China
Africa
Explore chapters and articles related to this topic
Geodesy Fundamentals
Published in Julio Sanchez, Maria P. Canton, William Perrizo, Space Image Processing, 2018
Julio Sanchez, Maria P. Canton
It would indeed be convenient if the earth were shaped like a sphere; the sphere is a simple geometrical figure that can be defined by a single parameter, its radius. Furthermore, calculations on the sphere are simple, fast, and easy to code. Formulas and laws from solid geometry and spherical trigonometry are used to solve spherical triangles on the earth’s surface. The laws of sine and cosine and the relationship between two angles and three sides, and three sides and an angle are particularly useful. Other formulas based on haversines are also simple and provide greater accuracy. Although we know that the earth is only approximately spherical, for the purpose of many calculations, the spherical earth assumption is sufficiently accurate.
Celestial Navigation—Spherical Trigonometry, Spherical Triangles, Azimuth, Sextant Altitude, Amplitude, and Line of Position
Published in George A. Maul, The Oceanographer's Companion, 2017
Celestial navigation is based on spherical trigonometry. The sine law and cosine law of a spherical triangle have their parallels in plane trigonometry, except that the sum of angles in a spherical triangle can be between 180° and 540°. Consider a spherical triangle with angles A, B, and C, with opposite sides of a, b, and c. Sides a, b, and c are arcs of great circles, which are formed by the intersection of a plane passing through the sphere's center. The laws are as follows:
Spherical trigonometry
Published in Martin Vermeer, Antti Rasila, Map of the World, 2019
The formulas of spherical trigonometry are extremely useful in geodesy. The surface of the Earth, which in first approximation is flat, is in the second approximation (i.e., in a small, but not very small, area) the surface of a sphere. Even for the Earth as a whole, the deviations from spherical shape are only 0.3%.
Maligned for mathematics: Sir Thomas Urquhart and his Trissotetras
Published in Annals of Science, 2019
For spherical trigonometry, Norwood bases his treatment on two axioms: ‘Napier's rules of circular parts’, initially (Book 2, p. 11) only illustrated by examples and referring back to Napier's book on logarithms for proof, but then proved in detail in an appendix (Book 2, pp. 74–80); and a complicated formula for the sine of half a contained angle, proved by an intricate geometrical argument (Book 2, pp. 60–63) involving a large figure with 19 lettered points and an appeal to Pitiscus.