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Legendre's Theorem On Spherical Triangles
In geometry, Legendre's theorem on spherical triangles, named after Adrien-Marie Legendre, is stated as follows: : Let ABC be a spherical triangle on the ''unit'' sphere with ''small'' sides ''a'', ''b'', ''c''. Let A'B'C' be the planar triangle with the same sides. Then the angles of the spherical triangle exceed the corresponding angles of the planar triangle by approximately one third of the spherical excess (the spherical excess is the amount by which the sum of the three angles exceeds ). The theorem was very important in simplifying the heavy numerical work in calculating the results of traditional (pre-GPS and pre-computer) geodetic surveys from about 1800 until the middle of the twentieth century. The theorem was stated by who provided a proof in a supplement to the report of the measurement of the French meridional arc used in the definition of the metre. Legendre does not claim that he was the originator of the theorem despite the attribution to him. maintains th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |