Trigonometrically, can be written in terms of the sum of two hyperbolic functions, : e^x = \sinh(x) + \cosh(x) , at .
|
|
Several mountains in the Sulitjelma massif were measured by Wahlberg in the summer of 1807. Using a mercury barometer, he determined the elevation of Vágŋatjåhkkå, and from that he trigonometrically calculated the elevations of Suliskongen, Vardetoppen, and Stortoppen. These measurements made with simple instruments correspond closely to modern measurements. A later researcher of the Sulitjelma massif was the German-Argentine botanist Paul Günther Lorentz (1835–1881).
|
|
LeMay took double driftsThe Double Drift Maneuver is a method of wind determination that calculates winds aloft by taking drift readings on two different headings, then calculating the wind trigonometrically by plotting vectors on a graph. until the B-17s had to separate to transit a cold front. At 11:15 a.m. they reassembled in clear weather on the other side, where LeMay checked their course again.
|
|
For both, the anisotropy may appear as a (continuous) dependence of velocity upon the direction of propagation. For S-waves, it may also appear as a (discrete) dependence of velocity upon the direction of polarization. For a given direction of propagation in any homogeneous medium, only two polarization directions are allowed, with other polarizations decomposing trigonometrically into these two. Hence, shear waves naturally "split" into separate arrivals with these two polarizations; in optics this is called birefringence.
|
|
The accuracy of DME ground stations is 185 m (±0.1 nmi). It's important to understand that DME provides the physical distance between the aircraft antenna and the DME transponder antenna. This distance is often referred to as 'slant range' and depends trigonometrically upon the aircraft altitude above the transponder as well as the ground distance between them. For example, an aircraft directly above the DME station at 6,076 ft (1 nmi) altitude would still show on the DME readout.
|
|
Ibn al-Shatir (1304–1375), in his A Final Inquiry Concerning the Rectification of Planetary Theory, eliminated the need for an equant by introducing an extra epicycle, departing from the Ptolemaic system in a way very similar to what Copernicus later also did. Ibn al-Shatir proposed a system that was only approximately geocentric, rather than exactly so, having demonstrated trigonometrically that the Earth was not the exact center of the universe. His rectification is later used in the Copernican model.
|
|
Burrow was one of the first members of The Asiatic Society founded by fellow orientalist William Jones and contributed to their research. In 1788, William Roy suggested that Burrow would be ideally qualified to conduct experiments in Bengal to examine trigonometrically to measure a meridian of the arc. In 1790 Burrow wrote to the directors of the East India Company to set up an "Indian Greenwich". It was turned down as the Madras Observatory was being considered around the same time.
|
|
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals and to giveJ. L. Coolidge, "A historically interesting formula for the area of a quadrilateral", American Mathematical Monthly, 46 (1939) 345–347. (JSTOR)E. W. Hobson: A Treatise on Plane Trigonometry.
|
|
A memorial to the Abbé de Lacaille and Thomas Maclear, at Aurora in the Western Cape of South Africa. The English portion of the inscription reads: "This is the site of the Maclear Beacon positioned in 1838 near the original North Terminal of the Arc of Meridian positioned by Abbé de Lacaille, the first surveyor to introduce Geodetic Surveying into South Africa." Open the image to see the Afrikaans portion. His desire to determine the distances of the planets trigonometrically, using the longest possible baseline, led him to propose, in 1750, an expedition to the Cape of Good Hope.
|
|
Today the surface of the Glaswaldsee is raised by a sandstone wall which used to enable the transportation of timber down river as part of the timber rafting industry in the valley of the Wolf. The Glaswaldsee is one of the first lakes of the Black Forest to be trigonometrically surveyed and mapped. In 1655 Landgrave Frederick Rudolph of Fürstenberg-Stühlingen directed the Basle priest, Jakob Mentzinger, to prepare a map of his sovereign territory in the Kinzig valley. To illustrate his approach to the national survey, Mentzinger recorded in the lower part of his map an enlarged view of the Glaswaldsee with the calculations made by him.
|
|
In 1609, Galileo Galilei drew one of the first telescopic drawings of the Moon in his book and noted that it was not smooth but had mountains and craters. Thomas Harriot had made, but not published such drawings a few months earlier. Telescopic mapping of the Moon followed: later in the 17th century, the efforts of Giovanni Battista Riccioli and Francesco Maria Grimaldi led to the system of naming of lunar features in use today. The more exact 1834–36 of Wilhelm Beer and Johann Heinrich Mädler, and their associated 1837 book , the first trigonometrically accurate study of lunar features, included the heights of more than a thousand mountains, and introduced the study of the Moon at accuracies possible in earthly geography.
|
|