagonals of the Bell triangle both contain the sequence 1, 1, 2, 5, 15, 52, ... of the Bell numbers (with the initial element missing in the case of the rightmost diagonal). The next diagonal parallel to the rightmost diagonal gives the sequence of differences of two consecutive Bell numbers, 1, 3, 10, 37, ..., and each subsequent parallel diagonal gives the sequence of differences of previous diagonals. In this way, as observed, this triangle can be interpreted as implementing the Gregory–Newton interpolation formula, which finds the coefficients of a polynomial from the sequence of its values at consecutive integers by using successive differences. This formula closely resembles a recurrence relation that can be used to define the Bell numbers.
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He in fact classified (though with a few errors) all multiple intersections of diagonals in regular polygons. His results (all done by hand) were confirmed with computer, and the errors corrected, by Bjorn Poonen and Michael Rubinstein in 1998.. The article contains a history of the problem and a picture featuring the regular triacontagon and its diagonals. In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem... \- English translation of the article from Gendaisūgaku (現代数学). This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper.
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There was no grid survey done—no lines, no concessions, no right-of-way corridors for roads. When it came time to punch roads through the wilderness, the farmers modelled the road network on what was familiar to them, which was the pattern of villages in Switzerland and southern Germany. This is a Continental Radial pattern and the result was major streets extended through diagonals cutting across the grid of smaller streets and converging at multiple-point intersections which, as the communities became more prosperous and if the automobile had not displaced the horse, might someday have become roundabouts decorated with circular gardens, fountains or statuary in the style of European cities. Five-point intersections created by converging diagonals are legion in the older areas.
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The Schönhardt polyhedron can be formed by two congruent equilateral triangles in two parallel planes, such that the line through the centers of the triangles is perpendicular to the planes. The two triangles should be twisted with respect to each other, so that they are neither translates of each other nor 180-degree reflections of each other. The convex hull of these two triangles forms a convex polyhedron that is combinatorially equivalent to a regular octahedron; along with the triangle edges, it has six edges connecting the two triangles to each other, with two different lengths, and three interior diagonals. The Schönhardt polyhedron is formed by removing the three longest connecting edges, and replacing them by the three diagonals of the convex hull.
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Using the notation in the diagram on the right, the sides are (AB), (BC), (CD), (DA). But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, i.e. (AB) = (CD) and (BC) = (DA), the law can be stated as : 2(AB)^2+2(BC)^2=(AC)^2+(BD)^2\, If the parallelogram is a rectangle, the two diagonals are of equal lengths (AC) = (BD), so : 2(AB)^2+2(BC)^2=2(AC)^2\, and the statement reduces to the Pythagorean theorem. For the general quadrilateral with four sides not necessarily equal, : (AB)^2+(BC)^2+(CD)^2+(DA)^2=(AC)^2+(BD)^2+4x^2, where x is the length of the line segment joining the midpoints of the diagonals.
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The bridge's Whipple truss technology was developed in 1847 by civil engineer Squire Whipple, who received a patent from the U.S. Patent Office the same year. Whipple was one of the first structural engineers to use scientific and mathematical methods analyzing the forces and stresses in framed structures to design the bridge, and his groundbreaking 1847 book, A Work on Bridge Building, had a significant influence on bridge engineering. Whipple's truss bridge design incorporated double-intersection diagonals into the standard Pratt truss, thus allowing the diagonals to extend across two truss bays. Engineer J. W. Murphy further modified Whipple's truss design in 1859 when he designed the first truss bridge with pinned eyebar connections, which utilized pins instead of trunnions.
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On the 4x4x4 board, there are 76 winning lines. On each of the four 4x4 boards, or horizontal planes, there are four columns, four rows, and two diagonals, accounting for 40 lines. There are 16 vertical lines, each ascending from a cell on the bottom board through the corresponding cells on the other boards. There are eight vertically-oriented planes parallel to the sides of the boards, each of these adding two more diagonals (the horizontal and vertical lines of these planes have already been counted). Finally, there are two vertically-oriented planes that include the diagonal lines of the 4x4 boards, and each of these contributes two more diagonal lines—each of these including two corners and two internal cells.
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Both top and bottom lateral bracing consists of eye rods stabilized at intersecting points with bolted plates. The top chords, end posts, and intermediate posts are channels with riveted cover plates and lacing bars. The hip verticals are double forged eye rods, while the diagonals are double punched eye bars. The counters are turnbuckles.
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If a player builds a new settlement, they also gain the use of two new resource fields, as settlements must always border four resource fields at their diagonals. New regions begin with no resources stored on them. Settlements may also be upgraded to cities, which permit a second improvement above and below the city.
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4...dxc6 is the main recapture. Black's structure is weakened, but has free diagonals for both bishops. White cannot win a pawn with 5.Nxe5 as 5...Qd4 forks White's knight and pawn, thus regaining the material, leading to positions where White has forfeited any structural advantage, which was the compensation for ceding the .
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The Howrah–Chennai main line is a part of the golden quadrilateral. The routes connecting the four major metropolises (New Delhi, Mumbai, Chennai and Kolkata), along with their diagonals, known as the golden quadrilateral, carry about half the freight and nearly half the passenger traffic, although they form only 16 per cent of the length.
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The rhombic dodecahedron has several stellations, the first of which is also a parallelohedral spacefiller. Another important rhombic dodecahedron, the Bilinski dodecahedron, has twelve faces congruent to those of the rhombic triacontahedron, i.e. the diagonals are in the ratio of the golden ratio. It is also a zonohedron and was described by Bilinski in 1960.
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The Howrah–Nagpur–Mumbai line is a part of the Golden Quadrilateral. The routes connecting the four major metropolises (New Delhi, Mumbai, Chennai and Kolkata), along with their diagonals, known as the Golden Quadrilateral, carry about half the freight and nearly half the passenger traffic, although they form only 16 per cent of the length.
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Nighthawks (1942) "Nighthawks" in the Art Institute of Chicago The best known of Hopper's paintings, Nighthawks (1942), is one of his paintings of groups. It shows customers sitting at the counter of an all-night diner. The shapes and diagonals are carefully constructed. The viewpoint is cinematic—from the sidewalk, as if the viewer were approaching the restaurant.
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The Flight of Europa is an elegant and modern depiction of an ancient act of violation. The strong diagonals make even the massive bull seem to float. Europa herself sits calmly, legs crossed, as Cupid whispers in her ear. Inspired by murals he saw in Crete, Manship added dolphins under the bull to represent the couples' destination.
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There are six tetrahedra to process instead of one single cube. The process is unambiguous, so no additional ambiguity handling is necessary. The downside is that the tessellation of a cube with tetrahedra requires a choice regarding the orientation of the tetrahedra, which may produce artificial "bumps" in the isosurface because of interpolation along the face diagonals.
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Bowstring truss A bowstring truss bridge, in London, Ontario, Canada The bowstring truss bridge was patented in 1841 by Squire Whipple. While similar in appearance to a tied-arch bridge, a bowstring truss has diagonal load-bearing members: these diagonals result in a structure that more closely matches a Parker truss or Pratt truss than a true arch.
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For objects with several symmetries, the center of symmetry is the point left unchanged by the symmetric actions. So the center of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being (amongst other properties) the fixed point of rotational symmetries. Similarly the center of an ellipse or a hyperbola is where the axes intersect.
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To this is added a 1x1x2 cuboid to form a 1x2x2 cuboid. This pattern continues, forming in succession a 2x2x3 cuboid, a 2x3x4 cuboid etc. Joining the diagonals of the exposed end of each new added cuboid creates a spiral (seen as the black line in the figure). The points on this spiral all lie in the same plane.
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The river flows generally eastward, with occasional diagonals southeast or northeast. It joins the Deschutes River at river mile 83.7 (134.7 km upstream from the mouth of the Deschutes). Named tributaries of the river from source to mouth are Dry and Bunchgrass creeks followed by the South Fork Warm Springs River. Then come Badger, Mill, and Beaver creeks.
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However, to save face, Stone told the Ohio Legislative Committee, investigating the disaster, that he fired Tomlinson. Joseph Tomlinson was replaced by A. L. Rogers. When construction began, Tomlinson observed that the I-beams intended for use as diagonals were smaller than the fabrication plans called for. The amount of camber created a problem during construction.
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The most common Pratt type is the through truss in which the deck is carried on the lower chord, with overhead lateral supports connecting the top chords. Finally, the Pennsylvania Petit is a Pratt truss with a polygonal top chord and includes reinforcing sub-struts and sub-ties. These half-length members reinforced the diagonals and helped resist stresses.
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The staging was extended upwards for use while assembling the spans. The spans were assembled on site. Staging was laid and rails put in place to carry a travelling crane. The long beams were hoisted in place first, followed by the vertical bracings, and then the outer and inner plates of the top chordal trusses and the diagonals.
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The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at a point called the "vertex centroid" and are all bisected by this point.Altshiller-Court, Nathan, College Geometry, Dover Publ., 2007.
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A forest fire is shown with many animals in the chaos. The scene starts at the top left corner where there are three main sparks present. These sparks of fire are coming from an unknown source and will begin to ignite more of the fire and most of the animals. Under the horse there are many diagonals painted red.
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Again this spark misses the deer and lands to ignite the ground behind him. The main large diagonals going across the canvas from the top middle to the bottom right is a tree. This tree is falling on the deer and his dramatic posture with his head up. It is another acceptance of fate for the animals.
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If P is an interior point in a convex quadrilateral ABCD, then :AP+BP+CP+DP\ge AC+BD. From this inequality it follows that the point inside a quadrilateral that minimizes the sum of distances to the vertices is the intersection of the diagonals. Hence that point is the Fermat point of a convex quadrilateral.
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These two lights come in from opposite directions. Top lighting may also be used for fill, as may limited footlights. McCandless described these angles as being the diagonals of a cube in the center of the acting area. However, the key to the McCandless method is that one light of the primary pair is "cool" relative to the other.
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1.P-76 P-34 2.P-26 P-84 3.P-25 P-85. The branch of this variation starts after both players advance their rook pawns and open their bishop diagonals. 4.G-78. Black plays the defensive move by developing their left gold to the seventh file so that it protects the 87 and 88 squares.
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Various "Time Paintings" are also on display, but many of these and other complicated works are hard to appreciate fully due to the low resolution and small image size. (There is a link to enlarge the images, but it does not work.) Of additional interest here is a portrait by James Lechay of Margules. The gallery Levis Fine Art has an online collection of intensely colored Margules paintings made up of the 1938 mixed media painting "The Boatyard", a 1939 gouache of a waterfront scene entitled "Diagonals in Purple and Red", a 1939 waterfront and airfield scene called "Diagonals with Airforms and Hedges", and a couple of 1943 paintings of airplanes in flight, one untitled and the other one named "Convergence." The Birnham Wood Gallery also has quite a few Margules works on display.
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The Land of Oz; note that the map is a mirror image of "actual" locations, but that the compass rose shows east on the right-hand side. Oz is roughly rectangular in shape, and divided along the diagonals into four countries: Munchkin Country (but commonly referred to as 'Munchkinland' in adaptations) in the East, Winkie Country in the West (sometimes West and East are reversed on maps of Oz, see West and East below), Gillikin Country in the North, and Quadling Country in the South. In the center of Oz, where the diagonals cross, is the fabled Emerald City, capital of the land of Oz and seat to the monarch of Oz, Princess Ozma.John Grant and John Clute, The Encyclopedia of Fantasy, New York, St. Martin's Griffin, 1999; "Oz", p. 739. .
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Dynamic programming is applied to all possible difference matrices to construct a series of optimal local alignment paths that are then summed to form the summary matrix, on which a second round of dynamic programming is performed.A common and popular structural alignment method is the DALI, or Distance-matrix ALIgnment method, which breaks the input structures into hexapeptide fragments and calculates a distance matrix by evaluating the contact patterns between successive fragments. Secondary structure features that involve residues that are contiguous in sequence appear on the matrix's main diagonal; other diagonals in the matrix reflect spatial contacts between residues that are not near each other in the sequence. When these diagonals are parallel to the main diagonal, the features they represent are parallel; when they are perpendicular, their features are antiparallel.
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In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant. Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, and cubes of orders five and six were first discovered by Walter Trump and Christian Boyer on November 13 and September 1, 2003, respectively. A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875, an article was published in the Cincinnati Commercial newspaper on the discovery of a perfect magic cube of order 8 by Gustavus Frankenstein. Perfect magic cubes of orders nine and eleven have also been constructed.
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While more rigidly composed than Hunches, they still retain a degree of playfulness. A gridded canvas may have sections divided by diagonals or arcs. The triangles, squares, and other geometric shapes combine to form interlocking relationships to each other, creating a rhythmic composition with interchangeable positive and negative space. "Organics" consist of freely curving shapes inspired by the natural world.
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It has a two-channel top chord with a cover plate and lacing; on the bottom chord are four angles with continuous plate. They are connected by verticals and diagonals of consisting of two angles and spacers each; the verticals further have two channels with lacing. Concrete wingwalls throughout provide substructure. The timber deck is supported by steel stringers and cross beams.
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The chords are normally kept aligned and held in place by vertical posts, diagonals, and sideways sway struts. Top chords will quickly fold if their joints somehow become misaligned. Buckling damage is cumulative, but mostly happens from collision damage or overstresses rather than from age and corrosion. The vertical clearance for vehicles is limited by the portals and sideways sway struts.
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In a square or other rectangle, all pairs of adjacent sides are perpendicular. A right trapezoid is a trapezoid that has two pairs of adjacent sides that are perpendicular. Each of the four maltitudes of a quadrilateral is a perpendicular to a side through the midpoint of the opposite side. An orthodiagonal quadrilateral is a quadrilateral whose diagonals are perpendicular.
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The Korean fighter kite, the bang-pae yeon is a rectangular, bowed "shield" kite with a hole in the middle of the sail. The frame uses five bamboo spars—one each across the top and the "waist" of the kite, a "spine," and two diagonals. Although cutting line and fights are similar to other Asian fighter kites, a large spool is always used.
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Congdon says that he realized the I-beams would carry more live load if they were rotated. Collins, Rogers, and Stone believed workers had installed the beams incorrectly (on their sides). To make the change, Stone had workers cut away portions of each diagonal I-beam's web at the bearing, enabling the web to fit over the lugs. This weakened the new diagonals.
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Boden's Mate is characterized by a king being mated by two bishops on criss-crossing diagonals, with possible flight squares blocked by friendly pieces. Samuel Boden, for whom the mate is named, administered an early example of it in the friendly game Schulder–Boden, London 1853.David Hooper and Kenneth Whyld, The Oxford Companion to Chess (2nd ed. 1992), p. 49. .
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The trusses have horizontal and parallel top and bottom chords, apart with inclined posts at each end. Diagonals are designed for tension with greater stress expected toward the span's end. A single counterbrace in the third panel and a pair in the fourth, each of round rods with turnbuckles. Bracing at the upper chord and at the lower chord adds strength.
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Structurally, the Elizabethton Covered Bridge contains one span, a covered wooden Howe Truss (typically constructed of timber diagonals and iron verticals) that is long. The total length is . The covered bridge contains one traffic lane and a single walkway, while the curb-to-curb width is and the out-to-out width is . The bridge substructure is masonry, stone, and concrete.
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The bridge deck has been replaced by steel I-beams covered with wooden planking, so the trusses now only carry the superstructure. The joints between the truss posts and diagonals have also been reinforced with steel plating. with The bridge was built about 1877; its builder is unknown. It is one three period bridges in the town (all spanning the same river).
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Fan triangulation of a convex polygon Fan triangulation of a concave polygon with a unique concave vertex. A fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing diagonals to all of the other vertices of the polygon. Not every polygon can be triangulated this way, so this method is usually only used for convex polygons.
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After open bishop diagonals for both players, another possible response to Black's pawn push (2. P-26) is for White to push their central pawn (2...P-54). After this 4-move sequence, White aims to support this central pawn by swinging their rook to the central file. With both players' bishops fully activated, this particular Central Rook variation is Cheerful Central Rook.
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The maximum possible number of triangles in a simple arrangement is known to be upper bounded by n(n − 1)/3 and lower bounded by n(n − 3)/3; the lower bound is achieved by certain subsets of the diagonals of a regular 2n-gon.; . For non-simple arrangements the maximum number of triangles is similar but more tightly bounded.; ; .
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It is named after the Greek astronomer and mathematician Ptolemy. The four points can be ordered in any of three distinct ways (counting reversals as not distinct) to form three different quadrilaterals, for each of which the sum of the products of opposite sides is at least as large as the product of the diagonals. Thus the three product terms in the inequality can be additively permuted to put any one of them on the right side of the inequality, so the three products of opposite sides or of diagonals of any one of the quadrilaterals must obey the triangle inequality.. As a special case, Ptolemy's theorem states that the inequality becomes an equality when the four points lie in cyclic order on a circle. The other case of equality occurs when the four points are collinear in order.
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Juzgados Federales de La Plata (ex Hotel Provincial). La Plata is a planned city, urban planning paradigm of the late 19th century. It is also an example of "hygiene", which was becoming important in that time. The trace of the city, designed by architect Pedro Benoit, characterized by a strict grid, and its many avenues and diagonals. The convergence of the two major diagonals, 73 and 74, which cross the city from east to west and from north to south, respectively, takes place in Plaza Moreno. This square, in whose center is the foundation stone, the heart of the city, is the main square of the city and it is between the City Hall and the cathedral located at 14 N ° 1943 between 51 and 53, High Gothic, with its towers 112 m high, could be completed only in 1999.
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Retrieved 2011-11-13.Oblong – Geometry – Math Dictionary. Icoachmath.com. Retrieved 2011-11-13. A rectangle with vertices ABCD would be denoted as . The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals.
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In MesZL, signs are sorted by their leftmost parts, beginning with horizontal strokes (single AŠ, then stacked TAB, EŠ16), followed by the diagonals GE23 and GE22, the Winkelhaken U and finally the vertical DIŠ. The relevant shape for the classification of a sign is the Neo-Assyrian one (after ca. 1000 BC); the standardization of sign shapes of this late period allows systematic arrangement by shape.
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Each developable roller family is based on a different construction principle. The prime polysphericons are a subfamily of the polysphericon family. They are based on bodies made by rotating regular polygons around one of their longest diagonals. These bodies are cut in two at their symmetry plane and the two halves are reunited after being rotated at an offset angle relative to each other.
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The unit cell of Cd3As2 is tetragonal. The arsenic ions are cubic close packed and the cadmium ions are tetrahedrally coordinated. The vacant tetrahedral sites provoked research by von Stackelberg and Paulus (1935), who determined the primary structure. Each arsenic ion was surrounded by cadmium ions at six of the eight corners of a distorted cube and the two vacant sites were at the diagonals.
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In 1899 Amedo bought the former whaling vessel Jason, renamed her Stella Polare and took her to Colin Archer's shipyard. The interior was stripped out and new beams, diagonals and knees heavily strengthened the ship. Amedo set off in June 1899 and Stella Polare had hard time but survived thanks to Archer's work. In 1899, Archer also fitted Zarya for the Russian polar expedition of 1900–02.
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After winning another promotion play-off in 1956, Espanya Industrial became independent of FC Barcelona and was renamed Club Deportivo Condal. The club wore blue shirts with two white diagonals stripes. Condal competed once in La Liga, in the 1956–57 season, being relegated as 16th and last. In 1968 the club rejoined the Barcelona family as its reserve team, and adopted the blaugrana colours.
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The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at (all intersect at)a point called the "vertex centroid", which is the midpoint of all three of these segments.Altshiller- Court, Nathan, College Geometry, Dover Publ., 2007.
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Lal Bangla consists of two tombs made out of red and yellow sandstone. One of the tombs contains two graves, believed to be that of Lal Kunwar, the mother of Shah Alam II (1759-1806) and Begum Jaan, his daughter. Both mausoleums consist of square rooms at diagonals with oblong halls between them. The mausoleum stands on a red sandstone platform with rooms at corners.
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There Miriam met her close friend David Nalibof, a physicist who worked for General Dynamics. Nalibof formulated computer programs that could plot and alter Miriam Schapiro's drawings. This was how her first feminist work, Big Ox #1 from 1968 was created. The diagonals of which represented the limbs of the "Vitruvian man," while the O depicted the center of the women, the vagina, the womb.
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Use the complex exponential function to create a log-polar grid in the plane. The left half-plane is then mapped onto the unit disc, with the number of radii equal to n. It can be even more advantageous to instead map the diagonals in these squares, which gives a discrete coordinate system in the unit disc consisting of spirals, see the figure to the right.
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Camp Massanetta is arranged in four "villages" labeled A, B, C and D. Buildings are of frame construction on concrete slabs with rough siding. Deep overhanging eaves are supported by diagonal braces with a modern look. Interiors are austere with open trusses and minimal finishes. The Bell Auditorium is the chief building in the camps, which continues the theme of deep overhangs supported by diagonals.
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In geometry, the Császár polyhedron () is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals; every pair of vertices is connected by an edge. The seven vertices and 21 edges of the Császár polyhedron form an embedding of the complete graph K_7 onto a topological torus. Of the 35 possible triangles from vertices of the polyhedron, only 14 are faces.
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Each character position therefore corresponded to a 12×20 pixel space. Internally each character shape was defined on a 5×9 pixel grid that was loosely based on the Signetics 2513 character ROM chip. This was then interpolated by smoothing diagonals to give a 10×18 pixel character, with a characteristically angular shape, surrounded to the top and to the left by two pixels of blank space.
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The intersection number is partly motivated by the desire to define intersection to satisfy Bézout's theorem. The intersection number arises in the study of fixed points, which can be cleverly defined as intersections of function graphs with a diagonals. Calculating the intersection numbers at the fixed points counts the fixed points with multiplicity, and leads to the Lefschetz fixed point theorem in quantitative form.
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Manet uses earthly and muted tones to illustrate an urban snow landscape; between the large peaks of white and diagonals of murky brown the Paris district of Petit-Montrouge is illustrate, overshadowed by the brown dirty snow and bleak beige sky. The buildings in the background were painted with muted colours to give an appearance of balancing precariously on a huge expanse of brown.
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In a more dreamscape world, the colors are vibrant and everything is 2D. The video won a Soul Train Music Award for Best R&B;/Soul or Rap Music Video in 1987. While reviewing the video, Vanity Fair magazine said in 1986 that Jackson "might be Michael's androgynous twin in the sweep of her arm, the accusatory glare in her eyes, the collapsing diagonals of her dancing".
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The dome, in the middle, reflects both Indian and British styles. In the centre is a tall copper-faced dome, surmounting a very tall drum in several sections, which stands out from the rest of the building. The dome is exactly in the middle of the diagonals between the four corners of the building. The dome is more than twice the height of the building itself.
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The passage from one visual to another must be simultaneous over the entire format. But when this problem occurs, there is a lag in the effects on the diagonals. At the end of one diagonal of the visual, there is one effect, and at the other end, there is another. ;Phasing: In most cases, the phasing problem comes from imprecise cutting of the material, as explained below.
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The inner truss of a Howe truss is statically indeterminate. There are two paths for stress during loading, a pair of diagonals in compression and a pair in tension. This gives the Howe truss a level of redundancy which allows it to withstand excessive loading (such as the loss of a panel due to collison). Prestressing is critical to the proper function of a Howe truss.
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Sometimes the puzzle itself will help. The puzzles generated by a computer tend to put words in patterns. Furthermore, the bigger the words and the more words, the easier they are to spot. In some computer-generated puzzles, if the person solving the puzzle sees one word, all they have to do to find more is to look in adjacent rows, columns, or diagonals.
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If a column is not found the program returns to the last good state and then tries a different column. As an alternative to backtracking, solutions can be counted by recursively enumerating valid partial solutions, one row at a time. Rather than constructing entire board positions, blocked diagonals and columns are tracked with bitwise operations. This does not allow the recovery of individual solutions.
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The spiral structure of idempotents in the four-spiral semigroup Sp4. In this diagram, elements in the same row are R-related, elements in the same column are L-related, and the order proceeds down the four diagonals (away from the center). The structure of the four-spiral semigroup Sp4. The set of idempotents (red coloured points) and the subsemigroups A, B, C, D, E are shown.
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Advertising poster for the comic opera The Mikado, which was set in Japan (1885)Ukiyo-e prints were one of the main Japanese influences on Western art. Western artists were inspired by different uses of compositional space, flattening of planes, and abstract approaches to color. An emphasis on diagonals, asymmetry, and negative space can be seen in the Western artists who were influenced by this style.
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Thus, a presentday Double Wing opening typically arises when the rook pawns are traded off the board first and only after this are the bishop diagonals opened (if they are opened at all), which prevents the Side Pawn Capture opening possibility. Consequently, the open bishop diagonal variations of Double Wing (without captured side pawns) are not commonly played by professional players (although they are occasionally seen).
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This method provides an approximation algorithm for the problem with an approximation ratio of two. A similar approach of partitioning into subproblems along shared diagonals leads to a fixed-parameter tractable algorithm for computing the rotation distance exactly. Determining the complexity of computing the rotation distance exactly without parameterization remains unsolved, and the best algorithms currently known for the problem run in exponential time.
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The two diagonals of a convex quadrilateral are the line segments that connect opposite vertices. The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides. They intersect at the "vertex centroid" of the quadrilateral (see below). The four maltitudes of a convex quadrilateral are the perpendiculars to a side—through the midpoint of the opposite side.
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The masked ranks, files and diagonals of sliding pieces can be used via a hash function to directly index a table of precomputed attack vectors based on the occupancy bits in the masked portion. One such scheme that uses a perfect hash function along with tricks to minimize the potential size of the table that must be stored in memory, is called "magic bitboards".
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In oblique projection typically all three axes are shown without foreshortening. All lines parallel to the axes are drawn to scale, and diagonals and curved lines are distorted. One tell-tale sign of oblique projection is that the face pointed toward the camera retains its right angles with respect to the image plane. Two examples of oblique projection are Ultima VII: The Black Gate and Paperboy.
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The siding does not rise all the way to the roof, and extends a shortway into the portals, sheltering the projecting upper ends. The abutments are made of roughly coursed dry laid stone. The trusses incorporate iron rods, which extend vertically from the bracing diagonals to the bottom chords. with The bridge was built about 1890 by Herman F. Townsend, a prominent local bridgewright.
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The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length \sqrt 3, while AC (shown in red) is a face diagonal and has length \sqrt 2. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal.
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The larger equipment such as the systems that project life-size people capable of image diagonals up to 2.3 m also have the same footprint, about the same size as a sheet of paper. The air-based system is formed by a series of metal plates, and the original Heliodisplay could run for several hours although current models can operate continuously.David Bernstein. Making Something Out of Nothing.
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Rc1, Qc3, c5), or if he wants to finish his development first (with Be2 and 0-0). The immediate 11.c5!? is a possible pawn sacrifice in order to open some diagonals for the bishops. As Lalic points out, "after 11...dxc5 Black's knight on e5 has lost its support and therefore all tactical motifs based on Qd5 and Bb5+ must be carefully checked".
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Specifically, let be an arbitrary cyclic quadrilateral and let , , , be the incenters of the triangles , , , . Then the quadrilateral formed by , , , is a rectangle. Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral.
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The deck is now supported by steel I-beams, and the original bridge trusses support only the bridge superstructure. The bridge has a total width of , with an wide roadway (one lane). The bridge trusses are a variant of a multiple kingpost truss. Each truss has verticals and diagonals in that style, but is further augmented by a laminated arch, consisting of heavy planks pegged together.
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From 1971 to 1976, Venet did not create any art, entering a period of retrospection. He took up teaching Art and Art Theory at the Paris-Sorbonne University, and frequented lectures in England, Italy, Poland and Belgium. He resumed his artistic activity in 1976, exhibiting works at "Documenta VI" in Kassel in 1977. In 1979, he created a series of wood reliefs, entitling them Arcs, Angels, Diagonals.
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In 1996, Vaynshtejn was probably the first to prove another beautiful characterization of tangential quadrilaterals, that has later appeared in several magazines and websites. It states that when a convex quadrilateral is divided into four nonoverlapping triangles by its two diagonals, then the incenters of the four triangles are concyclic if and only if the quadrilateral is tangential. In fact, the incenters form an orthodiagonal cyclic quadrilateral.
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Blanking of a CRT may not be perfect due to equipment faults or brightness set very high; in this case a white retrace line shows on the screen, often alternating between fairly steep diagonals from right to left and less-steep diagonals back from left to right, starting in the lower right of the display. In analog television systems the vertical blanking interval can be used for datacasting (to carry digital data), since nothing sent during the VBI is displayed on the screen; various test signals, time codes, closed captioning, teletext, CGMS-A copy-protection indicators, and various data encoded by the XDS protocol (e.g., the content ratings for V-chip use) and other digital data can be sent during this time period. In U.S. analog broadcast television, line 19 was reserved for a Ghost-canceling reference & line 21 was reserved for captioning data.
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Designed by AREP and MaP3 during a competition in 2007, the station is built on reclaimed land from the sea. The project was inspired by marina's landscape (seagulls, boat masts, cables). The structure shape was obtained by moving and rotating identical frames: "arches" and roof beams, connected together by braced brackets and cables diagonals. Arches and beams are welded on a central beam, with a triangular box section, sheltering technical catwalk.
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Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at a single point. In a hexagon that is tangential to a circle and that has consecutive sides a, b, c, d, e, and f,Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", , Accessed 2012-04-17. :a+c+e=b+d+f.
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'Parchment' ware: a variable group of hard, brittle, white, buff (through to yellow or orange) fabrics with a laminar fracture; abundant fine sand tempering. Frequent orange or brown painted decoration. Iron slag grits on the mortaria. Crambeck Parchment Ware is frequently over-painted with red designs, often in circumferential bands but also used in geometric patterns, dots, diagonals, and also to depict human features on stylised face pots.
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Diagonals, even if they were to run exactly 45 degrees off of the cardinal directions, are numbered as if they were north-south or east-west streets. Examples are North Lincoln Avenue and Ogden Avenue, which bends at Madison and changes from North Ogden to West Ogden. The northernmost street in Chicago is Juneway Terrace (7800 N), just north of Howard Street. The southern boundary is 138th Street.
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The "Meta Paintings" take liberties with color, scale, value range and composition, for example, using vantage point to impose diagonals on the flat horizontal and vertical harmonies of a Mondrian to problematize its absolutist purity of form, or obscuring Velázquez or Rembrandt images under layers of varnish that flatten them into dark, inky rectangles in gilded frames.Wainwright, Lisa. Catalog essay. David Klamen: Painting Paintings, Chicago: Richard Gray Gallery, 2010.
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Candara’s verticals show both entasis and ekstasis on opposite sides of stems, high-branching arcades in the lowercase, large apertures in all open forms, and unique ogee curves on diagonals. Its italic includes many calligraphic and serif font influences, which are common in modern sans-serif typefaces. Calibri and Corbel, from the same family, have similar designs and spacing. The family supports most of the WGL4 character set.
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The perpendicular bisectors p1 and p2 intersect in the centre O of the circumcircle CR with the distance x to the centre I of the incircle Cr. The circumcircle can be drawn around the centre O. The validity of this construction is due to the characterization that, in a tangential quadrilateral ABCD, the contact quadrilateral WXYZ has perpendicular diagonals if and only if the tangential quadrilateral is also cyclic.
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There is also some evidence that the angle blocks were damaged while the braces and counter-braces were rotated. The bridge was prestressed again. In every other panel connection, the diagonal braces were fitted to the angle blocks using shims rather than by tightening the vertical posts and putting the diagonals under compression. This meant that the shims carried the weight of a live load, rather than the braces themselves.
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There is also an indication in the construction record that several chord members were misaligned. Even if their bearings had been flat, they would not have met the lugs completely. This, too, would have created uneven loading and worsened metal fatigue. Gasparini and Fields conclude that the bridge might have survived the loss of the lug had the chords and diagonals been made stronger through active continuous connection.
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A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus. An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular. A convex quadrilateral with diagonal lengths p and q and bimedian lengths m and n is equidiagonal if and only if :pq=m^2+n^2.
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The area K of an equidiagonal quadrilateral can easily be calculated if the length of the bimedians m and n are known. A quadrilateral is equidiagonal if and only if. . :\displaystyle K=mn. This is a direct consequence of the fact that the area of a convex quadrilateral is twice the area of its Varignon parallelogram and that the diagonals in this parallelogram are the bimedians of the quadrilateral.
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Its superstructure incorporates the Town lattice truss design. Both chords and the diagonals, connected by wood pins at each intersection, are formed by heavy paired planks. Planks laid on stringers form the deck; alternating timbers protrude to create a series of four buttresses on the sides of the bridge. Vertical board sheathing on horizontal nailers constitutes the bridge's siding; the roof and buttresses are clad in wood shingles.
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Although the company named the settlement "New Amsterdam," the name did not catch on, reverting to Buffalo within ten years. Buffalo had the first road to Pennsylvania built in 1802 for migrants passing through to the Connecticut Western Reserve in Ohio. In 1804, Ellicott designed a radial grid plan that would branch out from the village forming bicycle-like spokes, interrupted by diagonals, like the system used in the nation's capital.
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Using gyrotrigonometry, a gyrovector addition can be found which operates according to the gyroparallelogram law. This is the coaddition to the gyrogroup operation. Gyroparallelogram addition is commutative. The gyroparallelogram law is similar to the parallelogram law in that a gyroparallelogram is a hyperbolic quadrilateral the two gyrodiagonals of which intersect at their gyromidpoints, just as a parallelogram is a Euclidean quadrilateral the two diagonals of which intersect at their midpoints.
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The bridge is significant as a "rare example of a double-intersection Pratt truss", which is a kind of Whipple truss. Its diagonals extend over two panels, and are made of wrought iron, suited for their being under tension. The Whipple truss design was developed by engineer Squire Whipple in 1847. As of 1994, it was the longest of only eight pin- connected Whipple through truss bridges surviving in Iowa.
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Persian rug with rectangular symmetry A long tradition of the use of symmetry in carpet and rug patterns spans a variety of cultures. American Navajo Indians used bold diagonals and rectangular motifs. Many Oriental rugs have intricate reflected centers and borders that translate a pattern. Not surprisingly, rectangular rugs have typically the symmetries of a rectangle—that is, motifs that are reflected across both the horizontal and vertical axes (see ).
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The Ryefield Bridge is a historic bridge connecting Ryefield Bridge Road in Harrison, Maine to West Andrew Hill Road in Otisfield, Maine, across the Crooked River. Built in 1912, it is one of the oldest surviving Warren truss bridges in the state, and is a rare example with double-intersection diagonals, added for increased rigidity. The bridge was listed on the National Register of Historic Places in 1999.
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11 (1998), no. 1, 135–156; link to a version on Poonen's website , beginning at 2:10 This holds, for example, for any regular polygon with an odd number of sides. The formula follows from the fact that each intersection is uniquely determined by the four endpoints of the two intersecting diagonals: the number of intersections is thus the number of combinations of the n vertices four at a time.
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Construction of the bridge was handled by the Jackson County Court, which paid a total of $1,788.35 to local craftspeople for completion of the structure. Nearly long, the Staats Mill Covered Bridge was constructed using the Long system, patented by Stephen Long in 1830. The distinctive feature of Long trusses are the "X"-braced diagonals in each of the panels. This bridge has 11 such panels, each long and deep.
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Four members of the "X team" traverse one of the diagonals of the square (from which the name Dutch Crossing derives), across and back. The other four members traverse the other diagonal. The groups interact with each other in the middle and with members of the "O team" at the corners. Simultaneously, eight members of the "O team" perform a grand right and left around the circumference of the square.
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The spans are , three at , , and , of which the three larger spans are timber trusses and the other timber girders. The trusses are deck-type Howe trusses of the deck-type, with timber compression diagonals, steel tie rods for the verticals and five bays. The piers are timber, with concrete bases. The bridge was listed on the (now defunct) Register of the National Estate on 18 April 1989.
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The entries in the triangle satisfy the identity :H(n, i) = F(i + 1) × F(n − i + 1). Thus, the two outermost diagonals are the Fibonacci numbers, while the numbers on the middle vertical line are the squares of the Fibonacci numbers. All the other numbers in the triangle are the product of two distinct Fibonacci numbers greater than 1. The row sums are the first convolved Fibonacci numbers.
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Such examples correspond to diagonals that are devoid of primes or nearly so. To gain insight into why some of the remaining odd diagonals may have a higher concentration of primes than others, consider 4 n^2 + 6 n + 1 and 4 n^2 + 6 n + 5. Compute remainders upon division by 3 as n takes successive values 0, 1, 2, .... For the first of these polynomials, the sequence of remainders is 1, 2, 2, 1, 2, 2, ..., while for the second, it is 2, 0, 0, 2, 0, 0, .... This implies that in the sequence of values taken by the second polynomial, two out of every three are divisible by 3, and hence certainly not prime, while in the sequence of values taken by the first polynomial, none are divisible by 3. Thus it seems plausible that the first polynomial will produce values with a higher density of primes than will the second.
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As a result of his research, Dewey asserted that seemingly unrelated time series often had similar cycles periods present and that when they did the phase of these cycles was mostly very similar (cycle synchrony). He also said that there were many cycles with periods that were related by powers or products of 2 and 3. This is illustrated in the table below. To construct this table starting from the period 17.75 years, multiply by three as you proceed along diagonals from lower left to upper right, and multiply by two as you proceed along diagonals from lower right to upper left. Dewey reported that the underlined numbers are commonly occurring periods (in years): 142.0 213.9 319.5 479.3 \----- 71.0 106.5 159.8 \----- 35.5 53.3 \---- ---- 17.75 \----- 5.92 8.88 \---- ---- 1.97 2.96 4.44 \---- ---- ---- 0.66 0.99 1.48 2.22 \---- ---- ---- 0.22 0.33 0.49 0.74 1.11 \---- ---- ---- ---- Volume IV of the Cycles Classic Library Collection contains 1380 reports of cycles period determinations by scientists, doctors, economists and cycles researchers.
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Internals of stressed skin construction on Murphy Moose showing frames and supporting skin A framework box can be distorted from being square, so it isn't rigid by itself, however adding diagonals that take either tension or compression fixes this, because the box cannot deviate from right angles without altering the diagonals. Sometimes flexible members like wires are used to provide tension, or rigid compression frames are used, as with a Warren or Pratt truss, however both these are full frame structures. When the skin or outer covering is in tension so that it provides a significant portion of the rigidity, the structure is said to have a stressed skin design. This may also be referred to as semi-monocoque, and overlaps with monocoque, which has less framing, sometimes only including longitudinal or lateral members, and also overlaps with rigid frame structures where a minor portion of the overall stiffness may be derived from the skin.
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These frames, enclosed in streamlined fairings apart, were also braced the upper fuselage longerons with shorter N-struts and with inverted V-struts to the central fuselage underside. Short, inverted V-struts attached the wing centre section to the upper fuselage. There were no wing bracing wires. The fuselage of the Mureaux was built around four duralumin tube longerons, with easily repaired connections to tubular diagonals and with removable panels covering the forward part.
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The Patriarch and four other figures dominate the composition, staggering unevenly across the canvas as opposed to moving in a straight line. "They punctuate the foreground," Filipovitch- Robinson writes, "directing the eye through the diagonals and curves of their bodies and gesture to the next line of figures behind them. Each subsequent line leads to the next." All age groups are represented in the painting, and Jovanović pays special attention to their facial details.
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This bridge is a bowstring truss bridge, patented by bridge designer Squire Whipple in 1841. It is a six-panel, pin- connected structure resting on earthen embankments in a farmyard. It is composed of an upper cord made of back-to-back channels with battens and a cover plate and a lower chord made of paired flat bars. The outside and center verticals are X-shaped members and the diagonals are crossed rods with turnbuckles.
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The capitals are wide and have relatively little variation in width, with letters like 'E' and 'F' quite wide. The 'M' is straight-sided with the diagonals meeting in the bottom centre of the letter. Capitals in several weights have very noticeably thicker strokes than the lower-case. On many but not all styles a straight leg on the 'R' and a 'Q' where the outstroke does not cut through the letter.
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Harmondsworth: Penguin Books; p. 129 The arcades of those churches with aisles generally have piers of one of three different types: Type A "consists of four attached shafts in the main axes and four hollows in the diagonals"; Type B which seems to have been in use earlier has "square piers with four attached demi-shafts"; or octagonal piers. Type A is very common in both Devon and Cornwall.Pevsner, N. (1970) Cornwall; 2nd ed.
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These include the square, the rhombus, and the kite. By Brahmagupta's theorem, in an orthodiagonal quadrilateral that is also cyclic, a line through the midpoint of one side and through the intersection point of the diagonals is perpendicular to the opposite side. By van Aubel's theorem, if squares are constructed externally on the sides of a quadrilateral, the line segments connecting the centers of opposite squares are perpendicular and equal in length.
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Schütz and Gruber, p. 58. According to Michael Matzke's M. Phil. thesis, "'Die Straßen Adolf Hitlers' - Reichsautobahnen 1933–1941", University of Vienna, October 2008, p. 55, , there were to have been three diagonals: between Duisburg and Passau and between Hamburg and Gleiwitz (now Gliwice, Poland) and Aachen. HAFRABA's main north-south route was truncated; it was only completed in 1962.Frederic Spotts, Hitler and the Power of Aesthetics, London: Hutchinson, 2002, , p. 395.
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The truss panels have pinned end diagonals that are under compression, diagonal bars spanning two panels under tension. The bridge in 2012 The bridge was built in 1871 for town by the Watson Manufacturing Company of Paterson, New Jersey. It was built at a location where wooden bridges had stood since the 17th century, on the major road leading north from Lancaster. The route was bypassed by the present alignment of Route 70 in 1965.
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A person at this level might say, "A square has 4 equal sides and 4 equal angles. Its diagonals are congruent and perpendicular, and they bisect each other." The properties are more important than the appearance of the shape. If a figure is sketched on the blackboard and the teacher claims it is intended to have congruent sides and angles, the students accept that it is a square, even if it is poorly drawn.
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The tablet depicts a square with its two diagonals. One side of the square is labeled with the sexagesimal number 30. The diagonal of the square is labeled with two sexagesimal numbers. The first of these two, 1;24,51,10 represents the number 305470/216000 ≈ 1.414213, a numerical approximation of the square root of two that is off by less than one part in two million. The second of the two numbers is 42;25,35 = 30547/720 ≈ 42.426.
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In 1898, Prince Luigi Amedeo organized an expedition towards the North Pole and consulted the famous polar explorer Fridtjof Nansen that had sailed the furthest north with the Colin Archer-built polar ship in 1893–1896. In 1899 Amedeo acquired , a steam whaler of 570 tons. He renamed her Stella Polare and took her to Colin Archer's shipyard in Larvik, Norway. The interior was stripped out and beams, diagonals and knees heavily strengthened the ship.
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Interior of a barn with a Fink truss, with the characteristic W shape. Fink design trusses are used today for pedestrian bridges and as roof trusses in building construction in an inverted (upside down) form where the lower chord is present and a central upward projecting vertical member and attached diagonals provide the bases for roofing.Crawley, Stanley W. and Robert M. Dillon (1993) Steel Buildings: Analysis and Design, John Wiley & Sons Inc.
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After opening both bishop diagonals (1. P-76 P-34), White has not revealed to Black what their strategy will be. If Black wishes to play a Ranging Rook opening (like Fourth File Rook), Black may only choose a particular Ranging Rook opening if White chooses a Static Rook opening while they may want to choose a different set of openings if White chooses a Ranging Rook opening. Therefore, pushing an edge pawn (2.
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After an empirical beginning, which lasted from 1963 to 1970, Devalle began to utilize geometry in a much more systematic way, for executional precision and truth in design obsessed him. Along with this work with photography there appeared tables that developed the creative process—real diaries of the sequence. Orthogonals, diagonals, and curves became autonomous subjects and in themselves created "effective surprises" ("Dal quadrato al cerchio", 1974, "Cinque quadrate in un quadrato", 1973).
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Another common variant is to add limits on the placement of numbers beyond the usual row, column, and box requirements. Often, the limit takes the form of an extra "dimension"; the most common is to require the numbers in the main diagonals of the grid to also be unique. The aforementioned "Number Place Challenger" puzzles are all of this variant, as are the Sudoku X puzzles in The Daily Mail, which use 6×6 grids.
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More importantly, the Nagel point N, the "area centroid" G, and the incenter I are collinear in this order, and NG = 2GI. This line is called the Nagel line of a tangential quadrilateral.. In a tangential quadrilateral ABCD with incenter I and where the diagonals intersect at P, let HX, HY, HZ, HW be the orthocenters of triangles AIB, BIC, CID, DIA. Then the points P, HX, HY, HZ, HW are collinear.
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At the centre of the city is Cathedral Square, surrounding the Anglican cathedral, Christ Church. The area around this square and within the four avenues of Christchurch is considered the central business district of the city. The city centre is laid out in a grid pattern, interrupted only by the curvilinear alignment of the Avon River, and the two diagonals High Street and Victoria Street. Christchurch has four pairs of one-way streets.
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As seen in the example for a 6 × 6 square (Figure 2), the properties of the mystic square are related to those of a 6 × 6 magic square. The sum of the diagonals is 111, the magic number for a 6 × 6 magic square. The sums of the rows increase arithmetically with a common difference of 12 and an average of 111. The columns also increase arithmetically with a common difference of 2 and an average of 111.
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The meson octet. Particles along the same horizontal line share the same strangeness, s, while those on the same left-leaning diagonals share the same charge, q (given as multiples of the elementary charge). In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model. American physicist Murray Gell-Mann and Israeli physicist Yuval Ne'eman both proposed the idea in 1961.
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Eight-inch refracting telescope at Chabot Space and Science Center Design specifications relate to the characteristics of the telescope and how it performs optically. Several properties of the specifications may change with the equipment or accessories used with the telescope; such as Barlow lenses, star diagonals and eyepieces. These interchangeable accessories don't alter the specifications of the telescope, however they alter the way the telescopes properties function, typically magnification, apparent field of view (FOV) and actual field of view.
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Figure 1: A geomagic square that is also alphamagic Sallows has produced a still more magical version--a square which is both geomagic and alphamagic. In the square shown in Figure 1, any three shapes in a straight line--including the diagonals--tile the cross; thus the square is geomagic. The number of letters in the number names printed on any three shapes in a straight line sum to forty five; thus the square is alphamagic.
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See theorems 5.1 and 5.2 of . However, every graph of maximum degree three has slope number at most four;, improving an earlier result of ; theorem 5.3 of . the result of for the complete graph shows that this is tight. Not every set of four slopes is suitable for drawing all degree-3 graphs: a set of slopes is suitable for this purpose if and only it forms the slopes of the sides and diagonals of a parallelogram.
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Although the most common ratio is 1:2, other ratios exist. The Royal Navy's flag code book, BR20 Flags of All Nations, states that both 1:2 and 3:5 versions are official. The 3:5 version is most commonly used by the British Army and is sometimes known as the War flag. In this version, the innermost points of the lower left and upper right diagonals of the St Patrick's cross are cut off or truncated.
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Some diagonals of a concave polygon lie partly or wholly outside the polygon. Some sidelines of a concave polygon fail to divide the plane into two half- planes one of which entirely contains the polygon. None of these three statements holds for a convex polygon. As with any simple polygon, the sum of the internal angles of a concave polygon is ×(n − 2) radians, equivalently 180×(n − 2) degrees (°), where n is the number of sides.
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She produced baskets that reflected her skillful weaving technique, astute material selection, remarkably straight lines, complicated diagonals, and complex patterns. Mary and William enjoyed significant success in their artist career of weaving Pomo baskets. They traveled widely and developed relationships with collectors and art dealers. The couple demonstrated their weaving skills at the Louisiana Purchase Exposition in Saint Louis in 1904. They had their own exhibit and jointly wove a basket that won the fair’s highest award.
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If there are also true reflection lines in the same direction then they are evenly spaced between the glide reflection lines. A glide reflection line parallel to a true reflection line already implies this situation. This corresponds to wallpaper group cm. The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a rhombus with the true reflection line as one of the diagonals.
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Peters, 130 Sky comprises the upper third of the painting, with the land carved into diagonals by a winding path. A large tree to the right of center, extending to the top of the canvas, is the sole vertical stanchion. Composed of patches of green and reddish ocher, the ground plane is loosely painted, with the undertone of the canvas showing through toward the bottom of the canvas. The handling gibes with Twachtman's prioritization of breadth over detail.
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Margrave Albert Achilles, who was also Elector of Brandenburg, presented the town Bayreuth in December 1457 with the coat of arms that it still bears today. Two fields show the black and white coat of arms of the Hohenzollerns. The black lion on gold with a red and white border was the municipal coat of arms of the burgraves of Nuremberg. Along the two diagonals are two Reuten, small triangular shovels with a slightly bent shaft.
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In fisheye lenses, the visual angle is close to or more than 180 degrees in at least one direction. For example, a "diagonal fish eye" would have a viewing angle of at least 180 degrees within the diagonals of the frame. A "circular fisheye" would represent the image in the form of a circle. Rectilinear ultra-wide angle lenses are used in photography and cinematography sometimes to achieve three-dimensional perspective distortion instead of simply two-dimensional barrel distortion.
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Hess 2004, p. 46–47 Googie architecture exploited this trend by incorporating energy into its design with elements such as the boomerang, diagonals, atomic bursts and bright colors.Hess 2004, p. 47 and pp. 192–193 According to Hess, commercial architecture was influenced by the desires of the mass audience.Hess 2004, p. 50–51 The public was captivated by rocket ships and nuclear energy, so, in order to draw their attention, architects used these as motifs in their work.
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Chinese Chippendale railings on Monticello's wings In architecture, Chinese Chippendale refers to a specific kind of railing or balustrade that was inspired by the "Chinese Chippendale" designs of cabinetmaker Thomas Chippendale. The infill between the top and bottom rails and the vertical supports is a series of interlocking diagonals, although rectilinear designs exist as well. The term may also be applied to latticework. The design was popular in the United States in the late 18th and early 19th centuries.
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The upper chord does not extend past the portal (the space formed by the last four vertical posts at either end of the bridge). The end panels need only a brace, connected from the top of the last vertical post to the end of the lower chord. Struts are used to connect the two parallels of the chords to prevent lateral bending and reduce vibration. Two diagonals, connecting to the top of the vertical posts, are used.
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Approximately in width and in length, the bridge is built atop a reinforced concrete abutment and pier. Its truss structure exhibits a double- intersection configuration, constructed of 14 bays, each measuring approximately wide and in height, with the diagonals extending across two bays each. The bridge is fabricated of wrought iron bracketed with pins. Spanning the full length of the bridge is a wooden pedestrian walkway that consists of an observation deck and wooden seating near the bridge's midspan.
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As seen in the illustration on the right, once the grid was scribed, diagonals (transverse lines) were scribed from the uppermost corner of a column in the grid to the opposite lowest corner. This line intersects the cross lines in the grid in equal intervals. By using a cursor, alidade or similar indicator of measure, the closest point where the transversal crosses the grid is determined. That indicates the fraction of the graduation for the measure.
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The major disadvantage of mirror diagonals is that unless the reflective coating is properly applied they can scatter light rendering lower image contrast compared to a 90-degree prism. Also they deteriorate with age as the reflective surface oxidizes. The newer Dielectric mirrors have largely solved the deterioration problem, and if properly made the Dielectric mirrors scatter less light compared to conventional mirrors. With short focal length instruments a mirror diagonal is preferred over a prism.
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Both the cross notation () and the name cross product were possibly inspired by the fact that each scalar component of is computed by multiplying non-corresponding components of a and b. Conversely, a dot product involves multiplications between corresponding components of a and b. As explained below, the cross product can be expressed in the form of a determinant of a special matrix. According to Sarrus's rule, this involves multiplications between matrix elements identified by crossed diagonals.
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When a planar graph G has maximum vertex degree three, its line graph is planar, and every planar embedding of G can be extended to an embedding of L(G). However, there exist planar graphs with higher degree whose line graphs are nonplanar. These include, for example, the 5-star K1,5, the gem graph formed by adding two non- crossing diagonals within a regular pentagon, and all convex polyhedra with a vertex of degree four or more.; .
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The maid to the left faces the light, her brightly lit profile and sleeve creating a diagonal. Her opposite number creates a broader but less defined reflection of her attention, making a diagonal space between them, in which their charge stands protected."The composition is anchored by the two strong diagonals that intersect at about the spot where the Infanta stands ..." López-Rey (1999), p. 217 A further internal diagonal passes through the space occupied by the Infanta.
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Other examples are across the Murrumbidgee River at Gundagai (1903) and at Borah Creek, south of the present bridge. The bridge carries a single-track railway on an open deck (with transomes). The spans are , five at and , of which the five larger spans are timber trusses and the others timber girders. The trusses are deck type Howe trusses, of the deck type, with five bays, timber compression diagonals and steel tie rods for the verticals.
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The East Shoreham Bridge is located in a rural area of southeastern Shoreham, on the Lemon Fair River. It is located about west of the Shoreham-Depot Road, and is accessible on foot via the former railroad right-of-way, now (along with the bridge) a state- owned property. It is a single-span Howe truss structure, in length, and set on dry-laid stone abutments faced in concrete. The trusses consist of wooden diagonals and iron rod verticals.
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Another approach to the harmonic conjugate is through the concept of a complete quadrangle such as KLMN in the above diagram. Based on four points, the complete quadrangle has pairs of opposite sides and diagonals. In the expression of harmonic conjugates by H. S. M. Coxeter, the diagonals are considered a pair of opposite sides: :D is the harmonic conjugate of C with respect to A and B, which means that there is a quadrangle IJKL such that one pair of opposite sides intersect at A, and a second pair at B, while the third pair meet AB at C and D.H. S. M. Coxeter (1942) Non-Euclidean Geometry, page 29, University of Toronto Press It was Karl von Staudt that first used the harmonic conjugate as the basis for projective geometry independent of metric considerations: :...Staudt succeeded in freeing projective geometry from elementary geometry. In his Geometrie der Lage Staudt introduced a harmonic quadruple of elements independently of the concept of the cross ratio following a purely projective route, using a complete quadrangle or quadrilateral.
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When \alpha = 1 and \kappa, \lambda are restricted to being only 0, then c_\kappa becomes \exists, the diagonals can be dropped out, and the following theorem of cylindric algebra (Pinter 1973): : c_\kappa (x + y) = c_\kappa x + c_\kappa y turns into the axiom : \exists (x + y) = \exists x + \exists y of monadic Boolean algebra. The axiom (C4) drops out. Thus monadic Boolean algebra can be seen as a restriction of cylindric algebra to the one variable case.
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Blackburne's mate is named for Joseph Henry Blackburne and is a rare method of checkmating. The checkmate utilizes enemy pieces (typically a rook) and/or the edge of the board, together with a friendly knight, to confine the enemy king's sideways escape, while a friendly bishop pair takes the remaining two diagonals off from the enemy king.Renaud and Kahn (1962), p. 94. Threatening Blackburne's mate, which sometimes goes in conjunction with a queen sacrifice, can be used to weaken Black's position.
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Electrons traveling at 45° to this bond can move freely throughout the crystal. The Fermi surface therefore consists of Fermi arcs forming pockets centered on the corner of the Brillouin zone. In the pseudogap phase these arcs gradually disappear as the temperature is lowered until only four points on the diagonals of the Brillouin zone remain ungapped. On one hand, this could indicate a completely new electronic phase which consumes available states, leaving only a few to pair up and superconduct.
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One of the rhombic triacontahedron's rhombi All of the faces of the rhombic triacontahedron are golden rhombi A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. In the rhombic triacontahedron the dihedral angle between any two adjacent rhombi is 144°, which is twice the isosceles angle of a golden triangle and four times its most acute angle..
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Opposing pairs of these are joined by a bar labeled "contraries" (earth-air, fire-water). At the four corners of the superimposed square are the four qualities defining the elements. Each adjacent pair of these is joined by a bar labeled "possible combination"; the diagonals joining them are labeled "impossible combination." Starting from the top, fire is formed from the combination of dryness and heat; air from wetness and heat; water from coldness and wetness; earth from coldness and dryness.
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Under Bruner's sponsorship, Olson explored young children’s mental representations of space, particularly how children's language influenced their ability to reconstruct spatial patterns. He found that while children had no difficulty reconstructing horizontal and vertical patterns, they had great difficulties with diagonals before they went to school. It seems that to succeed in conceptualizing a diagonal, it has to be reconceived in terms of relations between horizontal and vertical axes. This research led to his first book, Spatial Cognition: The Child's Acquisition of Diagonality.
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In pioneer days, this hill was called Blue Island, so named because at a distance it looked like an island set in a trackless prairie sea. In fact it, and the nearby Stony Island, were both islands in Lake Chicago, as it receded. On the North side, the diagonals Clark Street and Ridge Boulevard run along ridges that were once sandbars in the Lake. One special feature of the Chicago area was the now-vanished Mud Lake in the Des Plaines River watershed.
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This change proved particularly useful for diagonal movements, now highlighted by the continuous sequence of same-coloured squares in the diagonals, facilitating the movement of the recently added bishop and queen.Hooper & Whyld 1992, p. 48. The Libro de los juegos (1283) contains a description of the chessboard, mentioning eight rows and columns as the ideal number, with the 10×10 board being too tiresome and the 6×6 board being too quick for the practice of chess.Yalom 2004, p. 62.
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These lugs served to transmit stress from the chord to the angle block and thence to the diagonals. These upper angle blocks also had lugs facing inward, to which were attached (by means MacDonald did not describe) the lateral braces. The interior side of each upper angle block also had a recess to accept a lug and a tap bolt. The tap bolt was used to connect the lug on the end of the sway rod to the angle block.
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Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals and to giveJ. L. Coolidge, "A historically interesting formula for the area of a quadrilateral", American Mathematical Monthly, 46 (1939) 345–347. (JSTOR)E. W. Hobson: A Treatise on Plane Trigonometry.
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Problems in higher dimensions also lead to banded matrices, in which case the band itself also tends to be sparse. For instance, a partial differential equation on a square domain (using central differences) will yield a matrix with a bandwidth equal to the square root of the matrix dimension, but inside the band only 5 diagonals are nonzero. Unfortunately, applying Gaussian elimination (or equivalently an LU decomposition) to such a matrix results in the band being filled in by many non-zero elements.
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In profile, the repetition of strong diagonals in the coiffure, beard forearm and feet are forceful and aesthetically pleasing. The horizontal shoulders arm and legs helps gives the figure a sense of energy and movement 38. The Stance is meant to signify the mankishi's alertness and readiness to carry out his purpose whether it is protecting its owner from evil spirits or witches and sorcerers. Its head is usually elongated with sharp facial feature such as the eyes, chin, and rectangular nose.
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Each adjacent pair of these is joined by a bar labeled "possible combination"; the diagonals joining them are labeled "impossible combination". Starting from the top, fire is formed from the combination of dryness and heat; air from wetness and heat; water from coldness and wetness; earth from coldness and dryness. This diagram is reproduced in several texts including Saemtliche Schriften und Briefe (Saemtliche Schriften und Briefe, Reihe VI, Band 1: 166, Loemker 1969: 83, 366, Karl Popp and Erwin Stein 2000: 33).
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This expression is derived by partitioning all rook arrangements in classes; in class s are those arrangements in which s pairs of rooks do not stand on the diagonal. In exactly the same way, it can be shown that the number of n-rook arrangements on a n × n board, such that they do not attack each other and are symmetric to both diagonals is given by the recurrence equations B2n = 2B2n − 2 \+ (2n − 2)B2n − 4 and B2n + 1 = B2n.
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Facing ongoing secessionist pressures from his constituency, Governor Rocha proposed the creation of a new provincial capital in replacement of the city of Buenos Aires, which was federalized as the nation's capital in 1880. The proposal, useful to the mollification of the province's independence-leaning gentry, was quickly approved by Congress. Freemason architect Pedro Benoit was commissioned by Governor Rocha to plan the provincial capital city of La Plata, who created a compass pattern of diagonals and precisely-placed squares.
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One of the diagonals should be a single piece, while the other is framed into the first piece or made of two pieces connected to it. X-braces, usually made of slender metal rods with threaded ends, are installed between vertical posts to help reduce sway. Knee braces,, usually flat bars with eyelets on either end, are used to connect the last strut and last vertical posts on both ends of the bridge. Individual panels may be prefabricated off-site.
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Wolfram MathWorld: Magic Square Weisstein, Eric W. Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares). The mathematical study of magic squares typically deals with its construction, classification, and enumeration.
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Then any point on the arithmetic billiard path which has integer coordinates has the property that the sum of the coordinates is even (the parity cannot change by moving along diagonals of unit squares). The points of self-intersection of the path, the bouncing points, and the starting and ending corner are exactly the points in the rectangle whose coordinates are multiples of \gcd(a,b) and such that the sum of the coordinates is an even multiple of \gcd(a,b).
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The portals are adorned with decorative plaques identifying the date and manufacturer of the structure. The bridge was manufactured by the American Bridge Company and installed in 1912 by its construction arm, the United Construction Company of Albany, New York. It is one of a handful of known pre-1916 Warren truss bridges in the state, and a particularly rare example of a lighter-weight instance with double-intersection diagonals. The cost of construction was paid by the towns of Harrison and Otisfield.
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The crew of Stella Polare In 1898 the Italian prince and explorer Prince Luigi Amedeo, Duke of the Abruzzi wanted to do polar expeditions. He travelled to Norway and consulted the famous polar explorer Fridtjof Nansen that had sailed the furthest north with the Colin Archer built polar ship Fram in 1893-96. In 1899 Amedo bought Jason, renamed her Stella Polare and took her to Colin Archer's shipyard. The interior was stripped out and beams, diagonals and knees heavily strengthened the ship.
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His later work, though superficially in a Precisionist style, utilizes off-balance, expressionistic compositions with jagged diagonals.. Some of his work in the 1920s was also observed by critics as having an Oriental influence, believed to derive from his studies of Japanese ukiyo-e art. Dickinson produced fewer than two hundred works during his twenty-year career. He usually did not sign or date his works, which together with his stylistic experimentation makes it difficult to place them in a chronology.
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Thus if the number of sides n is odd, a tangential polygon is equilateral if and only if it is regular.. Viviani's theorem generalizes to equilateral polygons:. The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point. The principal diagonals of a hexagon each divide the hexagon into quadrilaterals. In any convex equilateral hexagon with common side a, there existsInequalities proposed in “Crux Mathematicorum”, .
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The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral (that is, the four intersection points of adjacent angle bisectors are concyclic) or they are concurrent. In the latter case the quadrilateral is a tangential quadrilateral. In quadrilateral ABCD, if the angle bisectors of A and C meet on diagonal BD, then the angle bisectors of B and D meet on diagonal AC.Leversha, Gerry, "A property of the diagonals of a cyclic quadrilateral", Mathematical Gazette 93, March 2009, 116–118.
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A well-covered graph, the intersection graph of the nine diagonals of a hexagon. The three red vertices form one of its 14 equal-sized maximal independent sets, and the six blue vertices form the complementary minimal vertex cover. In graph theory, a well-covered graph is an undirected graph in which every minimal vertex cover has the same size as every other minimal vertex cover. Equivalently, these are the graphs in which every maximal independent set has the same size.
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Cerebral diplopia or polyopia describes seeing two or more images arranged in ordered rows, columns, or diagonals after fixation on a stimulus. The polyopic images occur monocular bilaterally (one eye open on both sides) and binocularly (both eyes open), differentiating it from ocular diplopia or polyopia. The number of duplicated images can range from one to hundreds. Some patients report difficulty in distinguishing the replicated images from the real images, while others report that the false images differ in size, intensity, or color.
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The Hesse configuration, with four of its lines (the four broken diagonals of the 3×3 array of points) drawn as curves In geometry, the Hesse configuration, introduced by Colin Maclaurin and studied by ,. is a configuration of 9 points and 12 lines with three points per line and four lines through each point. It can be realized in the complex projective plane as the set of inflection points of an elliptic curve, but it has no realization in the Euclidean plane.
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An orthodiagonal quadrilateral (yellow). According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non- adjacent vertices are orthogonal (perpendicular) to each other.
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However, once the bishop is on the 95–59 diagonal, then the Snowroof player's bishop may be traded off if the opponent pulls their bishop back to attack along the 31–97 diagonal. Thus, the Snowroof player must weigh the pros and cons of a rook pawn trade vs a bishop trade. Yet another common possibility has the bishop moving B-77, B-59 aiming for a position on the 37 or 25 squares so that it may be utilized on these diagonals.
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These proceedings included cremation (in the included crematorium) as well as defleshing of the body before the cremation. Once the houses had served their purpose, they were burned to the ground and covered by earth, creating a sort of burial mound. Anthropologist William F. Romain in Mysteries of the Hopewell notes that these charnel houses were built in the form of a square, and their diagonals could be aligned to the direction of maximum and minimum moon-sets both north and south.
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A cluster of elevator shafts is exposed on the west facade, each shaft stopping at a different height. The building stands at the western end of a block-size plaza with extensive landscaping arranged in a dense pattern criss-crossed by diagonals. The north side of the plaza features the 50-foot "Man With a Briefcase" sculpture by Jonathan Borofsky, an aluminum slab with the outline of a giant businessman cut out of the center. The building is also Fort Worth's largest office tower.
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Just like in marching cubes, the intersections of these edges with the isosurface are approximated by linearly interpolating the values at the grid points. Adjacent cubes share all edges in the connecting face, including the same diagonal. This is an important property to prevent cracks in the rendered surface, because interpolation of the two distinct diagonals of a face usually gives slightly different intersection points. An added benefit is that up to five computed intersection points can be reused when handling the neighbor cube.
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The fact that the groups below the jagged line in the table above are constant along the diagonals is explained by the suspension theorem of Hans Freudenthal, which implies that the suspension homomorphism from to is an isomorphism for . The groups with are called the stable homotopy groups of spheres, and are denoted : they are finite abelian groups for , and have been computed in numerous cases, although the general pattern is still elusive. . For , the groups are called the unstable homotopy groups of spheres.
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The common fuselage was built around four spruce longerons, stiffened by diagonals or plywood sheet, though most of the fuselage was fabric covered; it had with a rounded decking. The single cockpit was at mid wing chord. The engine was mounted on steel tubes fixed to the ends of the longerons, with a firewall between engine and pilot. There was a triangular tailplane bearing a single piece elevator, with hinge just at the end of the fuselage where there was also a small tail skid.
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The settlement was initially called Lake Erie, then Buffalo Creek, soon shortened to Buffalo. Although the company named the settlement "New Amsterdam," the name did not catch on, reverting to Buffalo within ten years. Buffalo had the first road to Pennsylvania built in 1802 for migrants passing through to the Connecticut Western Reserve in Ohio. In 1804, Ellicott designed a radial grid plan that would branch out from the village forming bicycle-like spokes, interrupted by diagonals, like the system used in the nation's capital.
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A more detailed discussion how (crystallographic structure factor) phases link with the phases of the electron wave can be found in. Just as with proteins, it has been possible to determine the atomic structures of inorganic crystals by electron crystallography. For simpler structure it is sufficient to use three perpendicular views, but for more complicated structures, also projections down ten or more different diagonals may be needed. In addition to electron microscopy images, it is also possible to use electron diffraction (ED) patterns for crystal structure determination.
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Björn Åkesson, a civil engineer at Chalmers University of Technology in Sweden, has identified three proximate causes of the bridge collapse: (1) the failure of an angle block lug on the west end of the bridge due to fatigue (caused by bending and shear stress), (2) thrust stress from improperly fitting chords and diagonals, and (3) low temperatures, which caused the cast iron angle blocks to become brittle. The failure of the angle block caused the upper chord to buckle, and the bridge to collapse.
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Boating is an 1874 painting by French artist Édouard Manet in the collection of the Metropolitan Museum of Art, New York. Done in oil on canvas, the painting depicts a man (believed to be Manet's brother in law, Rodolphe Leenhoff) and an unknown woman boating on the River Seine at Argenteuil in the Paris suburbs. In the work Manet uses a delicate touch to exploit the broad planes of color and strong diagonals of Japanese prints. The work is on view in Gallery 818.
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The 'Ball Road-Little Salt Creek Bridge was a single- span steel pin-connected, Pratt bedstead truss bridge. The bridge spanned 40 feet and was 13 feet wide. The upper chord members were constructed from two channels with cover and batten plates, the upright end posts were constructed from two channels with lacing, and the lower chord members were constructed from two angles with batten plates. Verticals were constructed from four angles with double lacing and the diagonals were constructed from two punched rectangular eyebars.
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Another phase termed α-N2 exists below 35.6 K at low pressure and has a cubic structure. The space group is Pa3. At 21 K the unit cell dimension is 5.667 Å. Under 3785 bars this reduces to 5.433 Å. At low temperatures the α-phase can be compressed to 3500 atmospheres before it changes (to γ), and as the temperature rises above 20 K, this pressure rises to about 4500 atmospheres. The nitrogen molecules are located on the body diagonals of the unit cell cube.
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Horizontal wires were attached to these diagonals. More elaborate and formidable obstructions could be formed with multiple lines of stakes connected with wire running from side-to-side, back-to-front, and diagonally in every possible direction. Effective as these obstacles were, their construction took considerable time. Barbed wire obstacles were vulnerable to being pushed about by artillery shells; in World War I, this frequently resulted in a mass of randomly entangled wires that could be even more daunting than a carefully constructed obstacle.
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The diagonals are kept in place by tightening the nuts on the vertical posts. Cleats can be nailed to a wooden angle block to help keep braces and counter-braces seated. Alternatively, a hole may be drilled in the lug and brace/counter-brace and a dowel inserted to hold the beam in place. Iron angle blocks should have a hole cast in the upper lugs so that a bolt may pass through the lug and brace/counter-brace, securing the braces in place.
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For instance, a cubic crystal may have low-energy planes on the faces of the cube or on the diagonals. The planes are low-energy in the sense that if the crystal is cleaved along these planes, there will be relatively few broken bonds and a relatively small increase in energy over the unbroken crystal. Equivalently, these planes have a low surface energy. The planes with the lowest energy will form the largest facets, in order to minimize the overall thermodynamic free energy of the crystal.
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The brushwork creates a sense of motion, allowing for an aspect of hustle and bustle to be added to the street scene. The tilting downward of the perspective and the opposing diagonals in the brushwork create distortion and a sense of motion. The viewer feels confronted with the people in the street, as if they about to spill off the canvas and into our space. This stylistic choice also makes you feel closer to the women while farther away from the anonymous male figures in the background.
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The other end of the crucifix points again to the men who are climbing up the steps. Michelangelo also created many strong diagonals with the placement of his figures and the extension of their arms and legs towards a central point of convergence. The position of St Peter's body in this work is often noted as Michelangelo's most interesting innovation. He defied convention by placing Peter’s upper body so that he needs to crane upward and twist his neck to make eye contact with the viewer's gaze.
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The results of a factor analysis can be used to estimate each individual's score on the primary abilities based upon the individual's scores on the tests. Chapter X presents a method for obtaining the regression weights for estimating primary abilities from subject scores, and well as for estimating subjects scores from the primary traits (for estimating the components of variance of the subject scores). Appendices. I: Outline of Calculations for the Centroid Method with Unknown Diagonals. II: A Method of Finding the Roots of a Polynomial.
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Architectural elements such as pillars, beams or platforms continued to be used to convey moods. Landscapes stand on their own as they are detached from the characters' emotions and gain a new function as a place to escape from the constraints of court life. Like most emaki, the composition is based on the fukinuki yatai ("blown-off roof") technique, which consists of a perspective of looking down from above into the inner spaces resulting in a plunging view. Furthermore, diagonals are used to mark depth.
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As amazing as this performance was, if time permitted afterward, Koltanowski would occasionally demonstrate his mental grasp of the board by reciting the information contained in the squares by rank or file, or even the two long diagonals. He occasionally performed the tour on two boards simultaneously. In Palo Alto, California, he conducted his performance on three chalk boards, jumping the knight back and forth between boards mid-move, until all 192 squares were completed. He made two errors and immediately corrected himself both times.
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Sia proper, which survives today as the Dioulasoba neighborhood, was partly spared this total destruction. It was dramatically modified in 1932 when a large road artery was built through it and by the widening of streets in successive urban renewal projects. Between 1926 and 1929, the French colonial government constructed a typical European grid pattern of new avenues and streets in the city, intersected by diagonals radiating from a center, with square urban lots between them. This established the framework for the modern city center.
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Thus, La Plata is nicknamed "la ciudad de las diagonales" (city of diagonals). It is also called "la ciudad de los tilos" (city of linden trees), because of the large number of linden trees lining the many streets and squares. The linden tree is one of a number of deciduous Northern Hemisphere tree species which dominate La Plata's parks and streets; ash, horsechestnut, plane, sweetgum and tulip tree are among the other examples. Palms and subtropical broadleaf evergreen trees thrive but are comparatively infrequent.
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Schwedler invented the Schwedler truss, which was widely used worldwide in framed bridges and roofs until about 1900. It is a kind of curved chord or bowstring truss with the minimum number of diagonals, which are to bear only tension, not compression; it requires a slight downward curvature in the middle, usually replaced with extra diagonal bracing for appearance and cost saving.William Hubert Burr and Myron Samuel Falk, The Design and Construction of Metallic Bridges, New York: Wiley, 1905, repr. BiblioBazaar, 2009, , pp. 251-57.
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The Ninth Street Bridge in Boise, Idaho, also known as the Eighth Street Bridge, crosses the Boise River and is a 2-span, pin-connected Pratt through truss design constructed by the Missouri Valley Bridge & Iron Co. and completed in 1911. Each span is and includes six full panels and two end panels, supported by concrete piers at each end and midway in the river. Laced channel sections with cover plates form the upper chords, with eyebars on the lower chords. Eyebars with turnbuckles form the diagonals.
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Players take turns to move one piece to an adjacent square in any direction (including diagonals). Pieces can move further by jumping over one or more of their own or opponents' pieces, making a series of jumps where possible. When a player jumps into their boat, all the boats are moved clockwise around the board, one quarter turn. As a result, players will often find their own boat moves away from the dock they have moved one of their pieces to, giving the game its name.
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Part of the design of the B&R; rig involves inducing a "pre-bend" in the mast which provides some of the side-to-side and fore-and-aft stability of the rig. The pre-bend is achieved by tensioning the reverse diagonals and certain other so called intermediate shrouds. Because the spreaders are swept back at approximately a 25° to 30° angle, this tensioning bows the mast. Balanced and proper tensioning keeps the bow in the mast in the fore-aft direction and eliminates any curvature in the sideways direction.
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Distance-hereditary graphs were named and first studied by , although an equivalent class of graphs was already shown to be perfect in 1970 by Olaru and Sachs.Olaru and Sachs showed the α-perfection of the graphs in which every cycle of length five or more has a pair of crossing diagonals (, Theorem 5). By , α-perfection is an equivalent form of definition of perfect graphs. It has been known for some time that the distance-hereditary graphs constitute an intersection class of graphs, but no intersection model was known until one was given by .
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The truss consists of timber top and bottom chords, timber compression diagonals and tension rods as verticals; the tension rods could be used to adjust the geometry and counteract shrinkage. Furthermore, cast-iron shoes at all joints ensured proper truss action and a good transfer of member forces at the joints. Allan's design was lighter and more economical than the McDonald truss it replaced. They were also designed to be more accessible for painting and repair, and to use shorter lengths of timber which were much easier to obtain and to manoeuvre during construction.
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At the start of the game, each player takes a set of principality cards. Each principality begins with two settlements and a road between them. At the diagonals to the settlements lie a total of six resource fields (one in each of the six resources: brick, grain, lumber, ore, wool, and gold), the two in the middle being shared by the two settlements. Resource fields both produce resources, based on the outcome of the roll of one die, as well as store them, based on the orientation of the card itself.
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Ailerons filled almost half the span. Centrally mounted above the fuselage on a pedestal with about 2° of dihedral, they were braced to the fuselage on each side by a single faired wooden strut which ran from just inside mid-span to the bottom of the fuselage. The cross section of the EB.2's wooden fuselage was rhomboidal with its diagonals vertical and horizontal, defined by lattice work and fabric covered. Its open cockpit was immediately ahead of the wing, placing the pilot's head against the front of the central pedestal.
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The magnification through a telescope makes an object appear larger while limiting the FOV. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world. At higher magnifications the image quality significantly reduces, usage of a Barlow lens increases the effective focal length of an optical system—multiplies image quality reduction. Similar minor effects may be present when using star diagonals, as light travels through a multitude of lenses that increase or decrease effective focal length.
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However, they concluded that the game loses "by a hair" when compared to its rival, Virtua Fighter. The four reviewers of Electronic Gaming Monthly gave the game a positive review, chiefly praising the character design, graphics, and special moves. Maximum made note of the graphical and gameplay innovations such as gouraud shading, rotational backgrounds, dramatic camera angles, and the sidestep. However, they remarked that the poor quality directional pad on the original PlayStation controller "just isn't built for taking diagonals and quarter circle rolls", making it irritatingly difficult to pull off special moves.
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It is a small to medium-sized tree growing to 7–25 m tall. The leaves are narrow obovate, 20–40 cm in length and 10–20 cm in width. Fruit produced as mentioned earlier, is otherwise aptly known as the Box Fruit, due to distinct square like diagonals jutting out from the cross section of the fruit, given its semi spherical shape form from stem altering to a subpyramidal shape at its base. The fruit measures 9–11 cm in diameter, where a thick spongy fibrous layer covers the 4–5 cm diameter seed.
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Film critic Roger Ebert described it as "a jagged landscape of sharp angles and tilted walls and windows, staircases climbing crazy diagonals, trees with spiky leaves, grass that looks like knives". The sets are characterized by strokes of bold, black paint. The landscape of Holstenwall is painted on canvas, as opposed to a constructed set, and shadows and streaks of light are painted directly onto the sets, further distorting the viewer's sense of perspective and three- dimensionality. Buildings are clustered and interconnected in a cubist-like architecture, surrounded by dark and twisted back alleys.
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54-55 His backgrounds would be less detailed where he did not want the eye to be drawn. His figures would move actively along diagonals, and he utilised foreshortening to make a character appear to recede more deeply into the panel, so that they appeared to move towards the reader, off the page. During the 1960s Kirby also developed a talent for collages, initially utilising them within the pages of The Fantastic Four. He introduced the Negative Zone as a place within the Marvel Universe that would only be illustrated via collage.
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It is now predominant across the world. England until recently was an exception to this convention. Until 1974 referees in the Football League were required to run both diagonals during a match, most opting to run from right wing to right wing in the first half before switching to the left-wing diagonal for the second half. The chief reason for this alternation was to avoid linesmen wearing down the same part of the touchline during matches – this was important given the generally lower quality of pitches at the time.
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Unlike individual competitions tricks such as "round abouts", "chain reactions" form a large section of the choreography. Shapes (also known as patterns or images) that are an accepted part of choreography are diamonds, squares, diagonals, circles and lines. The routine is judged by the distribution of competitors across the floor, how "readable" the patterns are and the transitions between these patterns. Specialist formation choreographers include Ona Skaistutė Idzelevičienė,Biography of Žuvedra Coach Roberto Albanese,German Wikipedia Biography of Roberto Albanese Horst Beer,German Wikepdia Biography of Horst Beer and Rachael Holland.
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This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube). In the case of a cube, or of a trigonal trapezohedron where the two truncated vertices are the ones on the stretching axes, the resulting shape has three-fold rotational symmetry.
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A pantograph with a Studio Light A pantograph is a commonly used overhead suspension system for lamps and audio and video monitors in television studios. It is also used on a smaller scale in many photography studios. Using either motor driven cables or a spring system, the pantograph can be balanced so that a light touch can readjust the height of the load (usually a lamp). The system usually works through a series of connected diagonals that can be compressed or extended to adjust the height of the rig.
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Placement of Goliath's head has been a source of some debate for art historians. When exhibited at the National Gallery of Art, the head was placed between David's feet, as is the case in the statue's permanent home, the National Museum of the Bargello, in Florence, Italy. Another school of art historians have suggested that Verrocchio intended for Goliath's head to be placed to David's right, pointing to the diagonals of the ensemble. This placement was temporarily arranged at the National Gallery of Art, as well as Atlanta's High Museum, among others.
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A polygon is defined to be cyclic if its vertices are all concyclic. For example, all the vertices of a regular polygon of any number of sides are concyclic. A tangential polygon is one having an inscribed circle tangent to each side of the polygon; these tangency points are thus concyclic on the inscribed circle. A convex quadrilateral is orthodiagonal (has perpendicular diagonals) if and only if the midpoints of the sides and the feet of the four altitudes are eight concyclic points, on what is called the eight-point circle.
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In 2001 she began another museum project, an extension of the Ordrupgaard Museum near Copenhagen, Denmark, a museum featuring a collection of 19th century French and Danish art in the 19th-century mansion of its collector. The new building is 87 metres long and 20 metres wide, and is connected by a five-metre wide passage to the old museum. There are no right angles – only diagonals – in the concrete shell of the museum. The floor-to-ceiling glass walls of the gallery make the garden the backdrop of the exhibits.
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As in many other designs by Moronobu, the artist was inventive in his use of curvilinear forms juxtaposed against straight diagonals. Groupings of 12 images had been common for centuries in court and genre paintings. Among the more famous surviving early specimens were the painted single sheets by the master Tosa Mitsunobu (1434–1525). Thus Moronobu's adoption of a grouping of 12 was conventional enough, particularly as such an arrangement afforded a context in which to alter the furnishings, clothing, and design patterns, matched more or less to the months of the year.
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In chess, the distance between squares on the chessboard for rooks is measured in taxicab distance; kings and queens use Chebyshev distance, and bishops use the taxicab distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. To reach from one square to another, only kings require the number of moves equal to their respective distance; rooks, queens and bishops require one or two moves (on an empty board, and assuming that the move is possible at all in the bishop's case).
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The controls consist of four directions (allowing eight directions including diagonals) and a shot button. Each team has seven players,Match Day II review at crashonline.org including goalkeeper and there are league and cup options available. The game is considered highly addictive due to its difficulty level, the complete control over ball direction, power and elevation (using a Diamond Deflection System),Matchday 2 review at Your Sinclair Rock and Roll Years and the importance of tactics and player positioning over the field (barging if necessaryMatch Day 2 instructions at zxsoftware.co.
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The steps of this theorem require nothing beyond basic constructive Euclidean geometry. With the additional construction of a parallelogram having sides parallel to the diagonals, and tangent to the corners of the rectangle of incenters, the quadrilateral case of the cyclic polygon theorem can be proved in a few steps. The equality of the sums of the radii of the two pairs is equivalent to the condition that the constructed parallelogram be a rhombus, and this is easily shown in the construction. Another proof of the quadrilateral case is available due to Wilfred Reyes (2002).
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The 3 rows containing this conjugacy class are shown with boldface entries in the adjacent table. The proper rotations of the cube, which can be characterized by permutations of the body diagonals, are also described by conjugation in S4 . In general, the number of conjugacy classes in the symmetric group Sn is equal to the number of integer partitions of n. This is because each conjugacy class corresponds to exactly one partition of {1, 2, ..., n} into cycles, up to permutation of the elements of {1, 2, ..., n}.
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The diagonals are created through the disposition of the fish but van Utrecht is less interested in dynamic movement than Snyders and therefore his diagonal lines are more muted. The figures in van Utrecht's composition were painted by another painter, possibly Gerard Seghers. Whereas the market scenes represented in the 16th century a reflection of a social reality of increased wealth and material abundance, van Utrecht's market scenes are more concerned with the aesthetic effect of the work. Nevertheless, his Fishmonger’s Stall seems to convey a moralistic tale.
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She introduces tension through unexpected color pairings, diagonals, ambiguous figure-ground relationships, and contained fields whose shapes bump the picture edges like balls ricocheting on a billiard table—then painstakingly resolves it through "an obsessive tinkering with color and mass." Laurie Fendrich, 16B, Conté crayon on Arches paper, 24" x 18" (image size 16" x 14"), 2016. While committed to overall harmony and an ideal of perfect geometric form, Fendrich injects the warmth, spontaneity and quirkiness of the human touch through her handling of paint and form.Wei, Lilly.
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Slightly raised platforms and bridges connected various parts of the lobby to one another, with stairs and escalators, placed at diagonals to H Street NW, led to the below-ground levels. The structure had double-loaded corridors, which meant that guest rooms either faced inward at the atrium or outward at the city. All inward- facing rooms had balconies overlooking the atrium. The north walls of the atrium were decorated with Mediterranean-style pilasters, with a Mediterranean-style arcade formed by segmental arches on the first and second floor.
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The flag of Kropyvnytskyi The flag of Kropyvnytskyi is the city symbol of Kropyvnytskyi developed and widely introduced during the last decade of the 20th century. The flag has two horizontal bands of yellow, of equal width, separated by a central blue band which splits into a horizontal "Y" shape, the arms of which end at the corners of the hoist side (and roughly follow the flag's diagonals). The Y embraces a crimson isosceles triangle containing the golden monogram of St. Elizabeth within. The width of the pall makes one fifth of the flag.
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On either side vertical board-and-batten siding begins a foot below the lower chord and rises to a gabled metal roof, high, supported by tie-beam rafters with transverse metal rods and diagonal cross-bracing. Interior clearance is only , enforced by metal height restrictors near the portals. Two sets of heavy timber planks serve as the top and bottom chords, with a secondary lower chord at deck level. Twelve-inch (30 cm) diagonals, fastened at each intersection by two- inch (5 cm) treenails, radiate out from the middle to either end.
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While the flag appears symmetric, the white lines above and below the diagonal red are different widths. On the side closer to the flagpole (or on the left when depicted on paper), the white lines above the diagonals are wider; on the side farther from the flagpole (or on the right when depicted on paper), the converse is true. Thus, no change will be apparent when rotating the flag 180 degrees, but if mirrored the flag will be upside-down. Placing the flag upside down is considered lèse majesté and is offensive to some.
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No provision exists for mixing text and graphics, except for the limited "hardware split screen" of the Apple II (four lines of text at the bottom of the screen). Vector-based shape tables can be used to draw objects in hires graphics, but are slow in comparison to routines that draw bitmaps directly. They also only support the defining of horizontal and vertical lines. Diagonals and curves are not supported, although shapes can be drawn rotated to various angles, so that lines ostensibly defined as horizontal or vertical will appear diagonal.
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The edges of the resulting geometric graph are diagonals of a subset of the faces of the regular skew polyhedron with six square faces per vertex, so the Laves graph is embedded in this skew polyhedron. It is possible to interleave two copies of the structure, filling one-fourth of the points of the integer lattice, while preserving the fact that the adjacent vertices are exactly the pairs of points that are units apart, and all other pairs of points are farther apart. The two copies are mirror images of each other.
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The truss form is of the Pratt truss configuration with timber top and bottom chords and timber verticals, with steel rod crossed diagonals. This configuration allows the truss to transfer loads from where it is applied in both directions to the elastic supports provided at each node by the suspension cables. The top and bottom chords consist of pairs of horizontal timber whilst the verticals are single timbers. Splices in the chords have been affected with steel side plates, some of which may be original and some replaced.
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Parallelogram ABCD To prove that the diagonals of a parallelogram bisect each other, we will use congruent triangles: :\angle ABE \cong \angle CDE (alternate interior angles are equal in measure) :\angle BAE \cong \angle DCE (alternate interior angles are equal in measure). (since these are angles that a transversal makes with parallel lines AB and DC). Also, side AB is equal in length to side DC, since opposite sides of a parallelogram are equal in length. Therefore, triangles ABE and CDE are congruent (ASA postulate, two corresponding angles and the included side).
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For the Zwinger he also provided the sculptures for the Nymphenbad fountain. He died in Dresden. His most famous independent, free-standing sculpture is an over-lifesize marble Apotheosis of Prince Eugene (1718-21; Österreichische Galerie Belvedere, Vienna), where the main figure, depicted with the attributes of Hercules, and secondary figures of Fame and a fallen Turk are linked in a tour-de-force of complicated Berninian diagonals that did not satisfy Prince Eugene of Savoy's classicizing taste.Prince Eugene installed the sculpture in the officers' mess in the Upper Belvedere.
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A prism diagonal uses either a simple 90-degree angle prism, pentaprism or an Amici roof prism rather than a mirror to bend the light path. On longer focal ratio telescopes a well-made 90-degree prism diagonal is the optimum choice to deliver the highest image contrast short of using the telescope without a diagonal entirely. However prisms seem to be falling out of favor probably due to marketing forces which have been favoring short focal length instruments which tend to function better with a mirror diagonal.Gary Hand, Diagonals; Prisms vs.
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Berlin Wilhelmplatz planned layout In 1826, Schinkel submitted his suggestion to move the position of the Leopold I Memorial as a part of the largest yet transfiguration of the square under his supervision. The other statues were also allocated new locations along the diagonals and lateral axes of the square. Besides these changes, he graced the surface of the square with greenery, a lawn dotted with lime trees and encircled by an oval walking path, which traced the borders of the square. Altogether, the new upgrades gave the space the appearance of a park.
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There is evidence that some I-beams were then installed correctly, but that the angle blocks were damaged in the process. Furthermore, in every other joint, the diagonal chords were fitted to the angle blocks using shims rather than tightening the vertical beams and putting the diagonals under compression. Rather than rely on the truss design to carry live loads, the shims carried this weight by themselves. At the ends of the bridge, where Stone used only a single diagonal, only half of the angle block received load.
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13 Scott's residential buildings are few; one of the best known is the Cropthorne Court mansion block in Maida Vale, where the frontage juts out in diagonals, eliminating the need for lightwells. K2 red telephone boxes preserved as a tourist attraction near Covent Garden, London Battersea Power Station Scott continued working on churches during the inter-war years. Shortly after his work on the nave at Downside Abbey he was commissioned to design the small Roman Catholic Church of Our Lady & St Alphege, Bath, the first part of which was completed in 1929.
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Her most typical work favours strong outlines and sweeping diagonals, often with stern, unsmiling faces.Die Stadt, coloured crayon on black paper, 35x23cm However, there are also gentler, more naturalistic depictions, particularly of trees, that look back to German Romanticism of the nineteenth century, also powerful woodcut-like pen and ink portraits that owe much to Dürer. She very rarely dated her work. On works where a date appears it is very likely that they have been subsequently added to make them appear earlier than they in truth are.
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No Guard (ノーガード nō gādo) is a Double Static Rook shogi opening that is a subvariation of a Double Wing Attack opening with mutually open bishop diagonals. The opening gets its name from White omitting their defensive left gold development (...G-32) and instead opting for an early bishop trade in order to initiate a quick attack line with their bishop in hand. The missing defensive gold leaves White lacking a 'guard.' The opening is considered speculative since it is thought to favor Black and is not used by professional shogi players.
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The diagonal and vertical members form the truss web, and carry the shear stress. Individually, they are also in tension and compression, the exact arrangement of forces is depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression. Truss sections stabilize this building under construction in Shanghai and will house mechanical floors In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling.
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Palásti found an eight-point set with this property, and showed that for any number of points between three and eight (inclusive) there is a subset of the hexagonal lattice with this property. Palásti's eight-point example remains the largest known. Another of Palásti's results in discrete geometry concerns the number of triangular faces in an arrangement of lines. When no three lines may cross at a single point, she and Zoltán Füredi found sets of n lines, subsets of the diagonals of a regular 2n-gon, having n(n-3)/3 triangles.
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While Ket's earliest paintings are impressionistic in style, he was influenced decisively by the art of the Neue Sachlichkeit in 1929, and thereafter painted in a magic realist style. His meticulously composed and rendered still lifes feature favorite objects such as bottles, an empty bowl, eggs, and musical instruments. Ket juxtaposed these objects in angular arrangements, seen from a high vantage point, their cast shadows creating emphatic diagonals. These compositions reveal the influence of cubism as filtered through the posters of Cassandre, which are frequently depicted in Ket’s paintings.
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The forward vertical supported the wing at its front spar and the two diagonals met on the rear one. The lower frame extended forwards, with the pilot's seat projecting either side of it immediately ahead of the forward vertical frame. Underneath it, a curved skid was mounted and faired in, forming a long, deep, narrow box, reaching aft to the rear vertical frame. From the trailing edge rearwards the upper frame member was split into two, running parallel to each other and cross braced in the horizontal plane.
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Only the lower wing carried ailerons. The fuselage was built around four steel tube longerons with frames and diagonals. Spruce stringers and a canvas covering gave the outer fuselage ten faces forming only slightly curved sides and underside but a more rounded upper surface; the fuselage narrowed to the tail. The details of the nose would have depended on the choice of engine fitted: options were the two cylinder Centaure, three cylinder Poinsard or four cylinder, inverted in-line Train 4T, though it is not known if the Moineau flew with any of these.
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For a square n \times n king's graph, the total number of vertices is n^2 and the total number of edges is (2n-2)(2n-1). The neighbourhood of a vertex in the king's graph corresponds to the Moore neighborhood for cellular automata.. A generalization of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph in which each bounded face is a quadrilateral and each interior vertex has at least four neighbors) by adding the two diagonals of every quadrilateral face of the squaregraph..
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"In its complexity, deliberate confusion, slashing diagonals, tenebrism and intense colouration," she writes, "it most resembles the paintings of her French Romantic predecessors Géricault and Antoine-Jean Gros, as well as the more contemporary Eugène Delacroix." Ivanović painted very little in her final years, and is said to have been largely forgotten in Serbia by the 1870s. In June 1876, she became an honorary member of the Serbian Learned Society, which was later to become the Serbian Royal Academy and eventually the Serbian Academy of Sciences and Arts. She died in Székesfehérvár in September 1882.
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The richer structure of geomagic squares is reflected in the existence of specimens showing a far greater degree of 'magic' than is possible with numerical types. Thus a panmagic square is one in which every diagonal, including the so-called broken diagonals, shares the same magic property as the rows and columns. However, it is easily shown that a panmagic square of size 3 × 3 is impossible to construct with numbers, whereas a geometric example can be seen in Figure 3. No comparable example using connected pieces has yet been reported.
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The tangent lengths and tangency chords The eight tangent lengths (e, f, g, h in the figure to the right) of a tangential quadrilateral are the line segments from a vertex to the points where the incircle is tangent to the sides. From each vertex there are two congruent tangent lengths. The two tangency chords (k and l in the figure) of a tangential quadrilateral are the line segments that connect points on opposite sides where the incircle is tangent to these sides. These are also the diagonals of the contact quadrilateral.
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Some of the tiles, particularly those in a large panel under the portico to the left main entrance, are decorated with sage green and dark manganese purple that are characteristic of the earlier 'Damascus ware' coloring scheme. No other mosque makes such a lavish use of Iznik tiles; with later mosques Sinan used files more sparingly. The plan of the building is basically that of an octagon inscribed in a rectangle. The main dome rests on four semi-domes; not on the axes but in the diagonals of the building.
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If the pixel is in a region of uniform intensity, then the nearby patches will look similar. If the pixel is on an edge, then nearby patches in a direction perpendicular to the edge will look quite different, but nearby patches in a direction parallel to the edge will result in only a small change. If the pixel is on a feature with variation in all directions, then none of the nearby patches will look similar. The corner strength is defined as the smallest SSD between the patch and its neighbours (horizontal, vertical and on the two diagonals).
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With an initial state that carefully arranges the sites of these collisions, the Critters rule can be made to simulate a billiard-ball computer and thus, like Life, it can support universal computation. The Critters rule can also support more complex spaceships of varying speeds as well as oscillators with infinitely many different periods. Despite the complexity of its behavior, Critters obeys certain conservation laws and symmetry rules. For instance, the parity of the number of live cells along certain diagonals of the grid is not changed by the update rule, and remains unchanged throughout the evolution of any Critters pattern.
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The lifting superstructure comprises four steel lattice towers, connected at their upper level by steel lattice girders. The two De Burgh truss spans, each 31.7m, are of composite timber and steel construction, with paired timber top chords and vertical struts with steel rods forming diagonals within each panel. The approach spans range from approximately 9.1m to 11m in length and are of timber beam construction, comprising five parallel timber logs spanning between timber and trestle piers. Each span has been strengthened by the addition of four steel RSJs, one each located in between the timber logs.
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The color of a Zometool strut is associated with its cross section and also with the shape of the hole of the connector node in which it fits. Each blue strut has a rectangular cross section, each yellow strut has a triangular cross section, and each red strut has a pentagonal cross section. The cross section of a green strut is a rhombus, where the ratio of the diagonals is √2. The green struts, fitting in the "red" pentagonal holes, are not a part of the 1992 release of Zometool, and, consequently, using them is not as straightforward as the other colors.
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Your Commodore gave the game 6/10 for originality, 4/10 for playability, 4/10 for graphics, and 5/10 for value-for-money, saying "The game has some original ideas but they don't quite get together and the overall impression is uninspiring". Zzap! was more positive, awarding it 78%, calling it a "good arcade adventure", and praising the game's size. One of the three reviewers did not think the gameplay had enough variety to be worth the £2.99 price tag. Another complained that using diagonals to jump forward and backward was too difficult with a standard Atari joystick.
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Bactrian camels are exceptionally adept at withstanding wide variations in temperature, ranging from freezing cold to blistering heat. They have a remarkable ability to go without water for months at a time, but when water is available they may drink up to 57 liters at once. When well fed, the humps are plump and erect, but as resources decline, the humps shrink and lean to the side. When moving faster than a walking speed, they pace, by stepping forwards with both legs on the same side (as opposed to trotting, using alternate diagonals as done by most other quadrupeds).
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The Flint Covered Bridge is located in far northern Tunbridge, just south of the town line with Chelsea, carrying Bicknell Hill Road over the First Branch White River just east of Vermont Route 110. It is a single-span Queenpost truss bridge, long, set on stone abutments that have been faced in concrete. It is wide, with a roadway width of (one lane). The trusses have been strengthened by iron rods descending from the diagonals, and laminated stringers have been added below the deck, with steel cables criss-crossed between the deck members to increase lateral stability.
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'Travelers II' is done in > equally energetic strokes though rather than undulating curves the artist > has used short straight motions. Despite the use of flowing lines in > 'Travelers I', 'Travelers II', with its strong diagonals, has more of a > sense of motion. Her brushwork captures the sense of activity and the > anticipation of the passengers waiting for a train in a busy station. This > work is a bit more sophisticated than some of her other paintings; the > diagonal composition is restrained enough not to be obvious, and her use of > increasingly intense hues effectively shows projection into space.
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In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823.
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A common modification was to replace the switches with miniature snap-action switches (microswitches). Some of these, however, have the problem that their actuation is non-linear; they require considerable force to start moving compared to the force needed to complete the motion. When used in an otherwise unmodified CX40, this caused it to be more difficult to move along the diagonals, as one of the two switches being pushed would normally reach the threshold first, causing motion in that direction while the other was not yet pressed. In games that required fine control, like Jumpman, these solutions were generally unsuitable.
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The Epyx 500XJ was among a very few designs that broke from the Atari mould completely. Like the Competition Pro, the 500XJ's mechanism was based around a steel shaft pressing on microswitches and offered a similar feel. Unlike the Command Control, the 500XJ's shaft pressed directly on the switches, making it harder to press into the diagonals. More importantly, the base of the unit was completely changed, consisting of a moulded form that was designed to be easily gripped by the left hand with the index finger naturally positioned over a fire button located on the bottom right side of the case.
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In the case n = 6, the unique optimal polygon is not regular. The solution to this case was published in 1975 by Ronald Graham, answering a question posed in 1956 by Hanfried Lenz;. As cited by . it takes the form of an irregular equidiagonal pentagon with an obtuse isosceles triangle attached to one of its sides, with the distance from the apex of the triangle to the opposite pentagon vertex equal to the diagonals of the pentagon.. Its area is 0.674981.... , a number that satisfies the equation :4096 x10 +8192x9 − 3008x8 − 30848x7 + 21056x6 + 146496x5 − 221360x4 + 1232x3 + 144464x2 − 78488x + 11993 = 0\.
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In 1980, Ko Sarneel, became acting director and proposed a 5-year plan, which entailed an increase in the scope and quality of projects and manifestations for the public at large. Visual token of Sarneel's term of office are the round holes that still mark the building today. The artist John Körmeling, alumnus of Eindhoven University of Technology, transformed the building into an 'art factory' for twenty-four hours. The ribs and diagonals of this imaginary building were visualized within and through the existing one by means of laser beams that concurred high up in the sky.
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Root Rectangles to Generate diagonals for Dynamic Symmetry The application and psychology of Dynamic Symmetry in such a fast and modern medium such as photography, in particular Digital Photography, is challenging but not impossible. The Rule of Thirds has been the composition of choice for a majority of new and experienced photographers alike. Although this method is effective, Dynamic Symmetry can be applied to compositions to create a level of in depth creativity and control over the image. According to Bob Holmes, a photographer from National Geographic, a photographer must "be responsible for everything in the frame".
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Pop'n Stage is a dancing game based around the Pop'n Music design and songs, with ten "switches" (four diagonals and a center on each side, just like Pump It Up's panel placement). It is a combination of Pop'n Music and Dance Dance Revolution, using Pop'n-style graphics with DDR-style gameplay. The game has a bright, colorful interface and machine design, and is considered easy compared to most other Bemani games. The game is also keysounded, similarly to Pop'n Music, meaning that missing a step will result in corresponding sounds in the song not being played.
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A tango show in Buenos Aires Show tango, and Tango de Escenario (stage tango) is a more theatrical form of Argentine tango developed to suit the stage. In theory, all styles can be performed on stage, but the movement has to take stage elements into accounts, such as diagonals, centres, fronts, placement of lights, etc. Often, show tango routines includes embellishments, acrobatics, and solo moves that would be impractical on a social dance floor. Stage tango can be partially improvised, but in order for the general choreography to fit the set stage, some parts need to be rehearsed as a set routine.
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Chess strategy is the aspect of chess play concerned with evaluation of chess positions and setting of goals and long-term plans for future play. While evaluating a position strategically, a player must take into account such factors as the relative value of the pieces on the board, pawn structure, king safety, position of pieces, and control of key squares and groups of squares (e.g. diagonals, open files, and individual squares). Chess strategy is distinguished from chess tactics, which is the aspect of play concerned with the move-by-move setting up of threats and defenses.
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Barguzinsky Bay is bounded by the mainland on the southeast, the main landmass of Svyatoy Nos Peninsula (the "Holy Nose") on the northwest side, and the Chivyrkuisky Isthmus (that connects the two) on the northeast side. The isthmus separates it from the Chivyrkuisky Bay further to the northeast. The bay is roughly diamond-shaped, almost square, with diagonals measuring about 38 km (north- south) and 32 km (east-west). The entrance at the southwest, between the southwest tip of Svyatoy Nos (Cape Lower Head (Нижнее Изголовье) and Cape Krestovy on the mainland, is about 23 km wide.
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471–473 The diagonal of Christ's body with its hanging arms and the head of Mary Magdalene form a triangular composition. The diagonals of the main characters (Mary Magdalene, Christ and John) with their slender limbs form an X-shape in the centre of the relief along with another triangle whose top is formed by Joseph of Arimathaea's head.Opitz J, 1935/36, p. 88 The motif of the scene is derived from paintings by the Netherlandish artist Rogier van der Weyden (Descent from the Cross, 1435, Miraflores Altarpiece, 1445) and Dürer's woodcut depicting the Lamentation of Christ (1496).
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It can also be seen as a nonuniform truncated icosahedron with pyramids augmented to the pentagonal and hexagonal faces with heights adjusted until the dihedral angles are zero, and the two pyramid type side edges are equal length. This construction is expressed in the Conway polyhedron notation jtI with join operator j. Without the equal edge constraint, the wide rhombi are kites if limited only by the icosahedral symmetry. joined truncated icosahedron The sixty broad rhombic faces in the rhombic enneacontahedron are identical to those in the rhombic dodecahedron, with diagonals in a ratio of 1 to the square root of 2.
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The Warren truss consists of longitudinal members joined only by angled cross-members, forming alternately inverted Equilateral triangle-shaped spaces along its length. This gives a pure truss: each individual strut, beam, or tie is only subject to tension or compression forces, there are no bending or torsional forces on them. Loads on the diagonals alternate between compression and tension (approaching the centre), with no vertical elements, while elements near the centre must support both tension and compression in response to live loads. This configuration combines strength with economy of materials and can therefore be relatively light.
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An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in a n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal to the same number, the so-called magic constant of the cube, denoted M3(n).
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If there is one intersected side, the square becomes three triangles by adding the long diagonals connecting the intersection with opposite corners. If there are four intersected sides, we split the square in half by adding an edge between two of the four intersections, and then connect these two endpoints to the remaining two intersection points. For the other squares, we introduce a point in the middle and connect it to all four corners of the square as well as each intersection point. At the end of it all, we have a nice triangulated mesh of our point set built from a quadtree.
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Todo Argentina: Dardo Rocha Governor Rocha commissioned Benoit to plan the new city, which became the renowned urbanist's most ambitious project. Named La Plata after its mention in José Hernández's epic Martín Fierro, the city was planned by Benoit in a regular pattern of diagonals and precisely-placed squares. The La Plata Cathedral Benoit, as technical director of the urbanist project, designed most of the early public buildings in La Plata, as well. His designs for the La Plata Observatory, Economy Ministry, Police Headquarters, Engineering Department and Governors' Offices were completed shortly after the city's November 19, 1882, christening.
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It was shown by that the Schönhardt polyhedron can be generalized to other polyhedra, combinatorially equivalent to antiprisms, that cannot be triangulated. These polyhedra are formed by connecting regular k-gons in two parallel planes, twisted with respect to each other, in such a way that k of the 2k edges that connect the two k-gons have concave dihedrals. Another polyhedron that cannot be triangulated is Jessen's icosahedron, combinatorially equivalent to a regular icosahedron. In a different direction, constructed a polyhedron that shares with the Schönhardt polyhedron the property that it has no internal diagonals.
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Indian Railway network particularly High Density Network, which connects the four Metro Cities of Delhi, Kolkata, Chennai and Mumbai including the diagonals is over saturated. Challenges of higher economic growth require leap forward capacity development strategy on Indian Railways. Paradigms of such a strategy required a shift from dependence on purely budgetary sources and internal surplus of Railways to mobilization of non-budgetary financial resources from private sector, banks, financial institutions, multilateral and bilateral agencies through a mix of equity and debt. The financial resources available from the traditional sources were found to be grossly inadequate to meet the requirement.
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Although Gen Paul never received any formal training, he made a living from his art for almost 60 years. While his early works reflected the influences of his friends in Montmartre, Vlaminck, Utrillo and Frank Will, he soon developed dynamic form of expressionism reflecting influences as varied as Toulouse-Lautrec, Van Gogh, Cézanne, Goya, Velázquez and El Greco. Between 1925 and 1929, he produced many of his best works. The paintings during this phase are characterized by motion created by gestural brush strokes, daring compositions, forced perspectives, diagonals, zigzags, juxtaposed areas of abstraction and realism and flat areas of color.
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The flag is based on the flag of the Mozambican Liberation Front (FRELIMO), the leading political party in Mozambique. The FRELIMO flag, used for a brief period after the country gained its independence from Portugal, looks like the current flag but lacking the emblem, with green, black, and yellow horizontal stripes separated by white fimbriations and a red triangle in the hoist. On independence the colours were rearranged to form the national flag, in diagonals emanating from the upper hoist. Over this was a white cogwheel containing the hoe, rifle, book, and star that appear on the present flag.
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Korman's next paintings—exhibited in 2012—were geometrically divided by diagonals, horizontals and verticals, the shapes then filled with unadulterated color, forming unexpected patterns and configurations. Deadpan compositions of triangles within grids of rectangles, they exposed intrinsic qualities of hue, brightness and transparency through color juxtapositions (e.g., Quadrant, 2012; Focus, 2011); artcritical's Deven Golden described them as purely objective works with luminous, subtly fluctuating surfaces and patterns that resembled a child's geometric coloring book. In her next two exhibitions, Korman contemplated a basic problem—the division of a painting surface—finding freedom within the limitations of largely fixed, simple formats.
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The (red) side edges of tetragonal disphenoid represent a regular zig-zag skew quadrilateral A non-planar quadrilateral is called a skew quadrilateral. Formulas to compute its dihedral angles from the edge lengths and the angle between two adjacent edges were derived for work on the properties of molecules such as cyclobutane that contain a "puckered" ring of four atoms. Historically the term gauche quadrilateral was also used to mean a skew quadrilateral. A skew quadrilateral together with its diagonals form a (possibly non-regular) tetrahedron, and conversely every skew quadrilateral comes from a tetrahedron where a pair of opposite edges is removed.
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The team was shown another Lingo card filled with even numbers. Sixteen numbers were covered before the start of the round, arranged in a star shape along the diagonals, middle row and middle column; the centre space, where the free space was on a normal bingo card, was left uncovered. The hopper was loaded with 40 numbered balls (all the even numbers from 2 to 80 – this was unlike the main game in which only the numbers that actually appeared on the Lingo card were loaded into the hopper), plus one silver ball. The contestants were given £100 to start.
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Tschichold's "golden canon of page construction" here illustrated by a synthesis of Tschichold's figure thereof, with the diagonals and circle, combined with Rosarivo's construction by division of the page into ninths. These two constructions rely on the 2:3 page ratio to give a type area height equal to page width as demonstrated by the circle, and result in margin proportions 2:3:4:6 (inner:top:outer:bottom). For other page ratios, Rosarivo's method of ninths is equivalent to van de Graaf's canon, as Tschichold observed. Medieval manuscript framework according to Tschichold, in which a type area proportioned near the golden ratio is constructed.
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The number of and for first 6 terms of Moser's circle problem In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method. The greatest possible number of regions, , giving the sequence 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ... (). Though the first five terms match the geometric progression , it diverges at , showing the risk of generalising from only a few observations.
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Both Mary and Jesus are barefoot; Jesus is a fully naked uncircumcised child. All else is mainly shadow, and the figures gain monumentality in the light. If this painting was meant to honor the grandmother of Christ, it is unclear how the ungracious depiction of her wrinkled visage in this painting would have been seen as reverent or iconic. Further shock must have accrued, as stated by Bellori, at the Virgin Mary's revealing bodice. One could speculate that the parallel diagonals of Jesus’ phallus and leg suggest that both battle the snake, with one its metaphorical equal.
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A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. Diagonal lines drawn between the first two orders of embedded golden rectangles will define the intersection point of the diagonals of all the embedded golden rectangles; Clifford A. Pickover referred to this point as "the Eye of God".
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The inside of the wall shutters are marked out in battens with a typical geometric pattern, as used since Roman times. It is the same as on the upper panes of the street doors a cross, over which are diagonals. (They are seen on grillework as painted on walls depicting theatres in Rome and Pompeii, and used by Richard C Beacham in his replicas of early Roman stages at Warwick University). In the introduction of the Movie Theatre Heritage Register for New South Wales, 1896 1996 five stages of building development for cinema design are described.
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One variation stems from the Bishop Exchange opening, which is a Double Static Rook opening where both players advance their rook pawns and develop their left silvers to prevent each other from trading off their rook pawns. Here the Wrong Diagonal Bishop drop occurs immediately after the bishop trade off. The other variation – Primitive Wrong Diagonal Bishop (原始筋違い角) – has a very early bishop trade off and subsequent bishop drop. This occurs directly after the players' bishop diagonals are opened after the third move (or the fourth move if played by White).
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In front of the dog lies a perfect sphere, which has a radius equal to the apparent distance marked by the figure's compass. On the face of the building is a 4×4 magic square—the first printed in Europe—with the two middle cells of the bottom row giving the date of the engraving, 1514, which is also seen above Dürer's monogram at bottom right. The square follows the traditional rules of magic squares: each of its rows, columns, and diagonals adds to the same number, 34. It is also symmetrical, meaning that any number added to its symmetric opposite equals 17 (e.g., 15+2, 9+8).
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The simplest affine plane contains only four points; it is called the affine plane of order 2. (The order of an affine plane is the number of points on any line, see below.) Since no three are collinear, any pair of points determines a unique line, and so this plane contains six lines. It corresponds to a tetrahedron where non- intersecting edges are considered "parallel", or a square where not only opposite sides, but also diagonals are considered "parallel". More generally, a finite affine plane of order n has n2 points and lines; each line contains n points, and each point is on lines.
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Every antiparallelogram has an axis of symmetry through its crossing point. Because of this symmetry, it has two pairs of equal angles as well as two pairs of equal sides. Together with the kites and the isosceles trapezoids, antiparallelograms form one of three basic classes of quadrilaterals with a symmetry axis. The convex hull of an antiparallelogram is an isosceles trapezoid, and every antiparallelogram may be formed from the non-parallel sides (or either pair of parallel sides in case of a rectangle) and diagonals of an isosceles trapezoid.. Every antiparallelogram is a cyclic quadrilateral, meaning that its four vertices all lie on a single circle.
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Wilhelm and Baynes > 1967:320) The Yijing sub-commentary (tr. Visser 1913:57) explains, "The water of the Ho sent forth a dragon horse; on its back there was curly hair, like a map of starry dots. The water of the Lo sent forth a divine tortoise; on its back there were riven veins, like writing of character pictures." The Luoshu is a 3x3 grid of dots representing the numbers 1-9, with the sum in each of the rows, columns, and diagonals equal to 15 (which is the number of days in each of the 24 solar terms in the traditional Chinese calendar).
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However, diagonally opposite vertices are at distance 2 from each other, so the product of the diagonals is 4, bigger than the sum of products of sides. Therefore, the shortest path distances in this graph are not Ptolemaic. The graphs in which the distances obey Ptolemy's inequality are called the Ptolemaic graphs and have a restricted structure compared to arbitrary graphs; in particular, they disallow induced cycles of length greater than three, such as the one shown.. The Ptolemaic spaces include all CAT(0) spaces and in particular all Hadamard spaces. If a complete Riemannian manifold is Ptolemaic, it is necessarily a Hadamard space..
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Buttons around the tiles allow the player to flip rows, columns or diagonals, but not individual tiles. Success with this puzzle leads to the award of the Pharaoh's key which allows the astronaut to walk through walls on the third level. Medicines, zombie traps and the Pharaon's key can be used on the next level where the player must use the correct medicines in order to open clues to the puzzle in the center of the level containing the Jewel (medicine bottles believed to be correct from level 2 are on the bottom of the map). Walking into an alcove releases a zombie which must be trapped with the zombie traps.
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In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin. The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism.
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Suppose that the vertices of the polygon P are given by P_1,P_3,P_5,\ldots The image of P under the pentagram map is the polygon Q with vertices Q_2,Q_4,Q_6,\ldots as shown in the figure. Here Q_4 is the intersection of the diagonals (P_1P_5) and (P_3P_7) , and so on. test On a basic level, one can think of the pentagram map as an operation defined on convex polygons in the plane. From a more sophisticated point of view, the pentagram map is defined for a polygon contained in the projective plane over a field provided that the vertices are in sufficiently general position.
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The text-producing systems LaTeX and TeX produce DVI files from files written by the user. Those files used to be (and, to a moderate extent, still are) post-processed by a tool called dvips, which converted those DVI files into PostScript files, which are understood by many printers. Some older versions of dvips with embedded bitmapped fonts, which represented letters and symbols as pictures at a fixed resolution (for instance, at 300 dpi). When such files are printed on newer devices (some with resolution of 1200 dpi), the letters of the files that have bitmapped fonts display a remarkably low quality, with jagged lines on curves and diagonals.
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An LDU decomposition is a decomposition of the form : A = LDU, where D is a diagonal matrix, and L and U are unitriangular matrices, meaning that all the entries on the diagonals of L and U are one. Above we required that A be a square matrix, but these decompositions can all be generalized to rectangular matrices as well. In that case, L and D are square matrices both of which have the same number of rows as A, and U has exactly the same dimensions as A. Upper triangular should be interpreted as having only zero entries below the main diagonal, which starts at the upper left corner.
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The geometric and perspective scheme of the Kiss is set on a series of diagonals which follow the course of the steps and converge to the vanishing point, placed to the left of the two lovers. These lines represent the framework of the painting and brings the observer’s attention to the couple. The chromatism of the painting is inherited from the Renaissance schools of the Venetian masters where Hayez conducted his first studies. The brown of the cloak and the red of the boy's tights blend harmoniously with the light blue in the dress of the girl, while the neutral shades of the background help the couple stand out.
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For instance, the figure shows the vertices of the graph placed on a cycle, with the internal diagonals of the cycle forming a matching. By subdividing the cycle edges into two matchings, we can partition the Heawood graph into three perfect matchings (that is, 3-color its edges) in eight different ways. Every two perfect matchings, and every two Hamiltonian cycles, can be transformed into each other by a symmetry of the graph.. There are 28 six-vertex cycles in the Heawood graph. Each 6-cycle is disjoint from exactly three other 6-cycles; among these three 6-cycles, each one is the symmetric difference of the other two.
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In this first painting of the series, juxtaposed arabesques and distinctive diagonals interconnect dynamically, suggesting the bridge's complex architectonic engineering.Albert Gleizes, On Brooklyn Bridge (Sur Brooklyn Bridge), Guggenheim Museum, New York As in earlier works by Gleizes, this canvas is directly engaged with the environment. While highly abstract, Brooklyn Bridge maintains an evident visual basis. From 1914 to the end of the New York period, however nonrepresentational, works by the artist continued to be shaped by his personal experience, by the conviction that art was a social function, susceptible to theoretical formulation, and imbued with optimism.Daniel Robbins, 1964, Albert Gleizes 1881 – 1953, A Retrospective Exhibition.
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However, in the middle game, it has a more nuanced meaning of developing pieces – especially major pieces (rook and bishop) – in ways such that they become fully activated with their attacking lines cleared for offensive purposes. In a shogi opening, piece development will often result in pieces being clustered together in cramped configurations. To achieve sabaki is to change the configuration by clearing off certain obstructing pieces via piece exchanges so that attacking pieces are dominant on the board with newly obtained freedom of movement. With respect to the major pieces, this is typically done by clearing off the bishop's diagonals and the rook's ranks and files.
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As with the connection between diagonals and angle blocks, it was critical that there be no space between the I-beams and the lugs on top of the angle block because these lugs transferred axial forces to the next member. Space between the member and lug would reduce the effectiveness of this transfer and introduce shear stress to the lug. The problems with camber led to members of the chords being shortened and the lugs being shaved down, actions which introduced space between the lugs and the chord members. Construction workers used metal shims to fill the space between the lug and the chord members until a tight fit was achieved.
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The outboard panels were straight tapered to rounded wing tips, the aft spar running straight from the wing root to tip and mounting slightly tapered ailerons. The fuselage of the Grunau 8 had a deep-sided hexagonal cross section with a rounded nose and a continuous open, tandem cockpit with the rear seat under the wing, well behind its leading edge. The wing was supported over the cockpits by six struts, two inverted Vs from the upper longerons to the spars and a pair of cross-bracing diagonals. Behind the rear spar the wing root merged into the upper rear fuselage which tapered aft to a rectangular rear section.
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Conway calls it a kisrhombille for his kis vertex bisector operation applied to the rhombille tiling. More specifically it can be called a 3-6 kisrhombille, to distinguish it from other similar hyperbolic tilings, like 3-7 kisrhombille. The related rhombille tiling becomes the kisrhombille by cutting each rhombic face along its diagonals into four triangular faces It can be seen as an equilateral hexagonal tiling with each hexagon divided into 12 triangles from the center point. (Alternately it can be seen as a bisected triangular tiling divided into 6 triangles, or as an infinite arrangement of lines in six parallel families.) It is labeled V4.6.
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Annunciation, 1344 Madonna and Child, 1319 Investiture of Saint Louis of Toulouse, 1329 Maestà, 1335 Annunciation, 1344 Lorenzetti's final piece, telling the story of the Virgin Mary receiving the news from the Angel about the coming of baby Jesus, contains the first use of clear linear perspective. Though it is not perfect, and the gold background that is traditional for the time renders a flat feeling, the diagonals created on the floor do create depth. Madonna and Child, 1319 In Madonna and Child, there is a clear debt to Byzantine art. The image of the Madonna is noted for its frontality, which is a typical characteristic of Byzantine art.
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A 9-vertex graph in which every edge belongs to a unique triangle and every non-edge is the diagonal of a unique quadrilateral. The 99-graph problem asks for a 99-vertex graph with the same property. In graph theory, Conway's 99-graph problem is an unsolved problem asking whether there exists an undirected graph with 99 vertices, in which each two adjacent vertices have exactly one common neighbor, and in which each two non-adjacent vertices have exactly two common neighbors. Equivalently, every edge should be part of a unique triangle and every non-adjacent pair should be one of the two diagonals of a unique 4-cycle.
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Each work is underlaid by its own set of mathematic relationships that, once chosen intuitively, determines the elements depicted to produce a unified, harmonious whole, which is independent of any outside object (as in figurative art) or the artist's emotions (as in Abstract Expressionism). Typically, equal vertical and horizontal divisions of the canvas are cut through with intersecting diagonals, and new lines taken from intersections, to produce a system of superimposed grids or nets. On these are built the shapes, lines, curves, blocks of colour or spatial divisions that form the elements of the picture. The elements are repeated but subject to the effects of incremental changes according to logical progressions.
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Woman in a Green Hat shows a similar left lean, and verticals on her dress. The work is oppressively flat and rectangular. While it lacks pictorial depth, it is highly symmetrical, showing a near full-face and centered body view, with a number of playful deviations, including the lean of her head and torso and the thick vertical line in the background which is positioned slightly to the left.Fry, 68 As with much of Cézanne's mature work, it has many abstract forms, especially the vertical lines of her dress, which echo the diagonals of her hair and join the heavy line in the background on which her head seems to rest.
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The Howe and Pratt trusses found favor because they used far fewer members. The only maintenance a Howe truss requires is adjustment of the nuts on the vertical posts to equalize strain. The diagonals in a wooden Pratt truss proved difficult to keep in proper adjustment, so the Howe truss became the preferred design for a wooden bridge or for a "transitional" bridge of wood with iron verticals. Engineering professor Horace R. Thayer, writing in 1913, considered the Howe truss to be the best form of wooden truss bridge, and believed it to be the most commonly used truss bridge in the United States at that time.
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The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3 In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The integer n (where n is the number of integers on a side) is the order of the magic square and the constant sum is called the magic constant. If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be normal. Some authors take magic square to mean normal magic square.
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In the middle of the flag is a white disk whose diameter is equal to one-third of the length of the rectangle and whose center is located at the intersection of the diagonals of the rectangle. A red five-pointed star is located to the right of the disk, whose center is at a distance equal to one-thirtieth of the length of the flag from the center of the disk. Construction diagram of the flag according to the 1999 law. The location of the star's five points is determined by an imaginary disk centered on the star's center, its diameter equal to roughly 15% the length of the flag.
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An Amici prism is a type of roof prism which splits the image in two parts and thus allows an upright image without left-right mirroring. This means that what is seen in the eyepiece is the same as what is seen when looking at the sky, or a star chart or lunar map. The disadvantage of typical "correct image" Amici roof prism diagonals is that because the light path bounces around through a piece of glass, the total amount of light transmitted is less and the multiple reflections required can introduce optical aberrations. At higher magnifications (> 100x) brighter objects have a bright line through the object viewed.
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According to Sarrus's rule, the determinant of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals In 1881, Josiah Willard Gibbs, and independently Oliver Heaviside, introduced both the dot product and the cross product using a period () and an "x" (), respectively, to denote them.A History of Vector Analysis by Michael J. Crowe, Math. UC Davis In 1877, to emphasize the fact that the result of a dot product is a scalar while the result of a cross product is a vector, William Kingdon Clifford coined the alternative names scalar product and vector product for the two operations. These alternative names are still widely used in the literature.
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Train, Omnibus and Tram Staff Magazine, March 1933 – To that end, Beck devised a simplified map with stations, straight-line segments connecting them, and the River Thames; and lines running only vertically, horizontally, or on 45° diagonals. To make the map clearer and to emphasise connections, Beck differentiated between ordinary stations, marked with tick marks, and interchange stations, marked with diamonds. London Underground was initially sceptical of his proposal since it was an uncommissioned spare-time project and was tentatively introduced to the public in a small pamphlet in 1933. However, it immediately became popular, and the Underground has used topological maps to illustrate the network ever since.
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In the mathematical area of graph theory, the name "Husimi tree" has come to refer to two different kinds of graphs: cactus graphs (the graphs in which each edge belongs to at most one cycle) and block graphs (the graphs in which, for every cycle, all diagonals of the cycle are edges). Husimi studied cactus graphs in a 1950 paper, and the name "Husimi trees" was given to these graphs in a later paper by Frank Harary and George Eugene Uhlenbeck. Due to an error by later researchers, the name came to be applied to block graphs as well, causing it to become ambiguous and fall into disuse.See, e.g.
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The amount of advance of each line is normally less than the actual dot-size of the laser; the engraved lines overlap just slightly to create a continuity of engravure. As is true of all rasterized devices, curves and diagonals can sometimes suffer if the length or position of the raster lines varies even slightly in relation to the adjacent raster scan; therefore exact positioning and repeatability are critically important to the design of the machine. The advantage of rasterizing is the near effortless "fill" it produces. Most images to be engraved are bold letters or have large continuously engraved areas, and these are well-rasterized.
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A player may move any playing piece (including the flagship) one square diagonally to capture one of his opponent's playing pieces. (This move is similar to the capture-move of the pawn in Chess, except that captures can be made on any of the four diagonals.) This game uses displacement capture (like Chess), rather than custodial capture (like Hnefatafl), thus when a capture is made, the captured piece is removed from the board and the vacated square is occupied by the captor. Play continues until one player achieves his or her objective. If the flagship of the gold fleet reaches one of the outermost squares on the board, gold player wins.
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The position at this point is Double Wing Attack opening (where both players exchange their rook pawns off the board) with mutually open bishop diagonals (see: Double Wing Attack§Open bishop diagonal variation), which most commonly develops into a Side Pawn Capture opening after Black takes White's side pawn. However, these openings progress as usual only when White mirrors Black's defensive gold move with 4...G-32, which is the joseki move. In contrast, in the No Guard opening, White does not mirror Black's position and instead initiates a rook pawn trade before Black leaving their left gold on its starting square. 4...P-86 5.Px86 Rx86.
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In 2007, R. E. Schwartz showed that outer billiards has some unbounded orbits when defined relative to the Penrose Kite, thus answering the original Moser-Neumann question in the affirmative. The Penrose kite is the convex quadrilateral from the kites-and-darts Penrose tilings. Subsequently, Schwartz showed that outer billiards has unbounded orbits when defined relative to any irrational kite. An irrational kite is a quadrilateral with the following property: One of the diagonals of the quadrilateral divides the region into two triangles of equal area and the other diagonal divides the region into two triangles whose areas are not rational multiples of each other.
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Richinick, Jennifer, "The upside-down Pythagorean Theorem," Mathematical Gazette 92, July 2008, 313–;317. Let t and s (t > s) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then equals half the harmonic mean of and . Let a trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and CD. Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD. Then FG is the harmonic mean of AB and DC. (This is provable using similar triangles.) Crossed ladders.
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From series 11 onward, the star prize holiday was chosen by one of the contestants at random, using a similar style to the random money selector at the start of each game. When Nick Weir took over as host in 2000, the format of the super catchphrase changed considerably. Now, in a similar fashion as on Blockbusters, the contestant had to make their way from the left-hand side of the board to the right (in a horizontal line), making adjoining moves and passing on a square meant that they would be blocked and would have to find an alternative path (excluding diagonals). This format was also used in the Mark Curry series.
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The Basilica of Our Lady (Maastricht), whose enneahedral tower tops form a space-filling polyhedron. Slicing a rhombic dodecahedron in half through the long diagonals of four of its faces results in a self-dual enneahedron, the square diminished trapezohedron, with one large square face, four rhombus faces, and four isosceles triangle faces. Like the rhombic dodecahedron itself, this shape can be used to tessellate three-dimensional space.. An elongated form of this shape that still tiles space can be seen atop the rear side towers of the 12th-century Romanesque Basilica of Our Lady (Maastricht). The towers themselves, with their four pentagonal sides, four roof facets, and square base, form another space-filling enneahedron.
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The matter generated a political and financial crisis of large proportions, which were also aggravated by the outbreak of the Great War and the proximity of the first democratic elections that were to occur with the resignation of Mayor Anchorena and with the closing of the Municipal Counsel in 1915. The idea to construct the July 9 Avenue was maintained in the plan of 1925 where it was integrated into the North and South diagonals (proposed in 1919), forming at the ends two central monuments. 9 de Julio in Buenos Aires. The avenue's unusual width is because it spans an entire city block, the distance between two streets in the checkerboard pattern used in Buenos Aires.
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Diagonal, horizontal, and vertical lines in the number spiral correspond to polynomials of the form : f(n) = 4 n^2 + b n + c where b and c are integer constants. When b is even, the lines are diagonal, and either all numbers are odd, or all are even, depending on the value of c. It is therefore no surprise that all primes other than 2 lie in alternate diagonals of the Ulam spiral. Some polynomials, such as 4 n^2 + 8 n + 3, while producing only odd values, factorize over the integers (4 n^2 + 8 n + 3=(2n+1)(2n+3)) and are therefore never prime except possibly when one of the factors equals 1.
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For a cyclic polygon with an odd number of sides, all angles are equal if and only if the polygon is regular. A cyclic polygon with an even number of sides has all angles equal if and only if the alternate sides are equal (that is, sides 1, 3, 5, ... are equal, and sides 2, 4, 6, ... are equal). A cyclic pentagon with rational sides and area is known as a Robbins pentagon; in all known cases, its diagonals also have rational lengths. In any cyclic n-gon with even n, the sum of one set of alternate angles (the first, third, fifth, etc.) equals the sum of the other set of alternate angles.
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Minkowski universe In general relativity, no material body can catch up with or overtake a light pulse. No influence from an event A can reach any other location X before light sent out at A to X. In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure. This structure can be displayed using Penrose–Carter diagrams in which infinitely large regions of space and infinite time intervals are shrunk ("compactified") so as to fit onto a finite map, while light still travels along diagonals as in standard spacetime diagrams., , Aware of the importance of causal structure, Roger Penrose and others developed what is known as global geometry.
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The notation for recording moves gives the letters A-I to the horizontal lines, and the numbers 1–9 to northwest-southeast diagonals. I O O O O O H O O O O O O G + + O O O + + F + + + + + + + + E + + + + + + + + + D + + + + + + + + 9 C + + @ @ @ + + 8 B @ @ @ @ @ @ 7 A @ @ @ @ @ 6 1 2 3 4 5 One popular notation: an inline move can be denoted by the movement of the trailing marble (the "caboose"); broadside moves can be denoted by the initial positions of the two extremities of the lance followed by the final position of the first marble (with this notation, each broadside move has two notations possible, which could be avoided).
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The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are a, b, c, d, e, f, then the three main diagonals intersect in a single point if and only if .Cartensen, Jens, "About hexagons", Mathematical Spectrum 33(2) (2000–2001), 37–40. If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent.
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The post holes were bored using a rock auger and bar, with the debris removed using a long-handle implement called a "spoon". The uprights were then beaten into the ground, in pairs, five feet apart, using an iron lined yew beetle. Between each pair of upstream and downstream uprights a space of six feet was left for laying the baskets, with each pair braced with diagonals and transverse beams top and bottom. To the outside of this structure horizontal rails were then nailed, the first some from the ground, and then at regular two foot intervals above Two or three narrow gaps were left in the lower rails to allow access.
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The bridge was furnished with substantial battered abutments, composed of rough blocks of slate that were in excess of 40 meters in terms of length. The piers of the bridge comprised either four or five timber piles, each roughly 350mm across, which were connected by crosshead timbers and braced with diagonals. Iron was used for the bolts and bracing bars used to fix elements in place. These created a series of frames on which longitudinal beams carried both the road and railway; those beams that were underneath the tracks were substantially larger than those under the roadway due to the greater weight of trains in comparison to road vehicles during that time.
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The tied- up curtain in the foreground creates the impression that the viewer is looking at an intensely private, personal scene. There is also an element of trompe l'oeil as Dutch paintings were often hung with little curtains to conserve them, and the device of painted curtains is seen in other Dutch works of the period. The diagonals on the chequered floor create the impression of depth and three-dimensionality. The fact that it is a love letter that the woman has received is made clear by the fact that she is carryinga cittern, a form of lute used in the period as a symbol of love - often carnal love; luit was also a slang term for vagina.
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The kites are the quadrilaterals that have an axis of symmetry along one of their diagonals.. Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite (if the axis of symmetry is a diagonal) or an isosceles trapezoid (if the axis of symmetry passes through the midpoints of two sides); these include as special cases the rhombus and the rectangle respectively, which have two axes of symmetry each, and the square which is both a kite and an isosceles trapezoid and has four axes of symmetry. If crossings are allowed, the list of quadrilaterals with axes of symmetry must be expanded to also include the antiparallelograms.
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They interact and interpenetrate to allow the viewer to make new, multiple connections and see new patterns. As in a half-tone photograph, the image appears to be more meaningful than the elements that make it up. This effect, says the critic Gloria Carnevali, can be seen as forming "a new third dimension, one that exists between the painting and the observer", even a "new pictorial space". The use in Steele's work of elements in balanced opposition, and the tilted axes arising from the diagonals, produce symmetrical wholes that are not static but dynamic, complex and full of apparent movement, especially rotational, the eye eventually returning to its starting point before beginning a new journey around the picture.
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Two cases are possible for each rook: either it stands in the centre or it doesn't stand in the centre. In the second case, this rook is included in the rook quartet that exchanges squares on turning the board at 90°. Therefore, the total number of rooks must be either 4n (when there is no central square on the board) or 4n + 1\. This proves that R4n + 2 = R4n + 3 = 0. The number of arrangements of n non-attacking rooks symmetric to one of the diagonals (for determinacy, the diagonal corresponding to a1–h8 on the chessboard) on a n × n board is given by the telephone numbers defined by the recurrence Qn = Qn − 1 \+ (n − 1)Qn − 2.
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Murphy's design removed the need for riveted connections and allowed for easier and more widespread construction of truss bridges. In 1863, Murphy designed the first pin- connected truss bridge with both wrought iron tension and compression components and cast iron joint blocks and pedestals. Murphy's truss design consisted of double-intersection counter-diagonals, and along with the eyebar and pin connections, permitted longer iron bridge spans. alt=A black and white engraved portrait of an elderly man with a long beard and sporting a suit The technological design advances made by Whipple and Murphy, in addition to further advances in steel and iron fabrication, made wrought iron truss bridges a major industry in the United States.
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The computer, as the dealer, issues a card to each of the players and itself. Before the first card is dealt, and after each subsequent hand, until five cards have been dealt, each player must either make a bet or fold. If the left difficulty switch is set to "A", the dealer's first card is dealt face down; otherwise, it is dealt face up; likewise for the right difficulty switch for each player. Poker solitaire is different in that no bets are made and there is no dealer; rather, the goal is to arrange cards to create the best twelve poker hands in 25 cards, with five rows, five columns, and the two diagonals.
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A diagram of the parts of a king post truss A king post truss bridge The king post truss is used for simple roof trusses and short-span bridges. It is the simplest form of truss in that it is constructed of the fewest truss members (individual lengths of wood or metal). The truss consists of two diagonal members that meet at the apex of the truss, one horizontal beam that serves to tie the bottom end of the diagonals together, and the king post which connects the apex to the horizontal beam below. For a roof truss, the diagonal members are called rafters, and the horizontal member may serve as a ceiling joist.
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Imagine throwing a dart at a unit square (a square with an area of 1) so that the dart always hits an exact point in the square, in such a way that each point in the square is equally likely to be hit. Since the square has area 1, the probability that the dart will hit any particular subregion of the square is equal to the area of that subregion. For example, the probability that the dart will hit the right half of the square is 0.5, since the right half has area 0.5. Next, consider the event that the dart hits exactly a point in the diagonals of the unit square.
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As stated earlier, Mexicans play on a variant of Catch the Hare with only two main diagonals which is called coyote, and it is described by Stewart Culin. A variant of that Mexican game is found in El Paso, Texas, called el coyote by Ediciones Bob, S.A. [n.d.]. In this variant, the board uses a standard Alquerque board, but it is elongated on one side by two ranks (the standard Alquerque board is not elongated by one rank on each side, but specifically elongated by two ranks on one side to maintain a specific pattern). Instead of the standard 5 × 5 Alquerque board, it is a 5 × 7 board with 35 intersection points.
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In March 1873, Governor Mariano Acosta approved the projected sketch map for this town and named it Almirante Brown. The plan for the map was designed by Nicolás and José Canale, two renowned Italian architects, who included a number of diagonals and squares, which later inspired the urban design for the city of La Plata. The Canales also designed most of the public buildings in Adrogué (the Town Palace, the first church for Saint Gabriel, Castelforte, etc.) and the church of the Inmaculada Concepción in the neighbourhood of Belgrano ("La Redonda"). Adrogué was also the place of residence of some well-known families of British origin, including the high officials of the railroads.
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A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry. The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals.. A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem.
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Like early video game joysticks, the vast majority of D-pads are digital; in other words, only the directions provided on the D-pad buttons can be used, with no intermediate values. However, combinations of two directions (up and left, for example) do provide diagonals and many modern D-pads can be used to provide eight- directional input if appropriate. Although digital pads offer less flexibility than analog sticks, they can easily be manipulated (requiring little movement of the thumb) with very high accuracy. They are also far less demanding in maintenance and do not protrude very far from the controller, making them ideal for portable consoles such as the Game Boy, Nintendo DS and the PlayStation Portable.
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The wing shape in Bonelli's eagles can at times appear similar to that of honey buzzard but the latter raptor type are usually distinctly slimmer and slighter bodied with a much smaller, slimmer head. In flight, honey buzzards often have notched rather than square ended tails, less emarginated primaries and typically they fly with their wings held more at an angle. The sympatric species of honey buzzard tend to have bolder barring on the tail and underwings, broader dark trailing wing edges and all have no pale mantle patch or darker underwing-diagonals. An unlikely source of confusion is the northern goshawk (Accipiter gentilis), which is usually visibly smaller with much shorter wings, a slightly longer tail, different level flight style and many distinctive plumage characteristics.
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An unlicensed derivative of a Bail knotwork appears on the original cover of King Crimson's Discipline album; in later releases, it was replaced by a knotwork designed by Steve Ball, A Bain design was used to illustrate a rug by Quayle and Tranter, a carpet manufacturer based in Kidderminster, England. His son Iain Bain, an engineer, later wrote two books - "Celtic Knotwork" and "Celtic Key Patterns" that were intended to simplify the creation of knotwork and keypattern designs by using grid lines and diagonals rather than the mathematical formulae applied by his father.Susan E. Seright, "George Bain, Master of Celtic Art", 1999, page 23. The majority of Bain's surviving artworks are curated by the Groam House Museum in Rosemarkie, Scotland.
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Some pale adults have pale bases to all the underprimaries and the quills are sometimes unbarred, but more usually the feathers have dense but narrow dark bars. Dark morph juveniles are light rufous to pale tawny body above which contrasts strongly with dark brown greater coverts, rear scapulars, flight feathers and tail, in turn all highlighting the creamy lower back to tail coverts. Below dark morph juveniles can look similar to pale morph adults apart from trailing whitish edges and often irregular pale diagonals along tips of greater wing coverts, though usually these fade early on. Little is known plumage development but the young eagles moult into brown, becoming patchy with intermediate often showing 1-3 darker bars on wing linings.
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A -map graph is a map graph derived from a set of regions in which at most regions meet at any point. Equivalently, it is the half-square of a planar bipartite graph in which the vertex set (the side of the bipartition not used to induce the half-square) has maximum degree . A 3-map graph is a planar graph, and every planar graph can be represented as a 3-map graph. Every 4-map graph is a 1-planar graph, a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map graph.
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181.. One clear influence on its composition is Paolo Veronese's Mystic Marriage of Saint Catherine, from which it borrows its diagonals, the position of the Madonna and saints and the red drape hanging from columns Donald Posner, Annibale Carracci: A Study in the reform of Italian Painting around 1590, op. cit., Vol. I, pp. 44-45.. Carracci did not entirely reject his previous style, however, and so these lessons from Veronese are translated into a less otherwordly idiom, closer to the viewer's lived experience - Carracci opts for a glimpse of a landscape background rather than the celestial blue of so many of Veronese's works and the saints humbly clothed and standing on bare earth rather than the richly-dressed figures on stairs in Veronese's work.
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Influenced by various strains of Modernism including Post-Impressionism and Cubism, Blackshear developed a range of styles with bold, simplified forms and rhythmic or patterned elements often featuring strong diagonals and tilted planes. Her paintings are reminiscent of Regionalists such as Thomas Hart Benton and modernists like Fernand Léger, while her whimsical abstract drawings evoke Paul Klee. During the height of her career, between 1924 and 1940, African Americans were the central subjects of her work, and she became known for depicting them with warmth and clarity but without sentimentality. In 1939, critic C. J. Bulliet called her “Chicago’s most sympathetic, most understanding painter of the American Negro.” Blackshear also made two dioramas for the 1933 Century of Progress Exposition in Chicago.
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Eleven subdivisions of a pentagon In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin :1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... . They are also called the super-Catalan numbers, the little Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and the ancient Greek mathematician Hipparchus who appears from evidence in Plutarch to have known of these numbers.
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Texture decalling can be applied as Texture_splatting by projecting the position of the current fragment in the direction of the decal' normal, to the plane of the texture given by an origin point and normal, then using a 'up' or 'right' directional vector to compute the texture coordinate. This technique would be more closely compared with dual contouring which is listed under Isosurface, as a potential technique. DCL tetrahedra involves additional calculations for the diagonals across cube-faces, where dual contouring does not. This technique also has not addressed when two near points 'inside' a surface are a combined distance < 1 from the surface, where they should generate two points on the edge instead of 1; the related modification is Manifold Dual Contouring .
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If in a particular candidate solution a particular secondary column is satisfied, then the added row isn't needed. But if the secondary column isn't satisfied, as is allowed in the generalized problem but not the standard problem, then the added row can be selected to ensure the column is satisfied. But Knuth goes on to explain that it is better working with the generalized problem directly, because the generalized algorithm is simpler and faster: A simple change to his Algorithm X allows secondary columns to be handled directly. The N queens problem is an example of a generalized exact cover problem, as the constraints corresponding to the diagonals of the chessboard have a maximum rather than an exact queen count.
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A Warren truss The Warren truss was patented in 1848 by James Warren and Willoughby Theobald Monzani, and consists of longitudinal members joined only by angled cross-members, forming alternately inverted equilateral triangle-shaped spaces along its length, ensuring that no individual strut, beam, or tie is subject to bending or torsional straining forces, but only to tension or compression. Loads on the diagonals alternate between compression and tension (approaching the center), with no vertical elements, while elements near the center must support both tension and compression in response to live loads. This configuration combines strength with economy of materials and can therefore be relatively light. The girders being of equal length, it is ideal for use in prefabricated modular bridges.
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As a quilting pattern it also has many other names including cubework, heavenly stairs, and Pandora's box. It has been suggested that the tumbling blocks quilt pattern was used as a signal in the Underground Railroad: when slaves saw it hung on a fence, they were to box up their belongings and escape. See Quilts of the Underground Railroad.. In these decorative applications, the rhombi may appear in multiple colors, but are typically given three levels of shading, brightest for the rhombs with horizontal long diagonals and darker for the rhombs with the other two orientations, to enhance their appearance of three-dimensionality. There is a single known instance of implicit rhombille and trihexagonal tiling in English heraldry – in the Geal/e arms.
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The ascending progression of heads from right to left and the parallel diagonal of the edge of the umbrella are the most pronounced diagonals that give the scene motion. Another of her paintings, Woman in Bathing Suit (1930), is a painting of a female figure in a landscape. It is the basis in the 1920s and 30s of the Boston School varying their compositions of American Impressionism by modernizing them in regards to design and attitude. Van Ness retained the outdoor, sunlit figure with a bright palette that was found in American Impressionism, with her friend and teacher Frank Benson for example, while decreasing descriptive detail, representational volume and the emotional engagement of the viewer in order to experiment more with design and color.
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The board illustrated here, as also by Netz, is one proposed by Heinrich Suter in translating an unpointed Arabic text in which twice and equals are easily confused; Suter makes at least a typographical error at the crucial point, equating the lengths of a side and diagonal, in which case the board cannot be a rectangle. But, as the diagonals of a square intersect at right angles, the presence of right triangles makes the first proposition of Archimedes' Stomachion immediate. Rather, the first proposition sets up a board consisting of two squares side by side (as in Tangram). A reconciliation of the Suter board with this Codex board was published by Richard Dixon Oldham, FRS, in Nature in March, 1926, sparking a Stomachion craze that year.
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The composition X\gets R\to Y\gets S\to Z is found by first pulling back the cospan R\to Y\gets S and then taking the jointly-monic image of the resulting span X\gets R\gets\bullet\to S\to Z. Composition of relations will be associative if the factorization system is appropriately stable. In this case, one can consider a category , with the same objects as , but where morphisms are relations between the objects. The identity relations are the diagonals X \to X\times X. A regular category (a category with finite limits and images in which covers are stable under pullback) has a stable regular epi/mono factorization system. The category of relations for a regular category is always an allegory.
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Soldevilla's education in Paris and the bonds she formed between her teachers, students and fellow contemporaries led to her producing her most important body of work in the years between 1950-1957. Her collage work from this period is a study of the geometries of circles, rectangles, lines and colors, creating a rhythm with their variation of size and shape. Diagonals, opposing elements, contrasting colors and organic geometric style set Loló apart from her fellow contemporaries, as did her asymmetric metal kinetic sculptures.McEwen, Abigail The main philosophy of concrete art is that it is an extremely introverted art form, it has no narrative, no basis or reference in the natural world and has no defining qualities except the simple admiration of its colors and shapes.
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In the absence of alpha-helices, the main diagonal almost disappears and the cross-diagonals representing the beta-sheets dominate the plot. Relatively low number of tertiary hydrogen bonds can be found in the plot, with three high-density regions, one of which is connected to a loop at the residues around 63, a second is connected to the loop around 87, and a third region which is connected to the regions 26 and 35. The fifth loop around 111 is represented only one tertiary hydrogen bond in the HB plot. In the three-dimensional structure, tertiary hydrogen bonds are formed (1) near to the entrance, directly involved in conformational rearrangement during ligand binding; and (2) at the bottom of the "barrel".
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The report continues on to detail some of the internal decoration: > "The chancel has a neatly framed roof with quarter diagonals decorated with > rosettes in alternating spaces ... The lower windows in the sides, with the > western ad wheel windows are of the new diamond glass - one whole sheet each > with false diamonds and with the stained glass windows of the chancel were > imported expressly for the church. The upper windows in lead frames were > made in Maryborough. By night the church is lit by means of rose lights > containing 12 jets one of which stands in every arch." The church was constructed by local contractors: Mr Caldwell who was responsible for the masonry work and Mr Taylor, responsible for carpentering.
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In the far distance is a landscape with small treed islands, suggesting flooding, and a sea. The rightmost portion of the background may show a large wave crashing over land. Panofsky believes that it is night, citing the "cast-shadow" of the hourglass on the building, with the moon lighting the scene and creating a lunar rainbow. A 4×4 magic square has columns, rows, and diagonals that sum to 34. In this configuration, many other sets of four squares also sum to 34. Dürer includes the year in the two bottom squares, and the squares adding to 5 and 17 may refer to his mother's death in May of that year. (First number of second row is "5" and third row "9"). The print contains numerous references to mathematics and geometry.
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During the reign of Emperor Trajan, domes and semi-domes over exedras were standard elements of Roman architecture, possibly due to the efforts of Trajan's architect, Apollodorus of Damascus, who was famed for his engineering ability. Two rotundas in diameter were finished in 109 AD as part of the Baths of Trajan, built over the Domus Aurea, and exedras wide were built as part of the markets north-east of his forum. The architecture of Trajan's successor, Hadrian, continued this style. Three wide exedras at Trajan's Baths have patterns of coffering that, as in the later Pantheon, align with lower niches only on the axes and diagonals and, also as in the Pantheon, that alignment is sometimes with the ribs between the coffers, rather than with the coffers themselves.
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In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is a square tiling with each square divided into four isosceles right triangles from the center point, forming an infinite arrangement of lines. It can also be formed by subdividing each square of a grid into two triangles by a diagonal, with the diagonals alternating in direction, or by overlaying two square grids, one rotated by 45 degrees from the other and scaled by a factor of √2. Conway calls it a kisquadrille,John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table) represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille).
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Caravaggio's patron Vincenzo Giustiniani was an intellectual as well as a collector, and late in life he wrote a paper about art in which he identified twelve grades of accomplishment. In the highest class he named just two artists, Caravaggio and Annibale Carracci, as those capable of combining realism and style in the most accomplished manner. This Crowning with Thorns illustrates what Giustiniani meant: the cruelty of the two torturers hammering home the thorns is depicted as acutely observed reality, as is the bored slouch of the official leaning on the rail as he oversees the death of God; meanwhile Christ is suffering real pain with patient endurance; all depicted within a classical composition of contrasting and intersecting horizontals and diagonals. The theme of pain and sadism is central to the work.
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Samuel Boden Boden's Mate is a checkmating pattern in chess characterized by bishops on two criss-crossing diagonals (for example, bishops on a6 and f4 delivering mate to a king on c8), with possible flight squares for the king being occupied by friendly pieces. Most often the checkmated king has castled queenside, and is mated on c8 or c1. Many variants on the mate are seen, for example a king on e8 checkmated by bishops on g6 and a3, and a king on f1 checkmated by bishops on h3 and b6. Often the mate is immediately preceded by a sacrifice that opens up the diagonal on which the bishop delivers checkmate, and the mate is often a pure mate (as is the case for all but one of the examples given here).
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On the Pink Line, what was once the Blue Line's Douglas branch begins at 54th Avenue and Cermak Road in Cicero (5400 W. - 2200 S.). The line runs on at- grade tracks parallel to Cermak Road from the terminal to about a quarter-mile (400 m) east of Cicero Avenue, then diagonals northeast until it reaches a corridor parallel and adjacent to 21st Street at Kostner Avenue. It then continues east between 21st Street and Cullerton Street, climbing up from at- grade tracks to elevated tracks, through the North Lawndale, Little Village and Pilsen neighborhoods of Chicago, with stops at Kostner, Pulaski, Central Park, Kedzie, California, Western and Damen. The line turns north near Paulina Street stopping at 18th and Polk stations, then crosses over the Eisenhower Expressway (Interstate 290).
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All columns are placed on the exterior wall of the building and function as the flanges of the beam, while the trusses which span the total transverse width between columns function as the web of the cantilever beam. While earlier staggered truss systems utilized channels for web diagonals and verticals, today most of the trusses are designed with hollow structural sections (HSS) for vertical and diagonal members because they are more structurally efficient and easier to fabricate. The trusses are fabricated with camber to compensate for dead load and are transported to the site, stored and then erected—generally in one piece. Fabrication of this type of structure requires certified welders and overhead cranes capable of lifting 10 to 15-ton trusses and columns for projects up to 20 stories.
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Following the exhibitions of his works in the 1950s, the painter encountered a very negative attitude on the part of official critics, and this lack of recognition followed him constantly, nourished by the contemporary political atmosphere. His withdrawal to the sidelines did not mean isolation - he was visited by friends and he could fully concentrate on his work. He painted the cycles Bird Actors and Monuments, dynamic compositions of diagonals and curves, a galore of shapes, paraphrasing the political atmosphere and the false pathos of the time. Having made the cycles Space Jumble, Downfalls and Wrecks, in which colour still plays a significant role, Matal‘s work closed in the 1980s with the cycle Narrowing Space, translating the feelings of inner resignation, hopelessness, manifested in a loss of colour.
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In the next course up, a header is offset one and a half stretcher lengths to the left of the header in the course below, and then in the third course, a header is offset one stretcher length to the right of the header in the middle course. This accented swing of headers, one and a half to the left, and one to the right, generates the appearance of lines of stretchers running from the upper left hand side of the wall down to the lower right. Such an example of a raking monk bond layout is shown in the New Malden Library, Kingston upon Thames, Greater London. Elsewhere, raking courses in monk bond may be staggered in such a way as to generate a subtle appearance of indented pyramid-like diagonals.
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The old Economy Ministry buildingAerial view of La Plata's diagonals and plazas, as planned by Benoit Ongoing resentment over the apportionment of rapidly growing customs duties from the main port led to a failed insurrection in the Province of Buenos Aires against the newly elected administration of President Julio Roca in 1880. The province's voters, however, elected a candidate in 1881 who, despite his disadvantage in belonging to Roca's PAN, articulated a message of political integration with the suddenly prosperous Argentina: Dardo Rocha. Facing ongoing secessionist pressures from his constituency, Governor Rocha proposed the creation of a new provincial capital in replacement of the city of Buenos Aires, which was federalized as the nation's capital in 1880. The proposal, useful to the mollification of the province's Independence-leaning gentry, was quickly approved by Congress.
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In contrast to the dark side chapels, the high altar niche is well lit from a hidden source and becomes the main visual focus of the lower part of the interior. As a result, the congregation effectively become ‘witnesses’ to the theatrical narrative of St Andrew which begins in the High Altar chapel and culminates in the dome. Over the High Altar is an oil painting of the Martyrdom of Saint Andrew (1668) by French painter Guillaume Courtois, a depiction which shows Andrew tied to the diagonals of the form of the cross on which he was crucified. Andrew appears for a second time as if he were breaking through the curved pediment of the edicule frame to the high altar; this time he is represented by a white marble sculpture carved by Antonio Raggi.
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A body frame comprising welded steel tube longitudinals, uprights and diagonals to the waistrail: with heavy duty stress-panels and aluminium upper frame sections riveted thereupon was constructed to a joint design by either Weymann or Metro-Cammell in England or by the MCW group's South African subsidiary Bus Bodies (South Africa) in Port Elizabeth; this was permanently attached to a Leyland under-frame, not drivable unless bodied. To this under-frame, Leyland attached all running units comprising radiator, engine, axles, suspension, steering, gearbox, brakes, controls etc. Once under-frame and body were permanently married up, the frame would be clad in aircraft-grade aluminium and finished.Lamb 2007 The original idea was to offer a bus to one of three specifications: home market, right-hand drive export or left-hand drive export.
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Mexicans play on one version with only two main diagonals, and this is described by Stewart Culin in his book Chess and Playing Cards: Catalogue of Games and Implements for Divination Exhibited by the United States National Museum in Connection with the Department of Archaeology and Paleontology of the University of Pennsylvania at the Cotton States and International Exposition (1895), and calls it coyote, a game from Mexico, with only the main diagonal lines present. In some cases the diagonal lines were completely removed making it difficult to classify with the other tiger games such as Bagh-Chal, Rimau- rimau, and Buga-shadara. But other hunt games such as Sua Ghin Gnua and Tiger and Buffaloes also do not have diagonal lines but may still be classified as tiger games.
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A direct method using degrees follows: # Draw a circle and choose a point to be the pentagon's (e.g. top center) # Choose a point A on the circle that will serve as one vertex of the pentagon. Draw a line through O and A. # Draw a guideline through it and the circle's center # Draw lines at 54° (from the guideline) intersecting the pentagon's point # Where those intersect the circle, draw lines at 18° (from parallels to the guideline) # Join where they intersect the circle After forming a regular convex pentagon, if one joins the non-adjacent corners (drawing the diagonals of the pentagon), one obtains a pentagram, with a smaller regular pentagon in the center. Or if one extends the sides until the non-adjacent sides meet, one obtains a larger pentagram.
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The original plan from 1850 shows the north-west corner of the 'town reserves' (surrounded by the Avon River, Fitzgerald and Bealey Avenues and Barbadoes Street, with an additional small rectangular area to the west of Barbadoes Street) as the cemetery for the settlement. Individual town sections were shown on the survey plan, the Black Map, and numbered by the surveyors in a logical order, in contrast to the rural sections surrounding Christchurch, which were numbered at the time of and in the order of their purchase. The following streets were those laid out in the 1850 survey (listed east to west, then north to south, then diagonals). Where a street name is one of the original names as devised by surveyors Joseph Thomas and Edward Jollie, this is marked as such.
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On the branches of the cross are gilded letters Church Slavonic letters at the top: - "faithful" to the left - "KNZ" on the right - "DANIIL" at the bottom - "ISKCON" ("Pious Prince Daniel of Moscow") along the diagonals of the cross, adjacent to oval with a picture, are four crowns, each of which is decorated with rhinestones and ends with four-armed cross. At the top of the sign of the heraldic trefoil. The statute of the Order was amended by the Patriarch and Holy Synod on 14 April 2006: > With this award the Order of the I level, the Heads of Churches and the > Heads of State, awarded Merit, the Order of, a silk moire ribbon and orange > suspension order on the tape. ;2nd class The badge is similar to that of the 1st class, but it is made of silvered nickel silver.
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And so two men, lacking halos, use a piece of linen to carry the dead Christ and it seems as if all the participants in the bearing of the body are in suspended animation.Capellan 215 The two men and Christ form very strong diagonals in the shape of a V. The younger man on the right holding Christ is posited to be a representation of the slain youth, Grifonetto himself.Baldini 106 Besides the two men carrying the body, we have St. John and Nicodemus behind and to the left and Mary Magdalene holding the hand of Christ. The legs of St. John and Nicodemus do present a distracting problem, especially in the case of Nicodemus because due to the obstruction of the view, it is not clear what he is exactly doing, or what he is exactly looking at.
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The Reye configuration can be realized in three-dimensional projective space by taking the lines to be the 12 edges and four long diagonals of a cube, and the points as the eight vertices of the cube, its center, and the three points where groups of four parallel cube edges meet the plane at infinity. Two regular tetrahedra may be inscribed within a cube, forming a stella octangula; these two tetrahedra are perspective figures to each other in four different ways, and the other four points of the configuration are their centers of perspectivity. These two tetrahedra together with the tetrahedron of the remaining 4 points form a desmic system of three tetrahedra. Any two disjoint spheres in three dimensional space, with different radii, have two bitangent double cones, the apexes of which are called the centers of similitude.
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Cutty Sark during repairs after the fire The design for the renovation project by Grimshaw architects with, during design development stage, newly established Youmeheshe architects and Buro Happold engineers involved raising the ship out of her dry berth using a Kevlar web, allowing visitors to pass under the hull to view it. Unfortunately it was discovered that the proposed web would not follow the reverse curves of the ship's hull which would effectively mask the hull's shape from view. An alternate design for the support of the ship had to be developed; this involved installing a deep steel belt around the hull tied by diagonal steel members passing through the hold to a new steel-reinforced keel. Horizontal tubular steel struts passing through the hold brace the diagonals apart while many of the corroded original hull frames have been doubled.
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Besides London, he visited laboratories in Paris, Zurich, Munich, Vienna and Berlin, and then went to the United States in order to get acquainted with the biggest bridge structures and local mechanical laboratories. Proskouriakov was the first in Europe to reject then existing lattice bridge trusses with many vertical and diagonal members, which were extremely difficult for truss analysis. Instead, he designed a statically determinate triangular web truss with the minimum number of diagonals, which provided better distribution of stresses due to moving loads throughout a bridge structure. 230 px 230 px The research and practical activities of Lavr Proskouriakov were aimed at the elaboration of a perfect bridge structure, and he managed to achieve his goal: this was the noble long railway bridge across the Yenisei near Krasnoyarsk that was built between 1896 and 1899.
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Occasionally the division is instead along both diagonals (party per saltier) again creating four parts but now at top, bottom, left, and right. An example of party per cross is the Sovereign Arms of the United Kingdom, as used outside Scotland, which consists of four quarters, displaying the Arms of England, Scotland and Ireland, with the coat for England repeated at the end. (In the royal arms as used in Scotland, the Scottish coat appears in the first and fourth quarters and the English one second.). An example of party per saltier is the arms of the medieval Kingdom of Sicily which also consists of four sections, with top and bottom displaying the coat of the Crown of Aragon, and left and right the coat of the Sicily branch of the Hohenstaufen dynasty during their reign as Holy Roman Emperors.
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In the upper group, Saint Roch is in prison praying for relief for those suffering from the plague. Then light bursts into the prison, a divine messenger appears accompanied by Christ himself; with his left hand Christ gestures towards the afflicted while with his right, he points to the golden inscription "Eris in peste patronus" (Thou shalt be the patron in the plague). Meanwhile, the lower group has become aware of the miracle taking place above, and are hopeful of recovery; even the shrouded figure on the right is hopeful of being raised from the dead. In this picture, Rubens uses the "diagonals" technique often used by baroque painters, as a means to link the upper group of figures, who gesture and lean downwards, with the supplicants below, whose outstretched arms and gaze draw the eyes diagonally back upwards to the higher group.
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The tetrakis square tiling : The tetrakis square tiling is the tiling of the Euclidean plane dual to the truncated square tiling. It can be constructed square tiling with each square divided into four isosceles right triangles from the center point, forming an infinite arrangement of lines. It can also be formed by subdividing each square of a grid into two triangles by a diagonal, with the diagonals alternating in direction, or by overlaying two square grids, one rotated by 45 degrees from the other and scaled by a factor of . Conway calls it a kisquadrille,John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table) represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille).
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To construct a self-similarity matrix, one first transforms a data series into an ordered sequence of feature vectors V = (v_1, v_2, \ldots, v_n) , where each vector v_i describes the relevant features of a data series in a given local interval. Then the self-similarity matrix is formed by computing the similarity of pairs of feature vectors : S(j,k) = s(v_j, v_k) \quad j,k \in (1,\ldots,n) where s(v_j, v_k) is a function measuring the similarity of the two vectors, for instance, the inner product s(v_j, v_k) = v_j \cdot v_k. Then similar segments of feature vectors will show up as path of high similarity along diagonals of the matrix. Similarity plots are used for action recognition that is invariant to point of view and for audio segmentation using spectral clustering of the self- similarity matrix.
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And as Julia M. Busch points out, even the sculptures avoid reference to anything recognizably, bodily human. Stating that Frank's sculptures are "environmental", Busch goes on to define this term in a way that points to their "beyond-human" quality: "Environmental sculpture is never made to work at exactly human scale, but is sufficiently larger or smaller than scale to avoid confusion with the human image in the eyes of the viewer." Busch, Julia M., "A Decade of Sculpture: the New Media in the 1960s", page 27 Also, the canvases of the 1960s, for all their landscape-like qualities, usually avoid anything that can be read as a horizon or a sky: we literally don't know which way is up; for as Stanton (p. 12) points out, Jane Frank - starting with "Winter's End" (1958) - avoids horizontal orientation in favor of strong diagonals.
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The plan of the house is a windmill style, as seen with the four wings extending from the fireplace in the central core and the movement from each wing being along a diagonal line. Wing two contains the great living room with high windows and a walled terrace. The dining room, extended by a large porch, comprises the third wing; the fourth, towards the rear of the house, contains the kitchen and servants' quarters. Wright incorporates diagonals into several other places in his design – the dining room has a prow-shaped end bay and another prow-shaped projection, the reception room has a similar prow-shaped bay, the art glass light over the entry stairway is rotated 45 degrees, again emphasizing the diagonal, and the terminating piers of the porte cochere are offset from the end wall by 45 degrees.
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Women have been discouraged from becoming traditional artists but have expressed their creativity through textiles, an art form both beautiful and useful. For women in the 19th century a quilt could be like a diary. Much of what women packed for their journey to California consisted of their own handiwork: treasured quilts, best dresses, baby gowns, and other needlecraft. The meticulous stitches and the fabrics used give visitors a glimpse into the long-ago lives of California women. A few of the treasures that were displayed included: a baby coverlet made by Tamsen Donner (who perished in 1847 en route to CA with the Donner Party); a catalog of stitches – a sampler of diverse skills; a “best” quilt, Blazing Star variation, includes subtle stitched patterns of diagonals, wreaths, and feathers in the off blocks; quilted petticoats and much more.
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In the mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that this number can be computed in polynomial time as the determinant of the Laplacian matrix of the graph. It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph. Kirchhoff's theorem relies on the notion of the Laplacian matrix of a graph that is equal to the difference between the graph's degree matrix (a diagonal matrix with vertex degrees on the diagonals) and its adjacency matrix (a (0,1)-matrix with 1's at places corresponding to entries where the vertices are adjacent and 0's otherwise). For a given connected graph G with n labeled vertices, let λ1, λ2, ..., λn−1 be the non- zero eigenvalues of its Laplacian matrix.
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The flag of South Africa was designed in March 1994 and adopted on 27 April 1994, at the beginning of South Africa's 1994 general election, to replace the flag that had been used since 1928. The new national flag, designed by the then State Herald of South Africa Frederick Brownell, was chosen to represent the country's new democracy after the end of apartheid. The flag has horizontal bands of red (on the top) and blue (on the bottom), of equal width, separated by a central green band which splits into a horizontal "Y" shape, the arms of which end at the corners of the hoist side (and follow the flag's diagonals). The "Y" embraces a black isosceles triangle from which the arms are separated by narrow yellow or gold bands; the red and blue bands are separated from the green band and its arms by narrow white stripes.
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The Magic Square was used to designate spaces of political and religious importance. The Lo Shu square on the back of a small turtle (in the center), surrounded by the signs of the Chinese zodiac and the Eight trigrams, all carried by a large turtle (which, presumably, stands for the Dragon horse that had earlier revealed the trigrams to Fu Xi). This example drawn by an anonymous Tibetan artist. The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year).
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By the 1960s he had begun to paint large non-objective canvases in thickly applied diagonals of bold color and black. Brilliantly colored areas that appeared to be broken up at close range would fit together at a distance, producing what Wedin called a "hidden abstract" composition. Wedin's works are represented in many major private and institutional collections, including the Walker Art Center in Minneapolis, the American Swedish Institute in Minneapolis, the Mayo Clinic in Rochester, MN and the Smithsonian Institution in Washington, D.C. In 1996 Wedin was one of 33 artists whose work was featured in the exhibition "Pictures for a New Home: Minnesota’s Swedish-American Artists," at the James J. Hill House Gallery in St. Paul, sponsored by the Minnesota Historical Society. In 2008, Elof Wedin was one of the artists featured in the Weisman Art Museum's "By the People, for the People" exhibit of Works Progress Administration paintings.
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Mathematically, the points of the diamond cubic structure can be given coordinates as a subset of a three- dimensional integer lattice by using a cubic unit cell four units across. With these coordinates, the points of the structure have coordinates (x, y, z) satisfying the equations :x = y = z (mod 2), and :x + y + z = 0 or 1 (mod 4).. There are eight points (modulo 4) that satisfy these conditions: :(0,0,0), (0,2,2), (2,0,2), (2,2,0), :(3,3,3), (3,1,1), (1,3,1), (1,1,3) All of the other points in the structure may be obtained by adding multiples of four to the x, y, and z coordinates of these eight points. Adjacent points in this structure are at distance apart in the integer lattice; the edges of the diamond structure lie along the body diagonals of the integer grid cubes. This structure may be scaled to a cubical unit cell that is some number a of units across by multiplying all coordinates by .
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A game in international draughts, featuring a flying king When a man reaches the kings row (also called crownhead, the farthest row forward), it becomes a king, and is marked by placing an additional piece on top of the first man (crowned), and acquires additional powers including the ability to move backwards and (in variants where they cannot already do so) capture backwards. Like men, a king can make successive jumps in a single turn provided that each jump captures an enemy man or king. In international draughts, kings (also called flying kings) move any distance along unblocked diagonals, and may capture an opposing man any distance away by jumping to any of the unoccupied squares immediately beyond it. Because jumped pieces remain on the board until the turn is complete, it is possible to reach a position in a multi-jump move where the flying king is blocked from capturing further by a piece already jumped.
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Since this is one of the rare fables without human or animal characters, the subject has been a gift to artists and illustrators. From the earliest printed editions, the makers of woodcuts have taken pleasure in contrasting diagonals with the verticals and horizontals of the picture space, as well as the textures of the pliable reed and the sturdy tree trunk. Among 16th century emblem-makers there was even a prescription for how the scene should be presented. According to Hadrianus Junius (1565), ‘The way the picture should be drawn is straightforward: in it, one of the winds is blowing with puffed- out cheeks, breaking up the huge trees in its way, pulling them up, uprooting them and flinging them around; but a patch of reeds survives unscathed.’ Other contemporary examples of this approach are in Bernard Salomon's illustration in Les Fables d'Esope Phrygien (1554, see above) and the Latin poems of Hieronymus Osius (1564).
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The Hamiltonian cycle in the Cayley graph of the symmetric group generated by the Steinhaus–Johnson–Trotter algorithm inversion sets (sets of pairs of elements out of their natural order), inversion vectors, and inversion numbers The inversion sets form a gray code, thus also the inversion vectors (sums of the triangles' ascending diagonals) and inversion numbers. The numbers on the left are the permutations' reverse colexicographic indices (compare list in natural order) and form row 4 of triangle The inversion sets of permutations 12 places apart from each other are complements. Wheel diagram of all permutations of length n=4 generated by the Steinhaus-Johnson-Trotter algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red). The Steinhaus–Johnson–Trotter algorithm or Johnson-Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M. Johnson and Hale F. Trotter that generates all of the permutations of n elements.
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In this orientation, the oju opon ("face of the tray"), ese opon ("feet of the tray"), ona kanran ("straight path"), and the ona murun ("direct path") are respectively situated on the east, west, south and north sides of the tray's perimeter. On the diagonals from these cardinal directions are four additional sections or diviners: alaselosi ("the one who implements with the left") to the northeast, alabolotun ("the one who proposes with the right") to the southeast, afurukeresayo ("the one who has a diviner's fly-whisk and is happy") to the northwest, and ajiletepowo ("an early riser who sits down and prospers") to the southwest. The final section is the space in the center of the tray, the erilade opon ("the meeting place that crowns all"), for a total of nine sections. These sections come into play during consultations when the babalowo individually evokes the presence of Ifá and the nine ancient diviners before beginning the reading of the tray.
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While the quote from Apple II inventor Steve Wozniak on Gibson's page seems to imply that vintage Apple II graphics programmers routinely used subpixel rendering, it is difficult to make a case that many of them thought of what they were doing in such terms. The flag bit in each byte affects color by shifting pixels half a pixel-width to the right. This half-pixel shift was exploited by some graphics software, such as HRCG (High-Resolution Character Generator), an Apple utility that displayed text using the high-resolution graphics mode, to smooth diagonals. (Many Apple II users had monochrome displays, or turned down the saturation on their color displays when running software that expected a monochrome display, so this technique was useful.) Although it did not provide a way to address subpixels individually, it did allow positioning of pixels at fractional pixel locations and can thus be considered a form of subpixel rendering.
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Let us remove the first and the last files and the ranks that are occupied by rooks (since the number of ranks is even, the removed rooks cannot stand on the same rank). This will give a board of 2n − 2 files and 2n − 2 ranks. It is clear that to each symmetric arrangement of rooks on the new board corresponds a symmetric arrangement of rooks on the original board. Therefore, G2n = 2nG2n − 2 (the factor 2n in this expression comes from the possibility for the first rook to occupy any of the 2n squares on the first file). By iterating the above formula one reaches to the case of a 2 × 2 board, on which there are 2 symmetric arrangements (on the diagonals). As a result of this iteration, the final expression is G2n = 2nn! For the usual chessboard (8 × 8), G8 = 24 × 4! = 16 × 24 = 384 centrally symmetric arrangements of 8 rooks.
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Martin, 176 Wittkower sees in it "a heroic and aristocratic conception of Nature tamed and ennobled by the presence of man", as such works always contain a large man-made feature, here the castle "severely composed of horizontals and verticals" under which the party moves. They are placed at the meeting of two diagonals represented by the sheep and the river, "thus figures and buildings are intimately blended with the carefully arranged pattern of the landscape".Wittkower, 70 Kenneth Clark mentions the work as an example of the "ideal landscape" driven to promote itself in the hierarchy of genres by emulating (in the absence of much evidence of what classical landscape painting was like) an essentially literary vision, largely derived from the pastoral poems of Virgil: "the features of which it is composed must be chosen from nature, as poetic diction is chosen from ordinary speech, for their elegance, their ancient associations, and their faculty of harmonious combination. Ut pictura poesis".
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The chapel of San Martín takes advantage of the canvases of the northwest corner of the wall, to the point that one of its towers was used as sacristy and gave name to the courtyard that gives access to the Taifal enclosure. The factory, of Gothic-Mudéjar style, consists of two naves of three sections each, in origin orientated to the east and supported in two pillars with semicolumns attached in the half of the faces of the pillar, whose section is remembered in the quadrilobed that shelter the shield of arms of the King of Aragon in the spandrels of the portal, that is already of the first decade of the 15th century and in which we will stop later. Aragonese Courtyard, Tower and Chapel of San Martín The vaults of these naves, of simple rib vault, are lodged on formeros arches and pointed perpiaños arches, whereas the diagonals are of half point. At the corners of the vaults appear florets with the coat of arms of the Aragonese monarchy.
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At the very least, this observation gives little reason to believe that the corresponding diagonals will be equally dense with primes. One should, of course, consider divisibility by primes other than 3. Examining divisibility by 5 as well, remainders upon division by 15 repeat with pattern 1, 11, 14, 10, 14, 11, 1, 14, 5, 4, 11, 11, 4, 5, 14 for the first polynomial, and with pattern 5, 0, 3, 14, 3, 0, 5, 3, 9, 8, 0, 0, 8, 9, 3 for the second, implying that only three out of 15 values in the second sequence are potentially prime (being divisible by neither 3 nor 5), while 12 out of 15 values in the first sequence are potentially prime (since only three are divisible by 5 and none are divisible by 3). While rigorously-proved results about primes in quadratic sequences are scarce, considerations like those above give rise to a plausible conjecture on the asymptotic density of primes in such sequences, which is described in the next section.
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A bipartite graph with 4 vertices on each side, 13 edges, and no K3,3 subgraph, and an equivalent set of 13 points in a 4 × 4 grid, showing that z(4; 3) ≥ 13\. The number z(n, 2) asks for the maximum number of edges in a bipartite graph with n vertices on each side that has no 4-cycle (its girth is six or more). Thus, z(2, 2) = 3 (achieved by a three-edge path), and z(3, 2) = 6 (a hexagon). In his original formulation of the problem, Zarankiewicz asked for the values of z(n; 3) for n = 4, 5, and 6. The answers were supplied soon afterwards by Wacław Sierpiński: z(4; 3) = 13, z(5; 3) = 20, and z(6; 3) = 26.. The case of z(4; 3) is relatively simple: a 13-edge bipartite graph with four vertices on each side of the bipartition, and no K3,3 subgraph, may be obtained by adding one of the long diagonals to the graph of a cube.
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If M1 and M2 are the midpoints of the diagonals AC and BD respectively in a tangential quadrilateral ABCD with incenter I, and if the pairs of opposite sides meet at J and K with M3 being the midpoint of JK, then the points M3, M1, I, and M2 are collinear. The line containing them is the Newton line of the quadrilateral. If the extensions of opposite sides in a tangential quadrilateral intersect at J and K, and the extensions of opposite sides in its contact quadrilateral intersect at L and M, then the four points J, L, K and M are collinear.. If the incircle is tangent to the sides AB, BC, CD, DA at T1, T2, T3, T4 respectively, and if N1, N2, N3, N4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT1 = BN1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N1N3 and N2N4. Both of these lines divide the perimeter of the quadrilateral into two equal parts.
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If one of the short (uncrossed) edges of an antiparallelogram linkage is fixed in place, and the remaining linkage moves freely, then the crossing point of the antiparallelogram traces out an ellipse that has the fixed edge's endpoints as its foci. The other moving short edge of the antiparallelogram has as its endpoints the foci of another moving ellipse, formed from the first one by reflection across a tangent line through the crossing point.. For both the parallelogram and antiparallelogram linkages, if one of the long (crossed) edges of the linkage is fixed as a base, the free joints move on equal circles, but in a parallelogram they move in the same direction with equal velocities while in the antiparallelogram they move in opposite directions with unequal velocities.. As James Watt discovered, if an antiparallelogram has its long side fixed in this way it forms a variant of Watt's linkage, and the midpoint of the unfixed long edge will trace out a lemniscate or figure eight curve. For the antiparallelogram formed by the sides and diagonals of a square, it is the lemniscate of Bernoulli., pp. 58–59.
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Modern painted replica of the statue in Braga, Portugal Augustus is shown in this role of "Imperator", the commander of the army, as thoracatus —or commander-in-chief of the Roman army (literally, thorax-wearer)—meaning the statue should form part of a commemorative monument to his latest victories; he is in military clothing, carrying a consular baton and raising his right hand in a rhetorical adlocutio pose, addressing the troops. The bas-reliefs on his armored cuirass have a complex allegorical and political agenda, alluding to diverse Roman deities, including Mars, god of war, as well as the personifications of the latest territories he conquered: Hispania, Gaul, Germania, Parthia (that had humiliated Crassus, and here appears in the act of returning the standards captured from his legions); at the top, the chariot of the Sun illuminates Augustus's deeds. The statue is an idealized image of Augustus showing a standard pose of a Roman orator and based on the 5th-century BC statue of the Spear Bearer or Doryphoros by the sculptor Polykleitos. The Doryphoros's contrapposto stance, creating diagonals between tense and relaxed limbs, a feature typical of classical sculpture, is adapted here.
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Lozanić's triangle (sometimes called Losanitsch's triangle) is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into the symmetries exhibited by rows of paraffins (archaic term for alkanes). The first few lines of Lozanić's triangle are 1 1 1 1 1 1 1 2 2 1 1 2 4 2 1 1 3 6 6 3 1 1 3 9 12 9 3 1 1 4 12 19 19 12 4 1 1 4 16 28 38 28 16 4 1 1 5 20 44 66 66 44 20 5 1 1 5 25 60 110 128 110 60 25 5 1 1 6 30 85 170 236 236 170 85 30 6 1 1 6 36 110 255 396 472 396 255 110 36 6 1 1 7 42 146 365 651 868 868 651 365 146 42 7 1 1 7 49 182 511 1001 1519 1716 1519 1001 511 182 49 7 1 1 8 56 231 693 1512 2520 3235 3235 2520 1512 693 231 56 8 1 listed in . Like Pascal's triangle, outer edge diagonals of Lozanić's triangle are all 1s, and most of the enclosed numbers are the sum of the two numbers above. But for numbers at odd positions k in even-numbered rows n (starting the numbering for both with 0), after adding the two numbers above, subtract the number at position (k − 1)/2 in row n/2 − 1 of Pascal's triangle.
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