This modest event in an antipodal corner of the globe became news everywhere.
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The new array consists of six speakers arranged so that the subwoofers are positioned in pairs, antipodal to one another (back to back).
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These days, it's not unusual to hear Indians describe Modi as "our Trump," which is said in antipodal ways, either with pride or scorn.
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Another moment, antipodal but still as surprisingly affecting, comes when Herzog asks a roboticist whether he loves "Robot 8," his team's favorite soccer-playing cylinder.
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Or, rather, low: They are both booming basses, equally mighty in a way that illustrates, with only music, how alike these antipodal characters may be.
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Mr. Höller, Belgium-born and based in Sweden and Ghana, plumbs the antipodal reaches of human experience, and the conflicting feelings that come with it.
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Written in bold, black lettering on the stairs leading up to the exhibition's second floor gallery, visitors are confronted with antipodal sets of questions alternatively posed to privileged citizens of the developed world and migrants from the global south.
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The other is that a year from now, with another brutal antipodal summer behind the planet we hope, you're more likely to choose Forster's The Evangelist or the Go-Betweens' Oceans Apart when craving a taste of this particular artist who's not as famous as he deserves to be.
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Focusing the critical eye beyond the pure-aesthetic bokeh in the coming deluge of spiritually bankrupt hypnagogic pop, the A&R bigwigs at the Brooklyn-based firm opened the aperture wide enough to capture diverse and enterprising intercontinental artists of vast acclaim: Ariel Pink stationed in Los Angeles, Pill hunkered down in NYC, Tonstartssbandht enduring Orlando, Dungen operating somewhere in Stockholm, the antipodal Connan Mockasin skyping in from New Zealand for royalties reports—and this with the Colombian heritage of head honcho Andrés Santo Domingo also notwithstanding.
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South Georgia Island is antipodal to the northernmost part of Sakhalin Island. Lake Baikal is partially antipodal to the Straits of Magellan. The Russian Antarctic research base Bellingshausen Station is antipodal to a land location in Russian Siberia. Rottnest Island, off the coast of Western Australia, is approximately antipodal to Bermuda.
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Approximately 15% of land territory is antipodal to other land, representing approximately 4.4% of Earth's surface. Another source estimates that about 3% of Earth's surface is antipodal land. The largest antipodal land masses are the Malay Archipelago, antipodal to the Amazon basin and adjoining Andean ranges; east China and Mongolia, antipodal to Chile and Argentina; and Greenland and the Canadian Arctic Archipelago, antipodal to East Antarctica. There is a general paucity of antipodal land because the Southern Hemisphere has comparatively less land than the Northern Hemisphere and, of that, the antipodes of Australia are in the North Atlantic Ocean, while the antipodes of southern Africa are in the Pacific Ocean.
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Montana is one of only two contiguous states (along with Colorado) that are antipodal to land. The Kerguelen Islands are antipodal to the Montana–Saskatchewan–Alberta border. No towns are precisely antipodal to Kerguelen, though Chester and Rudyard are close.
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Easter Island is antipodal to an area close to Desert National Park, from Jaisalmer, India. The only town on Easter Island, Hanga Roa, is antipodal to the village of Serawa northeast of Jaisalmer. Serawa is the only village in India to be antipodal to a human settlement. Its neighbouring villages Mokla and the northern part of Bhadasar also have antipodes on Easter Island.
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An antipodal pair of a convex polygon is a pair of 2 points admitting 2 infinite parallel lines being tangent to both points included in the antipodal without crossing any other line of the convex polygon.
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Finline variants: A, standard (unilateral), B, bilateral, C, antipodal, D, strongly coupled antipodal E, insulatedHelszajn, p. 242 Unilateral finline is the simplest design and easiest to manufacture but bilateral finline has lower loss, as with bilateral suspended stripline, and for similar reasons. The high Q of bilateral finline often makes it the choice for filter applications. Antipodal finline is used where very low characteristic impedance is required.
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A radio (d-1)-coloring, that is, where k is equal to one less than the graph's diameter, is known as an antipodal coloring because antipodal vertices may be colored the same, but all nodes between them must be different.
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Luzon, the largest island of the Philippines, is antipodal to eastern Bolivia. As with the British Empire, the sun set neither on the French Empire, the Dutch Empire, nor the Spanish Empire at their peaks. Santa Vitória do Palmar, the most southerly town of more than 10,000 people in Brazil, is antipodal to Jeju Island, the southernmost territory of South Korea. Hawaii is antipodal to parts of Botswana.
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One can further restrict to the upper hemisphere of Sn and merely identify antipodal points on the bounding equator. This shows that RPn is also equivalent to the closed n-dimensional disk, Dn, with antipodal points on the boundary, ∂Dn = Sn−1, identified.
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Slotline variants: A, standard, B, antipodal, C, bilateral Antipodal slotline is used where very low characteristic impedances are required. With dielectric lines, low impedance means narrow lines (the opposite of the case with conducting lines) and there is a limit to the thinness of line that can be achieved because of the printing resolution. With the antipodal structure, the conductors can even overlap without any danger of short-circuiting. Bilateral slotline has advantages similar to those of bilateral air stripline.
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The Big Island of Hawaii is antipodal to the Okavango Delta in Botswana, with the island's largest city, Hilo, antipodal to Nxai Pan National Park. Desolate Kerguelen Island is antipodal to an area of thinly inhabited plains on the border between the Canadian provinces of Alberta and Saskatchewan and the US state of Montana. The only permanent settlement on Kerguelen Island, the research station Port- aux-Français, is antipodal to fields northeast of Senate, Saskatchewan. Other Canadian towns with antipodes on Kerguelen Island include: Consul, Nashlyn and Govenlock in the vicinity of Senate, and in Alberta Eagle Butte, Elkwater and Manyberries as well as the Red Coat Trail between Orion, Alberta and Etzikom.
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It says that any continuous function from Sn to Rn maps some pair of antipodal points in Sn to the same point in Rn. Here, Sn denotes the n-dimensional sphere in (n + 1)-dimensional space (so the "ordinary" sphere is S2 and a circle is S1). The antipodal map A : Sn → Sn, defined by A(x) = −x, sends every point on the sphere to its antipodal point. It is homotopic to the identity map if n is odd, and its degree is (−1)n+1. If one wants to consider antipodal points as identified, one passes to projective space (see also projective Hilbert space, for this idea as applied in quantum mechanics).
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When points swap, the list of antipodal pairs are updated. The upper and lower envelopes can be maintained using the standard data structure for kinetic convex hull. The maximum distance between pairs of antipodal can be maintained with a kinetic tournament. Thus, using kinetic convex hull to maintain the upper and lower envelopes, a kinetic sorted list on these intervals to maintain the antipodal pairs, and a kinetic tournament to maintain the pair of maximum distance apart, the diameter of a moving point set can be maintained.
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As the waves focus on the antipodal position, they put the crust at the focal point under significant stress and are proposed to rupture it, creating antipodal pairs. When the meteorite impacts a continent, the lower efficiency of kinetic energy conversion into seismic energy is not expected to create an antipodal hotspot. A second impact-related model of hotspot and LIP formation has been suggested in which minor hotspot volcanism was generated at large-body impact sites and flood basalt volcanism was triggered antipodally by focused seismic energy. This model has been challenged because impacts are generally considered seismically too inefficient, and the Deccan Traps of India were not antipodal to, and began erupting several Myr before, the end-Cretaceous Chicxulub impact in Mexico.
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When viewed in this dualized fashion the antipodal pairs, are pairs of segments, one from the upper envelope, one from the lower, with overlapping x ranges. Now, the upper and lower envelopes can be viewed as two different x-ordered lists of non overlapping intervals. If these two lists are merged, the antipodal pairs are the overlaps in the merged list. If a pair ab and c is an antipodal edge- vertex pair, then the x-interval for a and b must both intersect the x-interval for c.
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The pair of points with maximum pairwise distance must be one of the pairs of antipodal points of the convex hull of all of the points. Note that two points are antipodal points if they have parallel supporting lines. In the static case, the diameter of a point set can be found by computing the convex hull of the point set, finding all pairs of antipodal points, and then finding the maximum distance between these pairs. This algorithm can be kinetized as follows: Consider the dual of the point set.
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Gibraltar is approximately antipodal to Te Arai Beach about north of Auckland, New Zealand. This illustrates the old yet correct saying that the sun never sets on the British Empire; the sun still does not set on the Commonwealth of Nations. The northern part of New Caledonia, an overseas territory of France, is antipodal to some thinly populated desert in Mauritania, a part of the former French West Africa. Portions of Suriname, a former Dutch colony, are antipodal to Sulawesi, an Indonesian island spelled Celebes when it was part of the Netherlands East Indies.
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It consists of low, closely spaced to scattered hills about 0.3 to across and from tens of meters to a few hundred meters high. The outer boundary of this unit is gradational with the (younger) smooth plains that occur in the same region. A hilly and furrowed terrain is found antipodal to the Caloris basin, probably created by antipodal convergence of intense seismic waves generated by the Caloris impact.Schultz, P.H. and Gault, D.E. (1975) The Moon 12, 159-177. The so-called “Weird Terrain” was formed by the Caloris Basin impact at its antipodal point.
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Antipodal points on a circle are 180 degrees apart. In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it – so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter. This term applies to opposite points on a circle or any n-sphere. An antipodal point is sometimes called an antipode, a back-formation from the Greek loan word antipodes, which originally meant "opposite the feet".
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The female gametophyte corresponds to the embryo sac and covers an egg cell, a central cell, two synergid cells, and several antipodal cells.
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The positive temperature gradient of Pluto's atmosphere contributes to making a topographic depression a cold trap. The terrain on Pluto antipodal to Sputnik Planitia may have been altered by the focusing there of seismic energy from the formative impact. While this suggestion is tentative in view of the poor resolution of the imaging of the antipodal region, the concept is similar to what has been proposed for areas antipodal to the Caloris basin on Mercury and Mare Orientale on the Moon. A high seasonal thermal inertia of Pluto's surface is an important driver of deposition of nitrogen ice at low latitudes.
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In mathematics, the concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre; for example, taking the centre as origin, they are points with related vectors v and −v. On a circle, such points are also called diametrically opposite. In other words, each line through the centre intersects the sphere in two points, one for each ray out from the centre, and these two points are antipodal. The Borsuk-Ulam theorem is a result from algebraic topology dealing with such pairs of points.
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It is one of the few locations in the United States to have an antipodal point on land, and its community of Rudyard is the only populated such place. The Kerguelen Islands are on the opposite side of the earth from parts of Hill County, while the antipodal points of almost all other places in the United States lie in the Indian Ocean.
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Here the blue areas are the reflections of the Eastern Hemisphere. In geography, the antipode ( or ) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal () to each other are situated such that a straight line connecting the two would pass through Earth's center. Antipodal points are as far away from each other as possible.
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Every line through the origin intersects the unit sphere in exactly two points, one of which is on the lower hemisphere z ≤ 0. (Horizontal lines intersect the equator z = 0 in two antipodal points. It is understood that antipodal points on the equator represent a single line. See quotient topology.) Hence the directions in three-dimensional space correspond (almost perfectly) to points on the lower hemisphere.
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Together with the northern part of Liberty County, Montana, they are the only three areas of the Contiguous United States with antipodes on land. The north-eastern coast of Alaska from Utqiagvik, Alaska (former Barrow) over Prudhoe Bay to the Canadian border, and the coasts of the Canadian territories of Yukon, Northwest Territories, and Nunavut, are antipodal to Antarctica. The Heard Island and McDonald Islands, an uninhabited Australian territory, is antipodal to an area in central Saskatchewan, including the towns of Leask and Shellbrook. Tigres Island, the largest uninhabited island of Angola, is approximately antipodal to Johnston atoll, which is the third largest uninhabited island of the United States.
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The small, rocky, uninhabited island of Sala y Gómez, east-northeast of Easter Island, is antipodal to an area in the city of Ajmer, India, just east of Ana Sagar Lake. All the rest of India has its antipodes in the sea. Kiritimati, the largest island of Kiribati and the largest coral atoll in the world, is antipodal to Salonga National Park, which is the largest national park of the Democratic Republic of the Congo and the largest tropical rainforest reserve in Africa. Serra da Estrela Natural Park, the largest natural park of Portugal, is antipodal to Kahurangi National Park, the second largest national park of New Zealand.
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Three antipodal cells form on the opposite (chalazal) end of the ovule and later degenerate. The large central cell of the embryo sac contains two polar nuclei.
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Let X = S^2, that is the regular 2-sphere. Then the cut locus of every point on the sphere consists of exactly one point, namely the antipodal one.
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An antipodal pair of vertex and their supporting parallel lines. The rotating calipers method was first used in the dissertation of Michael Shamos in 1978. Shamos uses this method to generate all antipodal pairs of points on a convex polygon and to compute the diameter of a convex polygon in O(n) time. Godfried Toussaint coined the phrase "rotating calipers" and also demonstrated that the method was applicable in solving many other computational geometry problems.
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Cocos (Keeling) Islands, an Australian external territory in the Indian Ocean, is almost antipodal to Nicaragua's Corn Islands. Flores Island, the westernmost island of the Azores, is nearly antipodal to Flinders Island between Tasmania and the Australian mainland. Point Nemo, the point in the South Pacific Ocean most distant from any other land, is precisely opposite a desolate piece of desert in western Kazakhstan. By definition, the North Pole and the South Pole are antipodes.
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The ovule contains a megagametophyte, also known as an embryo sac, that is bipolar in structure and contains 8 cell nuclei. The antipodal cells are persistent, and the endosperm is triploid.
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Consider the parallel lines which contain the point set in the strip between them and are of minimal distance apart. One of the lines must contain an edge ab of the convex hull, and the other line must go through a point c of the convex hull such that (a,c) and (b,c) are antipodal pairs. ab and c are referred to as an antipodal edge-vertex pair. Consider the dual of the point set.
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Hamiltonian colorings are a variation on antipodal colorings where, instead of considering the regular distance between nodes, the detour distance is instead considered. Specifically, a Hamiltonian coloring's nodes have the property that the detour distance plus the difference in colors is greater than or equal to one less than n, the number of nodes in the graph. If the graph G is a path, then any Hamiltonian coloring is also an antipodal coloring, which is the inspiration for the definition of Hamiltonian coloring.
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Since the R3 line represents a point of RP2, we will obtain the same model of RP2 by identifying the antipodal points of the sphere. The lines of RP2 will be the great circles of the sphere after this identification of antipodal points. This description gives the standard model of elliptic geometry. The complex projective plane CP2, arises when K is taken to be the complex numbers, C. It is a closed complex 2-manifold, and hence a closed, orientable real 4-manifold.
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The group acts transitively on . The stabilizer subgroup of the unit vector (0,0,1) can be identified with , so that . The geodesics between two points on the sphere are the great circle arcs with these given endpoints. If the points are not antipodal, there is a unique shortest geodesic between the points. The geodesics can also be described group theoretically: each geodesic through the North pole (0,0,1) is the orbit of the subgroup of rotations about an axis through antipodal points on the equator.
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The arc of 1 is a single point, and –1 can be represented by an infinite number of arcs, because there are an infinite number of shortest lines between antipodal points of a sphere.
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When viewed in this dualized fashion the antipodal pairs, are pairs of segments, one from the upper envelope, one from the lower, with overlapping x ranges. Now, the upper and lower envelopes can be viewed as two different x-ordered lists of non overlapping intervals. If these two lists are merged, the antipodal pairs are the overlaps in the merged list. The overlaps in the merged list of x-intervals can be maintained by storing the endpoints of the intervals in a kinetic sorted list.
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This data structure is not local because one point may be in many antipodal pairs, and thus appear many times in the kinetic tournament. The existence of a local kinetic data structure for diameter is open.
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Seven pairs of hotspots and LIPs located on opposite sides of the earth have been noted; analyses indicate this coincident antipodal location is highly unlikely to be random. The hotspot pairs include a large igneous province with continental volcanism opposite an oceanic hotspot. Oceanic impacts of large meteorites are expected to have high efficiency in converting energy into seismic waves. These waves would propagate around the world and reconverge close to the antipodal position; small variations are expected as the seismic velocity varies depending upon the route characteristics along which the waves propagate.
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The antipodes of the Chatham Islands lie in France, just north of the city of Montpellier. The Antipodes Islands were named for their supposed antipodal position to Britain; although they are the closest land to the true antipodes of Britain, their location 49°41′S 178°48′E is directly antipodal to a point a few kilometres to the east of Cherbourg on the north coast of France. In Europe the term "Antipodes" is often used to refer to New Zealand and Australia (and sometimes other South Pacific areas), and "Antipodeans" to their inhabitants.
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Using linear algebra, a projective space of dimension is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space of dimension . Equivalently, it is the quotient set of by the equivalence relation "being on the same vector line". As a vector line intersects the unit sphere of in two antipodal points, projective spaces can be equivalently defined as spheres in which antipodal points are identified. A projective space of dimension 1 is a projective line, and a projective space of dimension 2 is a projective plane.
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A great circle divides the earth into two hemispheres and if a great circle passes through a point it must pass through its antipodal point. The Funk transform integrates a function along all great circles of the sphere.
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However, one can approximately visualize it as a disk, as follows. Any line through the origin intersects the southern hemisphere ≤ 0 in a point, which can then be stereographically projected to a point on a disk. Horizontal lines intersect the southern hemisphere in two antipodal points along the equator, either of which can be projected to the disk; it is understood that antipodal points on the boundary of the disk represent a single line. (See quotient topology.) So any set of lines through the origin can be pictured, almost perfectly, as a set of points in a disk.
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There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron: it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 (antipodal point) vertices, 5 edges, and 5 digonal faces.
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On the standard round n-sphere, the cut locus of a point consists of the single point opposite of it (i.e., the antipodal point). On an infinitely long cylinder, the cut locus of a point consists of the line opposite the point.
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Additionally they show that the ply of a planar cover may be arbitrarily large. They are not the only covers involving prisms: for instance, the hexagonal prism can also cover a non-planar graph, the utility graph K3,3, by identifying antipodal pairs of vertices.
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Line b is another geodesic which intersects a in two antipodal points. They share two common perpendiculars (one shown in blue). In spherical geometry, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other.
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Arecibo Catena (Arecibo Vallis until March 2013) is a catena on Mercury. It is located at latitude 27.5 S, longitude 28.4 W, in the hilly and chaotic terrain antipodal to Caloris Basin. It is named after Arecibo Observatory. Arecibo Vallis is connected to Petrarch crater.
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The islands appear in a number of fictional works. The title character in Edgar Allan Poe's 1838 novel, The Narrative of Arthur Gordon Pym of Nantucket, visits the islands. French writer Jules Verne's 1897 novel An Antarctic Mystery offers a follow up to Poe's book, and revisits the Kerguelen Islands. The 1874 short story "The Tachypomp" by Edward Page Mitchell tells of a hole through the center of the Earth with one end in the United States and the other in "Kerguellen's Land" (which is roughly antipodal to the United States and CanadaIn fact the islands' antipodal point, 49°15'N, 110°50'W, falls near Pakowki Lake, Alberta).
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Instead, such places observe the opposite phenomenon when the sun passes above the antipodal point of the Kaaba (in other words, the sun passes directly underneath the Kaaba), causing shadows in the opposite direction from those observed during rasd al-qiblat. This occurs twice a year, on 14 January 00:30 SAST (21:30 UTC the previous day) and 29 November 00:09 SAST (21:09 UTC the previous day). Observations made within five minutes of the rasd al-qiblat moments or its antipodal counterparts, or at the same time of the day two days before or after each event, still show accurate directions with negligible difference.
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The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is called a Riemannian circle in Riemannian geometry. Between two points that are directly opposite each other, called antipodal points, there are infinitely many great circles, and all great circle arcs between antipodal points have a length of half the circumference of the circle, or \pi r, where r is the radius of the sphere. The Earth is nearly spherical (see Earth radius), so great-circle distance formulas give the distance between points on the surface of the Earth correct to within about 0.5%.
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In addition, they lie almost directly opposite that basin on the planet. Both observations strengthen the suggestion that the hilly and lineated unit and the hummocky plains unit are directly related to the formation of Caloris, possibly through the focusing of seismic waves at the antipodal point.
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Since the plane at infinity is a projective plane, it is homeomorphic to the surface of a "sphere modulo antipodes", i.e. a sphere in which antipodal points are equivalent: S2/{1,-1} where the quotient is understood as a quotient by a group action (see quotient space).
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Cheyenne Wells is located at (38.821141, -102.353637). According to the United States Census Bureau, the town has a total area of , all land. A small area about 10 miles southwest of Cheyenne Wells is antipodal, or globally opposite, to Île Saint-Paul, an island in the southern Indian Ocean.
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Recall the notion of central symmetry: a Euclidean polyhedron is called centrally symmetric if it is invariant under the antipodal map : x \mapsto -x. \, Thus, in the plane central symmetry is the rotation by 180 degrees. For example, an ellipse is centrally symmetric, as is any ellipsoid in 3-space.
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It is 2-covered by the cuboctahedron, and can be realized as the quotient of the spherical cuboctahedron by the antipodal map. It is the only uniform (traditional) polyhedron that is projective – that is, the only uniform projective polyhedron that immerses in Euclidean three-space as a uniform traditional polyhedron.
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Any other closed great circle route starting on the equator and traveling at an angle between 0° (an equatorial route) and 90° (a polar route) would be between . In all of these cases, after half of the world has been traversed, every subsequent point will be antipodal to one already visited.
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The lower end of the embryo sac consists of the haploid egg cell positioned in the middle of two other haploid cells, called synergids. The synergids function in the attraction and guidance of the pollen tube to the megagametophyte through the micropyle. At the upper end of the megagametophyte are three antipodal cells.
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A spherical triangle The area of a spherical triangle on the unit sphere is . The isometry group of the unit sphere in is the orthogonal group , with the rotation group as the subgroup of isometries preserving orientation. It is the direct product of with the antipodal map, sending to ., Chapter II, Spherical geometry.
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The sphere, before being transformed, is not homeomorphic to the real projective plane, RP2. But the sphere centered at the origin has this property, that if point (x,y,z) belongs to the sphere, then so does the antipodal point (-x,-y,-z) and these two points are different: they lie on opposite sides of the center of the sphere. The transformation T converts both of these antipodal points into the same point, : T : (x, y, z) \rightarrow (y z, z x, x y), : T : (-x, -y, -z) \rightarrow ((-y) (-z), (-z) (-x), (-x) (-y)) = (y z, z x, x y). Since this is true of all points of S2, then it is clear that the Roman surface is a continuous image of a "sphere modulo antipodes".
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Null Island, , at the intersection of the prime meridian and the equator, has its antipodes at , at the intersection of the antimeridian and the equator. This point lies northeast of Nikunau in the Gilbert Islands and southwest of Baker Island, a United States territory. As can be seen on the purple/blue map, the Pacific Ocean is so large that it stretches halfway around the world; parts of the Pacific off the coast of Peru are antipodal to parts of the same ocean off the coast of Southeast Asia. For example, the island of Ko Chang—which is the second or third largest island in Thailand—is nearly antipodal to San Lorenzo Island, which is the largest island of Peru.
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The second half of the path can then be mirrored over to the antipodal side without changing the path at all. Now we have an ordinary closed loop on the surface of the ball, connecting the north pole to itself along a great circle. This circle can be shrunk to the north pole without problems.
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The plane was tested in flight in April 1945. The rocket engine could run for about a minute. Of much larger size, the Silbervogel antipodal bomber spaceplane was planned by the Germans late in World War II, however later calculations showed that it would not have worked, and would have been destroyed during reentry.Parsons, Zach.
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AMS, 1963) Huhhot and vicinities, LandSat-5 satellite image, 2005-07-12 Located in the south central part of Inner Mongolia, Hohhot is encircled by the Daqing Shan () to the north and the Hetao Plateau to the south. The city's antipodal location is located 14 kilometers (8.6 miles) from the village of Los Menucos in Río Negro Provence, Argentina.
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The complete "rotation" of the caliper around the polygon detects all antipodal pairs; the set of all pairs, viewed as a graph, forms a thrackle. The method of rotating calipers can be interpreted as the projective dual of a sweep line algorithm in which the sweep is across slopes of lines rather than across - or -coordinates of points.
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Real projective space admits a constant positive scalar curvature metric, coming from the double cover by the standard round sphere (the antipodal map is locally an isometry). For the standard round metric, this has sectional curvature identically 1. In the standard round metric, the measure of projective space is exactly half the measure of the sphere.
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The antipodes of Fiji are in eastern Mali, around the northernmost bend of the Niger River. The small western island of Yasawa is antipodal to the Niger about from Timbuktu, whereas the eastern cape of Vanua Levu corresponds to the old imperial city of Gao. The antipodes of the dependency of Rotuma are in Burkina Faso, west of Ouagadougou.
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The money is then used to help the Kalahari people. Dekar also houses a school and a clinic. About 15 to 20 km outside Dekar there is a game farm on the road to Ghanzi. Dekar is the closest populated place to the antipode of Honolulu, Hawai‘i. It’s nearly perfectly antipodal to the town of Wahiawā, Hawai‘i. .
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The northern part of Liberty County, Montana, especially the communities Goldstone, Fox Crossing and Sage Creek Colony, also have antipodes on Kerguelen Island. St. Paul Island and Amsterdam Island are antipodal to thinly populated parts of the eastern part of the US state of Colorado. They are situated ca. south-south-east of Firstview and south-south-west of Granada, Colorado, respectively.
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The tip of the pollen tube then enters the ovary and penetrates through the micropyle opening in the ovule. The pollen tube proceeds to release the two sperm in the megagametophyte. The cells of an unfertilized ovule are 8 in number and arranged in the form of 3+2+3 (from top to bottom) i.e. 3 antipodal cells, 2 polar central cells, 2 synergids & 1 egg cell.
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An orientable Riemannian surface of genus one that isometrically fills the circle cannot have less area than the hemisphere. The proof in this case again starts by gluing antipodal points of the boundary. The non-orientable closed surface obtained in this way has an orientable double cover of genus two, and is therefore hyperelliptic. The proof then exploits a formula by J. Hersch from integral geometry.
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Principles of Genetics (5th ed.). Wiley. . It is thought that the basal chromosome number in angiosperms is n = 7. One of these four cells (megaspore) then undergoes three successive mitotic divisions to produce an immature embryo sac (megagametophyte) with eight haploid nuclei. Next, these nuclei are segregated into separate cells by cytokinesis to producing 3 antipodal cells, 2 synergid cells and an egg cell.
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There are three leading models for swirl formation. Each model must address two characteristics of lunar swirls formation: # The lunar swirls are optically immature. # The lunar swirls are associated with magnetic anomalies. Models for creation of the magnetic anomalies associated with lunar swirls point to the observation that several of the magnetic anomalies are antipodal to the younger, large impact basins on the Moon.
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In mathematics, the Lusternik–Schnirelmann theorem, aka Lusternik–Schnirelmann–Borsuk theorem or LSB theorem, says as follows. If the sphere Sn is covered by n + 1 open sets, then one of these sets contains a pair (x, −x) of antipodal points. It is named after Lazar Lyusternik and Lev Schnirelmann, who published it in 1930... cites pp. 26–31 of this 68-page pamphlet for the theorem.
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It is classified as Trumpler type I,1,r or I,2,r. M37 is located in the antipodal direction, opposite from the Galactic Center as seen from Earth. Estimates of its age range from 347 million to 550 million years. It has 1,500 times the mass of the Sun and contains over 500 identified stars, with roughly 150 stars brighter than magnitude 12.5.
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The station is named for the 19th-century Russian explorer of the Antarctic Fabian von Bellingshausen. The station is connected by unimproved roads to the nearby stations: Chilean Base Presidente Eduardo Frei Montalva, Chinese Great Wall Station, and Uruguayan Artigas Base.USAIT 2006 It is antipodal to a location in Russian Siberia. In October 2018, it was the site of the first attempted murder in Antarctica.
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This means that the common endpoint of the x intervals for a and b must lie within the x-interval for c. The endpoints of both of the sets of x-intervals can be maintained in a kinetic sorted list. When points swap, the list of antipodal edge-point pairs are updated appropriately. The upper and lower envelopes can be maintained using the standard data structure for kinetic convex hull.
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In modern music, the twelve notes of the octave are equally space around the chromatic circle. On this circle, there are six pairs of antipodal notes, each representing an augmented-fourth interval. Each such pair specifies the successive open-strings of an augmented-fourths tuning. The set of augmented-fourths tunings has three properties that simplify learning by beginners and improvisation by experts: Regular intervals, string repetition, and lefty-righty symmetry.
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Dogtags on ball chain A ball chain is a type of chain consisting of small sheet metal balls connected via short lengths of wire. The balls are hollow and have two small antipodal holes. These holes accept a short length of wire deformed on the end like a rivet so that the end is bound inside the ball. The wire is then connected to another ball using the same method.
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In plant ovules, the chalaza is located opposite the micropyle opening of the integuments. It is the tissue where the integuments and nucellus are joined. Nutrients from the plant travel through vascular tissue in the funiculus and outer integument through the chalaza into the nucellus. During the development of the embryo sac inside a flowering plant ovule, the three cells at the chalazal end become the antipodal cells.
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In Euclidean geometry, a figure can be scaled up or scaled down indefinitely, and the resulting figures are similar, i.e., they have the same angles and the same internal proportions. In elliptic geometry this is not the case. For example, in the spherical model we can see that the distance between any two points must be strictly less than half the circumference of the sphere (because antipodal points are identified).
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Several barographs recorded the wave seven times over the course of five days: four times with the wave travelling away from the volcano to its antipodal point, and three times travelling back to the volcano. Hence, the wave rounded the globe three and a half times. Ash was propelled to an estimated height of . The eruptions diminished rapidly after that point, and by the morning of 28 August, Krakatoa was silent.
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The geodesics from a particular point if continued past the cut locus form an envelope illustrated in Fig. 15. Here the geodesics for which is a multiple of are shown in light blue. (The geodesics are only shown for their first passage close to the antipodal point, not for subsequent ones.) Some geodesic circles are shown in green; these form cusps on the envelope. The cut locus is shown in red.
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Then v(p) is the displacement vector of this projected point relative to p. According to the hairy ball theorem, there is a p such that v(p) = 0, so that s(p) = p. This argument breaks down only if there exists a point p for which s(p) is the antipodal point of p, since such a point is the only one that cannot be stereographically projected onto the tangent plane of p.
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Professor Walter Gregorii had Sänger rework his report, and a greatly reduced version was submitted to the RLM in September 1944, as UM 3538. It was the first serious proposal for a vehicle which could carry a pilot and payload to the lower edge of space. Two manned and one unmanned version were proposed: the (antipodal long-range glider) and the (intercontinental long-range glider). Both were to be launched from a rocket-powered sled.
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Therefore, any rigid body movement leads directly to SO(3), when we factor out the translational part. These identifications illustrate that SO(3) is connected but not simply connected. As to the latter, in the ball with antipodal surface points identified, consider the path running from the "north pole" straight through the center down to the south pole. This is a closed loop, since the north pole and the south pole are identified.
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Another viewpoint is that conjugate points tell when the geodesics fail to be length-minimizing. All geodesics are locally length-minimizing, but, for example, on a sphere, any geodesic passing through the north-pole can be extended to reach the south-pole, and hence any geodesic segment connecting the poles is not (uniquely) globally length minimizing. This tells us that any pair of antipodal points on the standard 2-sphere are conjugate points.Cheeger, Ebin.
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The real projective plane RP2, arises when K is taken to be the real numbers, R. As a closed, non- orientable real 2-manifold, it serves as a fundamental example in topology.The real projective plane appears 37 times in the index of Bredon (1993), for example. In this construction consider the unit sphere centered at the origin in R3. Each of the R3 lines in this construction intersects the sphere at two antipodal points.
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The two great circles are shown as thin black lines, whereas the spherical lune (shown in green) is outlined in thick black lines. This geometry also defines lunes of greater angles: {2}π-θ, and {2}2π-θ. In spherical geometry, a spherical lune is an area on a sphere bounded by two half great circles which meet at antipodal points. It is an example of a digon, {2}θ, with dihedral angle θ.
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A real version of the Hopf fibration is obtained by regarding the circle S1 as a subset of R2 in the usual way and by identifying antipodal points. This gives a fiber bundle S1 → RP1 over the real projective line with fiber S0 = {1, −1}. Just as CP1 is diffeomorphic to a sphere, RP1 is diffeomorphic to a circle. More generally, the n-sphere Sn fibers over real projective space RPn with fiber S0.
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The quotient can be identified with the real projective plane. It is non- orientable and can be described as the quotient of by the antipodal map (multiplication by −1). The sphere is simply connected, while the real projective plane has fundamental group . The finite subgroups of , corresponding to the finite subgroups of and the symmetry groups of the platonic solids, do not act freely on , so the corresponding quotients are not 2-manifolds, just orbifolds.
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At the other end of the cell, a cell wall forms around the nuclei and forms the antipodals. Therefore, the resulting embryo sac is a seven-celled structure consisting of one central cell, one egg cell, two synergid cells, and three antipodal cells. The bisporic and tetrasporic patterns undergo varying processes and result in varying embryo sacs as well. In Lilium which has a tetrasporic pattern, the central cell of the embryo sac is 4N.
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Besides the fixed-point theorems for more or less contracting functions, there are many that have emerged directly or indirectly from the result under discussion. A continuous map from a closed ball of Euclidean space to its boundary cannot be the identity on the boundary. Similarly, the Borsuk–Ulam theorem says that a continuous map from the n-dimensional sphere to Rn has a pair of antipodal points that are mapped to the same point.
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This observation is called rasd al-qibla ("observing the qibla"). This observation is not observable in the hemisphere opposite the Ka'bah, in which the events occur when the sun is below the horizon. This hemisphere includes most of the Americas, the Pacific Ocean, Australia, and Eastern Indonesia. People in these places can observe a comparable event when the sun passes directly above the antipodal point of the earth; the point that is directly opposite the Ka'bah.
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An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere. Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided. Concepts of spherical geometry may also be applied to the oblong sphere, though minor modifications must be implemented on certain formulas.
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However, Glushko's arrest during Stalinist purges in 1938 curtailed the development. Similar work was also done from 1932 onwards by the Austrian professor Eugen Sänger, who migrated from Austria to Germany in 1936. He worked there on rocket-powered spaceplanes such as Silbervogel (sometimes called the "antipodal" bomber). On November 12, 1932 at a farm in Stockton NJ, the American Interplanetary Society's attempt to static-fire their first rocket (based on German Rocket Society designs) failed in a fire.
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Getafe is home to a number of curiosities and special characteristics rare among other municipalities. Some of these include: Traditionally, the geographical center of the Iberian Peninsula is located in the Cerro de los Ángeles.Información del Cerro de los Ángeles The Perales del Río neighborhood boasts the world's largest population of the common kestrel (Falco tinnunculus). Getafe's antipodal point is in the southeast of the North Island of New Zealand, 15 km southeast of the agricultural town of Dannevirke.
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In the Northern Hemisphere, "the Antipodes" may refer to Australia and New Zealand, and Antipodeans to their inhabitants. Geographically, the antipodes of Britain and Ireland are in the Pacific Ocean, south of New Zealand. This gave rise to the name of the Antipodes Islands of New Zealand, which are close to the antipode of London. The antipodes of Australia are in the North Atlantic Ocean, while parts of Spain, Portugal, and Morocco are antipodal to New Zealand.
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Maximally sized collections of equiangular lines (up to identification of lines as antipodal points on the sphere) are examples of minimal sized spherical 5-designs. There are many sporadic small spherical designs; many of them are related to finite group actions on the sphere. In 2013 Bondarenko, Radchenko, and Viazovska obtained the asymptotic upper bound N(d,t) for all positive integers d and t. This asymptotically matches the lower bound given originally by Delsarte, Goethals, and Seidel.
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From the 9th century onward they were using spherical trigonometry and map projection methods to determine these quantities accurately. The calculation is essentially the conversion of the equatorial polar coordinates of Mecca (i.e. its longitude and latitude) to its polar coordinates (i.e. its qibla and distance) relative to a system whose reference meridian is the great circle through the given location and the Earth's poles, and whose polar axis is the line through the location and its antipodal point.
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This is because there are no antipodal points in elliptic geometry. For example, this is achieved in the hyperspherical model (described below) by making the "points" in our geometry actually be pairs of opposite points on a sphere. The reason for doing this is that it allows elliptic geometry to satisfy the axiom that there is a unique line passing through any two points. Every point corresponds to an absolute polar line of which it is the absolute pole.
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The island is listed with the New Zealand Outlying Islands. The island is an immediate part of New Zealand, but not part of any region or district, but instead Area Outside Territorial Authority, like all other outlying islands, other than the Solander Islands. It is the closest piece of land to the antipodal point of the United Kingdom, and Ireland, meaning that the furthest away city is Limerick, Ireland. Campbell Island is a UNESCO World Heritage Site.
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X-20 Dyna Soar is the project that has come closest to actually building a crewed boost-glide vehicle. This illustration shows the Dyna Soar during reentry. In the immediate post-war era, Soviet rocket engineer Aleksei Isaev found a copy of an updated August 1944 report on the Silbervogel concept. He had the paper translated to Russian, and it eventually came to the attention of Joseph Stalin who was intensely interested in the concept of an antipodal bomber.
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As noted above, the iterative solution to the inverse problem fails to converge or converges slowly for nearly antipodal points. An example of slow convergence is (Φ1, L1) = (0°, 0°) and (Φ2, L2) = (0.5°, 179.5°) for the WGS84 ellipsoid. This requires about 130 iterations to give a result accurate to 1 mm. Depending on how the inverse method is implemented, the algorithm might return the correct result (19936288.579 m), an incorrect result, or an error indicator.
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Note: The original link is dead, but this is the Internet Archive version at the Internet Archive. Retrieved 12 April 2011. "The Azores, that was my antipodal point, I had to sail up there and back to make it a proper circumnavigation..." that during a circumnavigation the sailor must pass two points on opposite sides of the earth (antipodes). For example, if starting in southern England, a place near the start will be opposite to the track near New Zealand.
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About 15% of the earth's land has an antipodes on land. Rough calculation shows that, of the 29% of the earth that is covered by land, if 15% of that has antipodes on land, then about 4% (0.15 x 29% = 4.35%) of the earth's surface has antipodes that are both land surfaces. Spilhaus estimates this at about 3%. The two largest human inhabited antipodal areas are located in East Asia (mainly eastern China) and South America (mainly northern Argentina and Chile).
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The group Spin(3) is isomorphic to the special unitary group SU(2); it is also diffeomorphic to the unit 3-sphere S3 and can be understood as the group of unit quaternions (i.e. those with absolute value 1). The connection between quaternions and rotations, commonly exploited in computer graphics, is explained in quaternions and spatial rotations. The map from S3 onto SO(3) that identifies antipodal points of S3 is a surjective homomorphism of Lie groups, with kernel {±1}.
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Every circle in Euclidean 3-space is a great circle of exactly one sphere. For most pairs of distinct points on the surface of a sphere, there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them. In this sense, the minor arc is analogous to “straight lines” in Euclidean geometry.
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At this point, the space-time becomes regular, the black hole singularity runs off to infinity, and the two horizons are related by a space-time symmetry. In the Nariai limit, the black hole and de Sitter horizon can be interchanged just by changing the sign of the coordinate z. When there is additional matter density, the solution can be thought of as an Einstein spherical universe with two antipodal black holes. Whichever black hole becomes larger becomes the cosmological horizon.
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An animation depicting a massive asteroid–Earth impact and subsequent impact crater formation. The asteroid connected with the extinction of the Cretaceous–Paleogene extinction event released an estimated energy of . corresponding to 100,000,000 Mt of energy, roughly 10,000 times the maximum combined arsenals of the US and Soviet Union in the Cold War. This is hypothesized to have produced sufficient ground-energy coupling to have caused severe mantle plume (volcanism) at the antipodal point (the opposite side of the world).
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Estimates of its age vary from 2 to 4 billion years. Consistent with this picture, imaging by the Galileo spacecraft found no evidence of disruption of the area of Callisto antipodal to Valhalla. Such disrupted terrain normally forms as a result of focusing of the seismic energy at the opposite point after the impact. The absence of such disruption supports the presence of a subsurface ocean, which would have absorbed much of the seismic energy, at the time of Valhalla's formation.
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This set can be the set of equivalence classes under the equivalence relation between vectors defined by "one vector is the product of the other by a nonzero scalar". In other words, this amounts to defining a projective space as the set of vector lines in which the zero vector has been removed. A third equivalent definition is to define a projective space of dimension as the set of pairs of antipodal points in a sphere of dimension (in a space of dimension ).
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The name of this clade is informal and is not assumed to have any particular taxonomic rank like the names authorized by the ICBN or the ICPN. Members of this clade exhibit unusual embryology compared to other legumes, either enlarged antipodal cells in the embryo sac or the production of multiple embryo sacs. There has been a shift from bee pollination to bird pollination several times in this clade. Mirbelioids produce quinolizidine alkaloids, but unlike most papilionoids, they do not produce isoflavones.
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It has been proposed that Ahuna Mons formed as a cryovolcanic dome. It is the closest cryovolcano to the Sun yet discovered. It is roughly antipodal to the largest impact basin on Ceres, diameter Kerwan. Seismic energy from the Kerwan-forming impact may have been focused on the opposite side of Ceres, fracturing the outer layers of the area and facilitating the movement of high viscosity cryovolcanic magma (consisting of muddy water ice softened by its content of salts) that was then extruded onto the surface.
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On the plane ( = 2), a point reflection is the same as a half-turn (180°) rotation; see below. Antipodal symmetry is an alternative name for a point reflection symmetry through the origin. Such a "reflection" preserves orientation if and only if is an even number.William H. Barker, Roger Howe Continuous Symmetry: From Euclid to Klein (Google eBook) American Mathematical Soc This implies that for = 3 (as well as for other odd ), a point reflection changes the orientation of the space, like a mirror- image symmetry.
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The octahedral recurrence is a dynamical system defined on the vertices of the octahedral tiling of space. Each octahedron has 6 vertices, and these vertices are labelled in such a way that : a_1b_1 + a_2b_2 = a_3b_3 Here a_i and b_i are the labels of antipodal vertices. A common convention is that a_2,b_2,a_3,b_3 always lie in a central horizontal plane and a_1,b_1 are the top and bottom vertices. The octahedral recurrence is closely related to C. L. Dodgson's method of condensation for computing determinants.
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These bracketing dates also make it possible that the site could be associated with the Permian–Triassic extinction event. The Permian–Triassic extinction occurred 250 million years ago and is believed to be the largest extinction event since the origin of complex multicellular life. Plate reconstructions for the Permian–Triassic boundary place the putative crater directly antipodal to the Siberian Traps, and Frese et al. (2009) use the controversial theory that impacts can trigger massive volcanism at their antipodes to bolster their impact crater theory.
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The Antipodes Islands are inhospitable and uninhabited volcanic islands in subantarctic waters to the south of – and territorially part of – New Zealand. The archipelago lies to the southeast of Stewart Island/Rakiura, and to the northeast of Campbell Island. They are very close to being the antipodal point to Normandy in France, meaning that the furthest away city from here is Cherbourg, France. The island group consists of one main island, Antipodes Island, of area, Bollons Island to the north, and numerous small islets and stacks.
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The projective plane with the spherical metric is obtained by identifying antipodal points on the unit sphere in \R^3 with its Riemannian spherical metric. In other words, this is the quotient of the sphere by the map x\mapsto -x. Let \Gamma denote the set of closed curves in this projective plane that are not null-homotopic. (Each curve in \Gamma is obtained by projecting a curve on the sphere from a point to its antipode.) Then the spherical metric is extremal for this curve family.
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In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visualised in elliptic space. A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune.
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The minimum distance between edge-point pairs can be maintained with a kinetic tournament. Thus, using kinetic convex hull to maintain the upper and lower envelopes, a kinetic sorted list on these intervals to maintain the antipodal edge-vertex pairs, and a kinetic tournament to maintain the pair of minimum distance apart, the diameter of a moving point set can be maintained. This data structure is responsive, compact and efficient. The data structure uses O(n) space because the kinetic convex hull, sorted list, and tournament data structures all use O(n) space.
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In addition to the twice yearly rasd al-qibla, in most locations the sun crosses the direct path between the location and the Ka'bah each day; at the instant this happens, the sun's shadow points in the direction of the qibla or its antipodal point. The time of this daily event depends upon the location and the day of the year, and can be determined using geographical data and calculations, but this is more complex than the yearly rasd al-qibla, the times of which are the same globally, with no calculations needed.
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A consequence of the hairy ball theorem is that any continuous function that maps an even-dimensional sphere into itself has either a fixed point or a point that maps onto its own antipodal point. This can be seen by transforming the function into a tangential vector field as follows. Let s be the function mapping the sphere to itself, and let v be the tangential vector function to be constructed. For each point p, construct the stereographic projection of s(p) with p as the point of tangency.
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The pressure wave from the third and most violent explosion was recorded on barographs around the world. Several barographs recorded the wave seven times over the course of five days: four times with the wave travelling away from the volcano to its antipodal point, and three times travelling back to the volcano; the wave rounded the globe three and a half times. Ash was propelled to a height of . The sound of the eruption was so loud it was reported that if anyone was within , they would have gone deaf.
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Every unit quaternion is naturally associated to a spatial rotation in 3 dimensions, and the product of two quaternions is associated to the composition of the associated rotations. Furthermore, every rotation arises from exactly two unit quaternions in this fashion. In short: there is a 2:1 surjective homomorphism from SU(2) to SO(3); consequently SO(3) is isomorphic to the quotient group SU(2)/{±I}, the manifold underlying SO(3) is obtained by identifying antipodal points of the 3-sphere , and SU(2) is the universal cover of SO(3).
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Polytene chromosomes in a Chironomus salivary gland cell Polytene chromosome Polytene chromosomes are large chromosomes which have thousands of DNA strands. They provide a high level of function in certain tissues such as salivary glands of insects Polytene chromosomes were first reported by E.G.Balbiani in 1881. Polytene chromosomes are found in dipteran flies: the best understood are those of Drosophila, Chironomus and Rhynchosciara. They are present in another group of arthropods of the class Collembola, a protozoan group Ciliophora, mammalian trophoblasts and antipodal, and suspensor cells in plants.
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To define the section plane select any third point R_0 not on the line from R_1 to R_2. Choosing R_0 to be on the surface normal at P_1 will define the normal section at P_1. If R_0 is the origin then the earth section is the great ellipse. (The origin would be co-linear with 2 antipodal points so a different point must be used in that case). Since there are infinitely many choices for R_0, the above problem is really a class of problems (one for each plane). Let R_0 be given.
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Dominant Logic is antipodal to the idea of using different methods and ways for generating profit. It is similar to the idea of kaizen which focuses on one process. In the field of strategic management, C. K. Prahalad and Richard A. Bettis described the concept of dominant logic in 1986. Prahalad and Bettis suggested that the way top managers deal with the increasing diversity of strategic decisions in a company, which are caused by acquisitions or structural changes in the core business, depends on the cognitive orientation of those top managers.
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There is another theory about the formation of Ithaca Chasma: when the impact that caused the great crater Odysseus occurred, the shock wave traveled through Tethys and fractured the icy, brittle surface. In this case Ithaca Chasma would be the outermost ring graben of Odysseus. However, age determination based on crater counts in high-resolution Cassini images showed that Ithaca Chasma is older than Odysseus making the impact hypothesis unlikely. The smooth plains on the trailing hemisphere are approximately antipodal to Odysseus, although they extend about 60° to the northeast from the exact antipode.
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The two largest monolithic antipodal land areas are most of Chile and Argentina along with eastern and central China and Mongolia, and most of Greenland along with a part of Antarctica. The Australian mainland is the largest landmass with its antipodes entirely in ocean, although some locations of mainland Australia and Tasmania are close to being antipodes of islands (Bermuda, Azores, Puerto Rico) in the North Atlantic Ocean. The largest landmass with antipodes entirely on land is the island of Borneo, whose antipodes are in the Amazon rainforest.
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A person walking completely around either pole will cross all meridians, but this is not generally considered a "circumnavigation". The path of a true (global) circumnavigation forms a continuous loop on the surface of Earth separating two regions of comparable area. A basic definition of a global circumnavigation would be a route which covers roughly a great circle, and in particular one which passes through at least one pair of points antipodal to each other. In practice, people use different definitions of world circumnavigation to accommodate practical constraints, depending on the method of travel.
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Schematic of PKP(BC) and PKP(DF) waves Location of the South Sandwich Islands, which are nearly antipodal to Alaska. The main observational constraints on inner core rotation come from seismology. When an earthquake occurs, two kinds of seismic wave travel down through the Earth: those with ground motion in the direction the wave propagates (p-waves) and those with transverse motion (s-waves). S-waves do not travel through the outer core because they involve shear stress, a type of deformation that cannot occur in a liquid.
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A similar result is the Borsuk–Ulam theorem, which says that a continuous map from the n-sphere to Euclidean n-space will always map some pair of antipodal points to the same place. Proof for 1-dimensional case: Take f to be any continuous function on a circle. Draw a line through the center of the circle, intersecting it at two opposite points A and B. Define d to be f(A)-f(B). If the line is rotated 180 degrees, the value −d will be obtained instead.
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Neurologists have focused objectively on organic nervous system pathology, especially of the brain, whereas psychiatrists have laid claim to illnesses of the mind. This antipodal distinction between brain and mind as two different entities has characterized many of the differences between the two specialties. However, it has been argued that this division is fictional; evidence from the last century of research has shown that our mental life has its roots in the brain. Brain and mind have been argued not to be discrete entities but just different ways of looking at the same system (Marr, 1982).
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For , every -critical graph (that is, every odd cycle) can be generated as a -constructible graph such that all of the graphs formed in its construction are also -critical. For , this is not true: a graph found by as a counterexample to Hajós's conjecture that -chromatic graphs contain a subdivision of , also serves as a counterexample to this problem. Subsequently, -critical but not -constructible graphs solely through -critical graphs were found for all . For , one such example is the graph obtained from the dodecahedron graph by adding a new edge between each pair of antipodal vertices.
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Because some distinct pairs of antipodes are all taken to identical points in the Roman surface, it is not homeomorphic to RP2, but is instead a quotient of the real projective plane RP2 = S2 / (x~-x). Furthermore, the map T (above) from S2 to this quotient has the special property that it is locally injective away from six pairs of antipodal points. Or from RP2 the resulting map making this an immersion of RP2 — minus six points — into 3-space. (It was previously stated that the Roman surface is homeomorphic to RP2, but this was in error.
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North Magnetic Pole Moving East Due to Core Flux, National Geographic, December 24, 2009 As of 2019, the pole is projected to have moved beyond the Canadian Arctic to .NP.xy Its southern hemisphere counterpart is the South Magnetic Pole. Since Earth's magnetic field is not exactly symmetrical, the North and South Magnetic Poles are not antipodal, meaning that a straight line drawn from one to the other does not pass through the geometric center of Earth. Earth's North and South Magnetic Poles are also known as magnetic dip poles, with reference to the vertical "dip" of the magnetic field lines at those points.
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To make the longest distance trip around the planet a traveler would have to pass through a set of antipodal points. All meridians can be crossed in one hemisphere—indeed, by walking around one of the poles—but such trips are shorter than a maximum circumnavigation. On the other hand, the greatest straight line distance that could in theory be covered is a trip exactly on the Equator, a distance of . The Earth's equatorial bulge makes this slightly longer than a north-south trip around the world along a set of meridian lines, which is a distance of .
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According to adjudicating bodies Guinness World Records and Explorersweb, Jason Lewis completed the first human-powered circumnavigation of the globe on 6 October 2007. This was part of a thirteen-year journey entitled Expedition 360. In 2012, Turkish-born American adventurer Erden Eruç completed the first entirely solo human-powered circumnavigation, travelling by rowboat, sea kayak, foot and bicycle from 10 July 2007 to 21 July 2012, crossing the equator twice, passing over 12 antipodal points, and logging in 1,026 days of travel time, excluding breaks. National Geographic lists Colin Angus as being the first to complete a global circumnavigation.
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However, his journey did not cross the equator or hit the minimum of two antipodal points as stipulated by the rules of Guinness World Records and AdventureStats by Explorersweb. People have both bicycled and run around the world, but the oceans have had to be covered by air or sea travel, making the distance shorter than the Guinness guidelines. To go from North America to Asia on foot is theoretically possible but very difficult. It involves crossing the Bering Strait on the ice, and around of roadless swamped or freezing cold areas in Alaska and eastern Russia.
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But more recently some geologists, such as Gillian Foulger view upper-mantle convection as a cause. This in turn has re-raised the antipodal pair impact hypothesis, the idea that pairs of opposite hot spots may result from the impact of a large meteor. Geologists have identified some 40-50 such hotspots around the globe, with Hawaii, Réunion, Yellowstone, Galápagos, and Iceland overlying the most currently active. An example of a hotspot volcanic belt is the Anahim Volcanic Belt in British Columbia, Canada, which was formed as a result of the North American Plate sliding westward over the Anahim hotspot.
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The sphere model is obtained by intersecting the lines and planes through the origin with a unit sphere centered at the origin. The lines meet the sphere in antipodal points which must then be identified to obtain a point of the projective plane, and the planes meet the sphere in great circles which are thus the lines of the projective plane. That this association "preserves" incidence is most easily seen from the lines and planes model. A point incident with a line in the projective plane corresponds to a line through the origin lying in a plane through the origin in the model.
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Development of the megagametophyte and fertilization in Arabidopsis thaliana. MMC - megaspore mother cell; FM - functional megaspore; AP - antipodal cells; CC - central cell; EC - egg cell; SC - synergid cell; PT - pollen tube; SP - sperm; VN - vegetative nucleus; EM - embryo; EN - endosperm; SUS - suspensor A megaspore mother cell, or megasporocyte, is a diploid cell in plants in which meiosis will occur, resulting in the production of four haploid megaspores. At least one of the spores develop into haploid female gametophytes (megagametophytes).Solomon, Eldra P., 2005, Biology, Thomson, Brooks/Cole, United States The megaspore mother cell arises within the megasporangium tissue.
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The Deccan Traps eruption coincided roughly with the nearly antipodal Chicxulub impactor and the Cretaceous–Paleogene extinction of the dinosaurs, and there is considerable speculation that the three events were related. As the Indian plate drifted north, the hotspot continued to punch through the plate, creating a string of volcanic islands and undersea plateaux. The Laccadive Islands, the Maldives, and the Chagos Archipelago are atolls resting on former volcanoes created 60–45 million years ago that subsequently submerged below sea level. About 45 million years ago the Central Indian Ridge crossed over the hotspot, and the hotspot passed under the African Plate.
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For very high supersonic/low hypersonic flight speeds, inserting a cooling system into the air duct of a hydrogen jet engine permits greater fuel injection at high speed and obviates the need for the duct to be made of refractory or actively cooled materials. This greatly improves the thrust/weight ratio of the engine at high speed. It is thought that this design of engine could permit sufficient performance for antipodal flight at Mach 5, or even permit a single stage to orbit vehicle to be practical. The hybrid air-breathing SABRE rocket engine is a pre-cooled engine under development.
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A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v, are also shown. The great-circle distance, orthodromic distance, or spherical distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In spaces with curvature, straight lines are replaced by geodesics.
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Angus was joined bicycling in Europe by his then fianceé Julie Wafaei, who purchased a rowboat for them to cross the Atlantic. The British adventurer Jason Lewis, claims that Angus' journey was not a circumnavigation, because it did not pass through two antipodal points on the globe, although this is not required by Guinness World Records . The ship's log on the Russian research vessel Professor Khromov cite a high-seas rescue in support of the expedition. Angus had to fly to Canada for medical treatment during the expedition, but flew back to Russia to continue from the point he had left beforehand.
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This is the only metric on the Möbius band, up to uniform scaling, that is both flat and complete. The group of isometries of this Möbius band is 1-dimensional and is isomorphic to the orthogonal group SO(2). Constant positive curvature: A Möbius band of constant positive curvature cannot be complete, since it is known that the only complete surfaces of constant positive curvature are the sphere and the projective plane. The projective plane P2 of constant curvature +1 may be constructed as the quotient of the unit sphere S2 in R3 by the antipodal map A: S2 → S2, defined by .
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Ocean topography (see scale) and some paths traveled by sound waves during the 1991 Heard Island Feasibility Test. Beginning in 1975, Munk and Carl Wunsch of the Massachusetts Institute of Technology pioneered the development of acoustic tomography of the ocean. With Peter Worcester and Robert Spindel, Munk developed the use of sound propagation, particularly sound arrival patterns and travel times, to infer important information about the ocean's large-scale temperature and current. This work, together with the work of other groups, eventually motivated the 1991 "Heard Island Feasibility Test" (HIFT), to determine if man-made acoustic signals could be transmitted over antipodal distances to measure the ocean's climate.
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The shadows cast during these times point in the exact opposite direction shown during the rasd al- qibla. The antipodal events occur on 12, 13, or 14 January at 00:30 SAST (21:30 UTC on the previous day), and again on 28 or 29 November 00:09 SAST (21:09 UTC). During any of these events, observations made within a five- minute interval, and at the same time one or two days before or after the prescribed date, are accurate with negligible deviation. A practical problem occurs in locations whose angular distances to Mecca are almost equal to 90° at the edge of the hemisphere centred in Mecca.
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The tesseral variation has one cycle per latitude, one bulge and one depression; the bulges are opposed (antipodal), in other words the western part of the northern hemisphere and the eastern part of the southern hemisphere, for example. Similarly, the depressions are opposed, in this case the eastern part of the northern hemisphere and the western part of the southern hemisphere. Finally, fortnightly and semi-annual tides have zonal deformations (constant along a circle of latitude), as the Moon or Sun gravitation is directed alternately away from the northern and southern hemispheres due to tilt. There is zero vertical displacement at 35°16' latitude.
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As a first-order approximation, Earth's magnetic field can be modeled as a simple dipole (like a bar magnet), tilted about 10° with respect to Earth's rotation axis (which defines the Geographic North and Geographic South Poles) and centered at Earth's center. The North and South Geomagnetic Poles are the antipodal points where the axis of this theoretical dipole intersects Earth's surface. If Earth's magnetic field were a perfect dipole then the field lines would be vertical at the Geomagnetic Poles, and they would coincide with the Magnetic Poles. However, the approximation is imperfect, and so the Magnetic and Geomagnetic Poles lie some distance apart.
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Sequence of probes around the convex hull of a polygon to determine its diameter using Rotating Caliper method. In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points. The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon."Rotating Calipers" at Toussaint's home page Every time one blade of the caliper lies flat against an edge of the polygon, it forms an antipodal pair with the point or edge touching the opposite blade.
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Lazarev's character is based on a real person as well, but his real-life role was to penetrate Vlasov detachments to convince Vlasovites to give themselves up. In the film, Lazarev voluntarily gives himself up to partisans, and two partisan leaders (of antipodal characters), Commander Lokotkov and Commissar Petushkov, put the collaborator to the test. For some partisans, he will be always a traitor and treated with suspicion, but for others this former Red Army officer, by joining the group of partisans, has to prove himself on the battlefield as a patriot and hero. In the end he got killed in action distinguishing himself by bravery and heroism.
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The identity rotation is a point, and a small angle of rotation about some axis can be represented as a point on a sphere with a small radius. As the angle of rotation grows, the sphere grows, until the angle of rotation reaches 180 degrees, at which point the sphere begins to shrink, becoming a point as the angle approaches 360 degrees (or zero degrees from the negative direction). This set of expanding and contracting spheres represents a hypersphere in four-dimensional space (a 3-sphere). Just as in the simpler example above, each rotation represented as a point on the hypersphere is matched by its antipodal point on that hypersphere.
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The meridian of the British Royal Observatory in Greenwich, in southeast London, England, is the international prime meridian, although some organizations—such as the French Institut Géographique National—continue to use other meridians for internal purposes. The prime meridian determines the proper Eastern and Western Hemispheres, although maps often divide these hemispheres further west in order to keep the Old World on a single side. The antipodal meridian of Greenwich is both 180°W and 180°E. This is not to be conflated with the International Date Line, which diverges from it in several places for political and convenience reasons, including between far eastern Russia and the far western Aleutian Islands.
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This correlation in the case of can be described geometrically using the model of the real projective plane which is a "unit sphere with antipodesthe points of a sphere at opposite ends of a diameter are called antipodal points. identified", or equivalently, the model of lines and planes through the origin of the vector space . Associate to any line through the origin the unique plane through the origin which is perpendicular (orthogonal) to the line. When, in the model, these lines are considered to be the points and the planes the lines of the projective plane , this association becomes a correlation (actually a polarity) of the projective plane.
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However, this effect could be largely mitigated, even reversed, by a release of enormous quantities of water vapor and carbon dioxide caused by the initial global heat pulse after the impact. If the asteroid hit an ocean (which would be the case with the majority of impact events), water vapor would form the majority of any ejected matter, and would likely result in a major greenhouse effect and a net increase in temperature. If the impact event is sufficiently energetic it can cause mantle plume (volcanism) at the antipodal point (the opposite side of the world). This volcanism could alone therefore create a volcanic winter, irrespective of the other impact effects.
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In Torchwood: Miracle Day (2011), The Blessing is revealed to be an antipodal geological formation connected to the Earth's morphic field running from Shanghai and Buenos Aires. Captain Jack Harkness theorises that it may have been caused by the interaction of Racnoss Huon particles and Silurian hibernation matrixes, though its origins are unknown. The Families are unsure of whether or not to classify the Blessing as alive, though it is stated to have a degree of sentience. One of its features is that it has the ability to show approachings human the content of their own souls, which has caused some to commit suicide, others to find conviction.
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The simplest model for elliptic geometry is a sphere, where lines are "great circles" (such as the equator or the meridians on a globe), and points opposite each other (called antipodal points) are identified (considered the same). This is also one of the standard models of the real projective plane. The difference is that as a model of elliptic geometry a metric is introduced permitting the measurement of lengths and angles, while as a model of the projective plane there is no such metric. In the elliptic model, for any given line and a point A, which is not on , all lines through A will intersect .
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In addition to these processes, impact events such as ones that created the Addams crater on Venus and the Sudbury Igneous Complex in Canada are known to have caused melting and volcanism. In the impact hypothesis, it is proposed that some regions of hotspot volcanism can be triggered by certain large-body oceanic impacts which are able to penetrate the thinner oceanic lithosphere, and flood basalt volcanism can be triggered by converging seismic energy focused at the antipodal point opposite major impact sites. Impact- induced volcanism has not been adequately studied and comprises a separate causal category of terrestrial volcanism with implications for the study of hotspots and plate tectonics.
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Eruç logged while rowing across three oceansthe Pacific, Indian and Atlanticand cycling across three continentsAustralia, Africa and North America. He became the first person to solo circumnavigate the globe entirely on his own power. He crossed the equator two times, passed over twelve pairs of antipodal points and spent five years and eleven days of his life completing the endeavorthe world record time for a human-powered circumnavigation. The total elapsed time of over five years included several long periods of downtime spent away from the route, for a total of about 26 months, with Eruç always continuing again from the exact location where he had last stopped.
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One of the major contributions of the research group led by Bhattacharyya was the demonstration of the antipodal nature of constituents of Vetiver Oil. Overall, he was known to have isolated over 100 compounds falling under terpenoids and coumarins categories. Bhattacharyya published his researches in over 250 articles and he and his team held patents for some of the processes they developed. On the academic front, he gathered a team of researchers under a new division for research on essential oils and established the department of chemistry of Indian Institute of Technology, Mumbai where he served as a senior professor for over a decade.
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In geodetic applications, where is small, the integrals are typically evaluated as a series . For arbitrary , the integrals (3) and (4) can be found by numerical quadrature or by expressing them in terms of elliptic integrals . provides solutions for the direct and inverse problems; these are based on a series expansion carried out to third order in the flattening and provide an accuracy of about for the WGS84 ellipsoid; however the inverse method fails to converge for nearly antipodal points. continues the expansions to sixth order which suffices to provide full double precision accuracy for and improves the solution of the inverse problem so that it converges in all cases.
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Every smooth surface or curve in Euclidean space is a metric space, in which the (intrinsic) distance between two points of is defined as the infimum of the lengths of the curves that go from to along . For example, on a closed curve C of length , for each point of the curve there is a unique other point of the curve (called the antipodal of ) at distance from . A compact surface fills a closed curve if its border (also called boundary, denoted ) is the curve . The filling is said isometric if for any two points of the boundary curve , the distance between them along is the same (not less) than the distance along the boundary.
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In the same paper where Gromov stated the conjecture, he proved that :the hemisphere has least area among the Riemannian surfaces that isometrically fill a circle of given length, and are homeomorphic to a disk. Proof: Let M be a Riemannian disk that isometrically fills its boundary of length 2L . Glue each point x\in \partial M with its antipodal point -x , defined as the unique point of \partial M that is at the maximum possible distance L from x . Gluing in this way we obtain a closed Riemannian surface M' that is homeomorphic to the real projective plane and whose systole (the length of the shortest non-contractible curve) is equal to L .
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As a result, over northern South America and the south Atlantic, near Singapore's antipodal point, the magnetic field is relatively weak, resulting in a lower repulsion to trapped particles of the radiation belts there, and as a result these particles reach deeper into the upper atmosphere than they otherwise would. The shape of the SAA changes over time. Since its initial discovery in 1958, the southern limits of the SAA have remained roughly constant while a long-term expansion has been measured to the northwest, the north, the northeast, and the east. Additionally, the shape and particle density of the SAA varies on a diurnal basis, with greatest particle density corresponding roughly to local noon.
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This theory argues that the high albedo of the swirls is the result of an impact with a comet. The impact would cause scouring of the top-most surface regolith by the coma’s turbulent flow of gas and dust, which exposed fresh material and redeposited the fine, scoured material in discrete deposits. According to this model, the associated strong magnetic anomalies are the result of magnetization of near-surface materials heated above the Curie temperature through hyper-velocity gas collisions and micro-impacts as the coma impacted the surface. Proponents of the cometary impact model consider the occurrence of many swirls antipodal the major basins to be coincidental or the result of incomplete mapping of swirl locations.
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If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron. The triangular hebesphenorotunda also has clusters of faces that can be aligned with corresponding faces of the rhombicosidodecahedron: the three lunes, each lune consisting of a square and two antipodal triangles adjacent to the square. The faces around each (33.5) vertex can also be aligned with the corresponding faces of various diminished icosahedra. Johnson uses the prefix hebespheno- to refer to a blunt wedge-like complex formed by three adjacent lunes, a lune being a square with equilateral triangles attached on opposite sides.
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Accordingly, the Sith reject altruism, self-abnegation and kindness, as they regard such attitudes as founded on delusions that fetter one's perceptions and power. In connection with their philosophy, the Sith draw on the Dark Side of the Force through severe negative emotions, a technique antipodal to that of their archenemies, the Jedi, who rely on the Force's "light side," i.e., the Force as experienced through disciplined states of quietude and compassion. Notably, both the Jedi and Sith shun romantic and familial love, as the Jedi fear such love will lead to attachment, and thus selfishness, and the Sith fear it will compromise their ruthlessness and connection to the Dark Side of the Force.
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Aviation records take account of the wind circulation patterns of the world; in particular the jet streams, which circulate in the northern and southern hemispheres without crossing the equator. There is therefore no requirement to cross the equator, or to pass through two antipodal points, in the course of setting a round-the-world aviation record. Thus, for example, Steve Fossett's global circumnavigation by balloon was entirely contained within the southern hemisphere. For powered aviation, the course of a round-the-world record must start and finish at the same point and cross all meridians; the course must be at least long (which is approximately the length of the Tropic of Cancer).
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In mathematics--specifically, in Riemannian geometry--a Wiedersehen pair is a pair of distinct points x and y on a (usually, but not necessarily, two- dimensional) compact Riemannian manifold (M, g) such that every geodesic through x also passes through y (and the same with x and y interchanged). For example, on an ordinary sphere where the geodesics are great circles, the Wiedersehen pairs are exactly the pairs of antipodal points. If every point of an oriented manifold (M, g) belongs to a Wiedersehen pair, then (M, g) is said to be a Wiedersehen manifold. The concept was introduced by the Austro- Hungarian mathematician Wilhelm Blaschke and comes from the German term meaning "seeing again".
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The original definition of the surrealist object art comes from the French poet Comte de Lautréamont. In his poem Les Chants de Maldoror he describes the beauty of the young man Mervyn using antipodal metaphors: "He is as beautiful (..) as the chance encounter of a sewing machine and an umbrella on a dissecting table". In 1937 the French editor Gallimard prepared the publication of the collected works of Lautréamont in an illustrated luxury edition, and André Breton invited besides other artists also Paalen to contribute with an illustration Breton selected (from two proposals) the drawing Vieil océan (old Ocean), which was published in the Gallimard edition next to the appropriate text.Comte de Lautréamont, Oeuvres complètes, Paris 1938, p.
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The narrator criticizes Sam throughout, showing him talking a good game, but always opting to remain passive: "without the courage to live, to defy—especially to defy his smug psychoanalyst—Sam will never quite be a man". He sees himself as a rebel and wants desperately to be a man, but he is incapable of manly aggression or courage; this, for Mailer, is a cardinal sin: courage and risk-taking are key to psychic growth. "Yoga" is a portrait of American ambivalence and bad faith. Similarly, Philip H. Bufithis argues that the main conflict in "Yoga" lies in the distinction between thought and action: "reflection upon experience is antipodal to its enjoyment".
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He has also organised semi competitive road events in the UK. He has made films and written books about his journeys. In 1981 Sanders set the original record for World record for cycling around the World, riding 13,609 miles (21,900 km) around the Northern Hemisphere in 138 days. In 1984 he repeated the world cycling circumnavigation riding about 22,000 km in a time of 79 days. Guinness World Records set the rules in 2003 and did not record Sanders' time as he did not cross antipodal points on the globe Sanders still holds the Guinness World Record for fastest ride around the coast of Great Britain, riding a verified 4,800 miles (7,720 km) in 22 days.
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At the climax of "The Gathering" she meets The Mother (Frances Fisher), the Shanghai representative of the Families, who introduces her to the Blessing, an antipodal geological formation which is said to show an individual the contents of their soul. When asked what the Blessing reveals to her Jilly appears unfazed, replying "That I'm right." She is present for a final philosophical stand-off between Torchwood – represented by Jack Harkness (John Barrowman) and Gwen Cooper – and the Families and throws her allegiance behind the Families' plan for world power, responding to a moral appeal by Cooper by declaring that she considers all altruism to be fraudulent. After Torchwood end the Miracle and Oswald blows up the Shanghai facility, Kitzinger escapes alive.
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Cuba and Sri Lanka have cooperated in a number of sectors with the goal of mutual development and economic progress. This cooperation has been especially noted in the sectors of risk management and biotechnology.Cuba and Sri Lanka Strengthen Cooperation Mathaba News Network - December 16, 2008 Ties in the agriculture sector have been developed, and the similar climates of both countriesSri Lanka - Cuba, Antipodal and photographic reflections Sri Lanka Daily News - January 7, 2004 have enabled the countries to work on developing crops such as papaya and coconut. Many traders from the Havana region of Cuba have settled in the North & North West of Sri Lanka in the early 20th century and made communities which no longer seem to be visible.
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Spherical geometry obeys two of Euclid's postulates: the second postulate ("to produce [extend] a finite straight line continuously in a straight line") and the fourth postulate ("that all right angles are equal to one another"). However, it violates the other three: contrary to the first postulate, there is not a unique shortest route between any two points (antipodal points such as the north and south poles on a spherical globe are counterexamples); contrary to the third postulate, a sphere does not contain circles of arbitrarily great radius; and contrary to the fifth (parallel) postulate, there is no point through which a line can be drawn that never intersects a given line.Gowers, Timothy, Mathematics: A Very Short Introduction, Oxford University Press, 2002: pp. 94 and 98.
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Whilst on a mission in Los Angeles, Gwen asks Rhys to remove her father Geraint (William Thomas) from a hospital which she believes to be unsafe. Rhys subsequently has Geraint sent to an "overflow camp", unaware that it contains a facility for burning the severely injured alive, and in "The Categories of Life" and "The Middle Men" has to go undercover to help rescue his father-in-law. After escaping from the facility with Geraint, Rhys is briefly held hostage in an attempt to force Gwen to surrender Jack Harkness, but is rescued by Andy and his team. In "The Gathering", Rhys figures out the antipodal connection between Buenos Aires and Shanghai, which directs the Torchwood team to their final mission.
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Operators may also receive and transmit on different frequencies, called split operation, in order to be heard by distant stations without interference to their signal from the pileup. This can also help the operation to make a substantial number of contacts with parts of the planet that have unfavourable propagation from the area visited, lying perhaps in the region on the Earth's surface which is diametrically opposite to it—its antipodal point. Examples would be the Central Pacific from Europe, or the Caribbean from Japan. For smaller operations to remote locations, smaller radios which run off of a 12 V DC power supply and antenna systems which are more easily transported are favored over larger and more difficult to transport equipment.
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Now 1899, the Chums receive a telephone call with instructions to head southwest and await course correction via the airship's new Tesla device (or radio). The Inconvenience sails over several unknown and sparsely populated islands, where work details can be observed from the deck, until finally setting down on an island called St. Masque, the last island where they could take on perishable supplies. The Chums receive their assignment from extended radio communiques, arriving at a volcano antipodal to Colorado Springs, to observe what would happen there during Dr. Tesla's experiments in Colorado. Waiting for the experiment, the Chums begin a quarrelsome debate over what the replacement figurehead should be (having lost their previous one of President McKinley's head in a collision with a Chicago skyscraper).
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Rex clears his name with the CIA by exposing the real traitor Brian Friedkin (Wayne Knight) and rejoins the organisation whilst Gwen, Jack and Esther go back into hiding. In the series finale Rex travels to Buenos Aires to meet Esther, whilst Jack and Gwen head to Shanghai, each pair seeking one of two access points to the Blessing, an antipodal geological formation connected to the Earth's morphic field. Flashbacks reveal that Esther has transfused Rex with Jack's mortal blood; by releasing this blood the two men are able to reset the human morphic field and restore death. At Esther's funeral Rex discovers that he has acquired Jack's self healing abilities when he is shot by the Families' CIA mole Charlotte (Marina Benedict) and resurrects.
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Twice every year, the Sun culminates at the zenith of the Muslim holy site the Ka'bah at local solar noon, allowing the qibla (Muslim sacred direction) to be found in other parts of the world by observing the shadows cast by vertical objects. These moments occur on 27 and 28 May at 12:18 Saudi Arabia Standard Time (SAST) (09:18 UTC), and on 15 and 16 July, when solar noon is at 12:27 SAST (09:27 UTC). At these times the sun appears in the direction of the Ka'bah and is visible to any observer on earth, and shadows cast by vertical objects indicate the direction. At two other moments, the sun passes the nadir (antipodal zenith) of Mecca, casting shadows that point in the opposite direction, and thus also determine the qibla.
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An idea originated by Robert P. Carmichael in 1955 is that hydrogen-fueled engines could theoretically have much higher performance than hydrocarbon-fueled engines if a heat exchanger were used to cool the incoming air. The low temperature allows lighter materials to be used, a higher mass-flow through the engines, and permits combustors to inject more fuel without overheating the engine. This idea leads to plausible designs like Reaction Engines SABRE, that might permit single- stage-to-orbit launch vehicles, and ATREX, which could permit jet engines to be used up to hypersonic speeds and high altitudes for boosters for launch vehicles. The idea is also being researched by the EU for a concept to achieve non-stop antipodal supersonic passenger travel at Mach 5 (Reaction Engines A2).
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Stevenson has starred in several feature films, primarily in supporting roles. He made his debut in The Theory of Flight (1998) with Kenneth Branagh and Helena Bonham Carter, where he played the part of a gigolo hired to help Bonham Carter's character to lose her virginity. In 2002, Stevenson starred in a short film No Man's Land, which was the antipodal picture from actor/director Edward Hicks prior to his graduation from the London Film School. In the 12½ minute film, set during World War I, Stevenson portrayed an experienced private who is forced to help a novice officer (David Birkin), back to safety after they both find themselves trapped and isolated in "No Man's Land" during the Battle of Ypres. In 2004, Stevenson starred alongside Clive Owen and Keira Knightley in King Arthur.
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The hypersphere of rotations for the rotations that have a "horizontal" axis (in the xy-plane). Also, each rotation is actually represented by two antipodal points on the sphere, which are at opposite ends of a line through the center of the sphere. This reflects the fact that each rotation can be represented as a rotation about some axis, or, equivalently, as a negative rotation about an axis pointing in the opposite direction (a so-called double cover). The "latitude" of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees.
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This loop cannot be shrunk to a point, since no matter how you deform the loop, the start and end point have to remain antipodal, or else the loop will "break open". In terms of rotations, this loop represents a continuous sequence of rotations about the z-axis starting and ending at the identity rotation (i.e. a series of rotations through an angle φ where φ runs from 0 to 2π). Surprisingly, if you run through the path twice, i.e., from north pole down to south pole and back to the north pole so that φ runs from 0 to 4π, you get a closed loop which can be shrunk to a single point: first move the paths continuously to the ball's surface, still connecting north pole to south pole twice.
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There is some evidence to link the Deccan Traps eruption to the contemporaneous asteroid impact that created the nearly antipodal Chicxulub crater in the Mexican state of Yucatán. Although the Deccan Traps began erupting well before the impact, argon-argon dating suggests that the impact may have caused an increase in permeability that allowed magma to reach the surface and produced the most voluminous flows, accounting for around 70% of the volume. The combination of the asteroid impact and the resulting increase in eruptive volume may have been responsible for the mass extinctions that occurred at the time that separates the Cretaceous and Paleogene periods, known as the K–Pg boundary. A more recent discovery appears to demonstrate the scope of the destruction from the impact alone, however.
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Mariner 10 photomosaic The Discovery quadrangle lies within the heavily cratered part of Mercury in a region roughly antipodal to the 1550-km-wide Caloris Basin. Like the rest of the heavily cratered part of the planet, the quadrangle contains a spectrum of craters and basins ranging in size from those at the limit of resolution of the best photographs (200 m) to those as much as 350 km across, and ranging in degree of freshness from pristine to severely degraded. Interspersed with the craters and basins both in space and time are plains deposits that are probably of several different origins. Because of its small size and very early segregation into core and crust, Mercury has seemingly been a dead planet for a long time—possibly longer than the Moon.
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Erden Eruç ( Air-den Air-rooch; born 14 July 1961) is a Turkish-American adventurer who became the first person in history to complete an entirely solo and entirely human-powered circumnavigation of the Earth on 21 July 2012 in Bodega Bay, California, United States. The journey had started from Bodega Bay a little more than five years earlier on 10 July 2007. The modes of transport included a rowboat to cross the oceans, a sea kayak for shorelines, a bicycle on the roads and hiking on trails, along with canoes for a few river crossings. The route he followed was long, crossed the equator twice and all lines of longitude, and passed over twelve pairs of antipodal points, meeting all the requirements for a true circumnavigation of the globe.
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The source of the Siberian Traps basaltic rock has been attributed to a mantle plume, which rose until it impacted against the bottom of the Earth's crust, producing volcanic eruptions through the Siberian Craton. It has been suggested that, as the Earth's lithospheric plates moved over the mantle plume (the Iceland plume), the plume produced the Siberian Traps in the Permian and Triassic periods, later going on to produce volcanic activity on the floor of the Arctic Ocean in the Jurassic and Cretaceous, and then generating volcanic activity in Iceland. Other plate tectonic causes have also been suggested. Another possible cause may be the impact that formed the Wilkes Land crater in Antarctica, which is estimated to have occurred around the same time and been nearly antipodal to the traps.
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262 f. In fact, the god (under the name Vetis) is placed in the last case (number 16) of the outer rim of the Piacenza Liver—before Cilens (Nocturnus), who ends (or begins in the Etruscan vision) the disposition of the gods. In Martianus Capella's division of heaven, he is found in region XV with the dii publici; as such, he numbers among the infernal (or antipodal) gods. The location of his two temples in Rome—near those of Jupiter (one on the Capitoline Hill, in the low between the arx and the Capitolium, between the two groves where the asylum founded by Romulus stood, the other on the Tiber Island near that of Iuppiter Iurarius, later also known as temple of Aesculapius)Ovid Fasti I 291–294.
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He took his inspiration from the classics of modern painting, mainly the work of František Kupka. From 1960 he produced non–figurative paintings, in the beginning with quite a variable artistic form, which later became stabilized in two main lines, antipodal in a certain way and built on common aesthetic principle. It was based on the expression of the dynamism of life, sensualistic relation to reality and a harmosation principle dominating the whole of the painting. Vašíček reacted to the topical incentives of world art, for instance by increased interest in the expression value of the surface structure of the painting matter, by return to the principles of geometric abstraction, the Freedom of Tashist painting and spontaneity of gestic art, transforming all of these incentives into his own individual version rooted in the world of the artist's original thinking.
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The 2D kinetic minimum box builds on the 2D kinetic convex hull in a manner similar to the kinetic width data structure which maintains the pair of minimum-distance parallel lines that have the entire point set between them. In this case, since a box consists of two pairs of parallel lines (that are perpendicular to each other), analogy can be made with running two perpendicular kinetic width problems, and the data-structure needs to maintain sets of four points two antipodal pairs which have perpendicular supporting lines. In the dual view where a point maps to a line , four envelopes (left, right, upper, lower) are computed. The range in x-values of a line segment in one of these envelopes corresponds to the range in the supporting slopes of the corresponding convex hull vertex in the primal view.
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In 2006, the Adventure publication of the National Geographic Society honored Canadians Colin Angus and Julie Wafaei as Adventurers of the Year for their "journey around the world" by human power, however, the Society stated they do not "act as an official arbiter of geographic issues". Angus' journey did not cross the equator or hit the minimum of two antipodal points as stipulated by the rules of Guinness World Records or AdventureStats by Explorersweb. Additionally, in the February 2013 issue of Outside Magazine, Angus's then traveling partner Tim Harvey went on the record to say the pair "put up an emergency sail, using it for about 95 nautical miles" crossing the Bering Sea between Alaska and Siberia. As journalist Nick Heil pointed out, this alone was enough to disqualify a human-powered claim of any description.
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As distinct from all the aforementioned geodesic lines, which may appear straight but are actually arcs of great circles projected on the spheroidal surface of the earth and, accordingly, are not truly straight but rather curving lines, authentically straight lines can be projected through the interior of the earth between almost any two points on the surface of the earth (some extreme topographical situations being the rare exceptions). If a line projected from the summit of Cayambe in Ecuador (see highest points) to the axial centre of the earth is extended to its antipode on the island of Sumatra, then the resulting diametrical line would be the longest truly straight line that could be produced anywhere on earth. As the variable circumference of the earth approaches , such a maximum "diametrical" or "antipodal" line would be on the order of long.
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In the present day, Angelo's granddaughter Olivia (Nana Visitor) explains that the descendants of three local businessmen who wished to purchase Jack's powers—"the Three Families"—are responsible for the miracle, using Jack's blood in conjunction with what they call "the Blessing". In "The Gathering", the team ultimately track down the Families and the Blessing, which is revealed to be an antipodal geological formation connected to the Earth's morphic field running from Shanghai and Buenos Aires; the team divide, attempting to reach both access points. To end the miracle, in "The Blood Line", Jack has Gwen kill him so that his mortal blood can reset the human morphic field; Gwen kills him with a bullet through the chest, while Rex—who transfused himself with Jack's blood to keep it safe—allows the Blessing to drain him too, in Buenos Aires. Rex survives, and with the morphic field restored, Jack resurrects.
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If the geographic coordinates (latitude and longitude) of a point on the Earth's surface are (φ, θ), then the coordinates of the antipodal point are (−φ, θ ± 180°). This relation holds true whether the Earth is approximated as a perfect sphere or as a reference ellipsoid. In terms of the usual way these geographic coordinates are given, this transformation can be expressed symbolically as :x° N/S y° E/W ↦ x° S/N (180 − y)° W/E, that is, for the latitude (the North/South coordinate) the magnitude of the angle remains the same but N is changed to S and vice versa, and for the longitude (the East/West coordinate) the angle is replaced by its supplementary angle while E is exchanged for W. For example, the antipode of the point in China at (a few hundred kilometres from Beijing) is the point in Argentina at (a few hundred kilometres from Buenos Aires).
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Jurišić received a B.A. from the University of Ljubljana in 1987, and an M.Sc. and Ph.D. from the University of Waterloo in 1990 and 1995.Antipodal covers : a thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of doctor of philosophy in combinatorics and optimization Jurišić wrote a book of problems for mathematics competitions in 1989, and in 2005 he became a co-founder of the Slovenian Society of Cryptology. Aleksandar Jurišić is a full professor of cryptography and computer security at the Faculty of Computer and Information Science at the University of Ljubljana, where he is the head of the Laboratory for cryptography and computer securityFRI 20 : 1996-2016 : 20 let Fakultete za računalništvo in informatiko Univerze v Ljubljani, 2016, page 27 Laboratory for cryptography and computer security, Faculty of Computer and Information Science, University of Ljubljana and a researcher at the Institute of Mathematics, Physics, and Mechanics (IMFM), in Ljubljana, Slovenia.
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After many failed attempts to derive the parallel postulate from other axioms, the study of the still hypothetical hyperbolic geometry by Johann Heinrich Lambert (1728–1777) led him to introduce the hyperbolic functions and compute the area of a hyperbolic triangle (where the sum of angles is less than 180°). Then the Russian mathematician Nikolai Lobachevsky (1792–1856) established in 1826 (and published in 1829) the coherence of this geometry (thus the independence of the parallel postulate), in parallel with the Hungarian mathematician János Bolyai (1802–1860) in 1832, and with Gauss. Later in the 19th century, the German mathematician Bernhard Riemann developed Elliptic geometry, another non-Euclidean geometry where no parallel can be found and the sum of angles in a triangle is more than 180°. It was proved consistent by defining point to mean a pair of antipodal points on a fixed sphere and line to mean a great circle on the sphere.
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As described in the Inferno, the first twenty-four hours of Dante's journey took place on earth and started on the evening of Maundy Thursday, 24 March (or 7 April) 1300 (Inf. I and II), and the next full day (Good Friday) was spent exploring the depths of Hell with Virgil as a guide (Inf. III–XXXIV.69). Dante and Virgil spent the next day ascending from Hell to see the stars (Inf. XXXIV.70–139). They arrive at the shore of the Mountain of Purgatory – the only land in the Southern Hemisphere – at 6 AM on the morning of Easter Sunday,Robin Kirkpatrick, Purgatorio, notes on Canto I: "Thus behind all the references that the canto makes to regeneration and rebirth there is the realization that all life and all redemption depends upon Christ's Resurrection from the dead." which is 6 PM on Sunday evening in Jerusalem, since the two points are antipodal.
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Of particular interest are the so-called "PKiKP" waves—pressure waves (P) that start near the surface, cross the mantle-core boundary, travel through the core (K), are reflected at the inner core boundary (i), cross again the liquid core (K), cross back into the mantle, and are detected as pressure waves (P) at the surface. Also of interest are the "PKIKP" waves, that travel through the inner core (I) instead of being reflected at its surface (i). Those signals are easier to interpret when the path from source to detector is close to a straight line—namely, when the receiver is just above the source for the reflected PKiKP waves, and antipodal to it for the transmitted PKIKP waves. While S waves cannot reach or leave the inner core as such, P waves can be converted into S waves, and vice versa, as they hit the boundary between the inner and outer core at an oblique angle.
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The song was well-suited to the station's album-oriented format of the time, and included the lyric "Flying to the sun, sweet Caroline". The New Riders of the Purple Sage continued touring and releasing albums throughout the late 1970s and early 1980s to an increasingly fallow reception; none of the albums that followed New Riders (1976) charted on the Billboard 200 in antipodal contrast to the widespread mainstream success of the outlaw country movement (exemplified by Willie Nelson and Waylon Jennings) and such second-wave country rock groups as The Eagles, Pure Prairie League, and Firefall. The band continued to open several Grateful Dead and Jerry Garcia Band shows in 1977 and 1978, including the final concert preceding the closure of Winterland Ballroom on December 31, 1978. In 1974, Torbert left NRPS; he and Matthew Kelly had co-founded the band Kingfish (best known for Bob Weir's membership during the Grateful Dead's late-1974 to mid-1976 touring hiatus) the year before.
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Since Eros is irregularly shaped, parts of the surface antipodal to the point of impact can be within 9 kilometres of the impact point (measured in a straight line through the asteroid) even though some intervening parts of the surface are more than 9 kilometres away in straight-line distance. A suitable analogy would be the distance from the top centre of a bun to the bottom centre as compared to the distance from the top centre to a point on the bun's circumference: top-to- bottom is a longer distance than top-to-periphery when measured along the surface but shorter than it in direct straight-line terms. Compression from the same impact is believed to have created the thrust fault Hinks Dorsum. Data from the Near Earth Asteroid Rendezvous spacecraft collected on Eros in December 1998 suggests that it could contain 20 billion tonnes of aluminum and similar amounts of metals that are rare on Earth, such as gold and platinum.
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Signals are transmitted in a 38° cone, using right-hand circular polarization, at an EIRP between 25 and 27 dBW (316 to 500 watts). Note that the 24-satellite constellation is accommodated with only 15 channels by using identical frequency channels to support antipodal (opposite side of planet in orbit) satellite pairs, as these satellites are never both in view of an earth-based user at the same time. The L2 band signals use the same FDMA as the L1 band signals, but transmit straddling 1246 MHz with the center frequency 1246 MHz + n×0.4375 MHz, where n spans the same range as for L1.GLONASS transmitter specs In the original GLONASS design, only obfuscated high-precision signal was broadcast in the L2 band, but starting with GLONASS-M, an additional civil reference signal L2OF is broadcast with an identical standard-precision code to the L1OF signal. A combined GLONASS/GPS Personal Radio Beacon The open standard-precision signal is generated with modulo-2 addition (XOR) of 511 kbit/s pseudo-random ranging code, 50 bit/s navigation message, and an auxiliary 100 Hz meander sequence (Manchester code), all generated using a single time/frequency oscillator.
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Its boundary is composed of 600 tetrahedral cells with 20 meeting at each vertex. Together they form 1200 triangular faces, 720 edges, and 120 vertices. The edges form 72 flat regular decagons. Each vertex of the 600-cell is a vertex of six such decagons. The mutual distances of the vertices, measured in degrees of arc on the circumscribed hypersphere, only have the values 36° = , 60° = , 72° = , 90° = , 108° = , 120° = , 144° = , and 180° = . Departing from an arbitrary vertex V one has at 36° and 144° the 12 vertices of an icosahedron, at 60° and 120° the 20 vertices of a dodecahedron, at 72° and 108° again the 12 vertices of an icosahedron, at 90° the 30 vertices of an icosidodecahedron, and finally at 180° the antipodal vertex of V.S.L. van Oss (1899); F. Buekenhout and M. Parker (1998) These can be seen in the H3 Coxeter plane projections with overlapping vertices colored. Just like the icosidodecahedron can be partitioned into 6 central decagons (60 edge = 6×10), the 600-cell can be partitioned into 72 decagons (720 edges = 72 × 10). :640px Its vertex figure is an icosahedron, and its dual polytope is the 120-cell, with which it can form a compound.
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