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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] |
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] |
Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French people, French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his contributions to the Least squares, method of least squares, and was the first to officially publish on it, though Carl Friedrich Gauss had discovered it before him. Life Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire in Paris from 1775 to 1780 and at the École Normale Supérieure, École Normale from 1795. At the same time, he was associated with the Bureau des Longitudes. In 1782, the Prussian Academy of Sciences, Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Excess
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Trigonometry Legendre
A sphere (from Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ''center'' of the sphere, and the distance is the sphere's ''radius''. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings. Basic terminology As mentioned earlier is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of a second, where the second is defined by a hyperfine transition frequency of caesium. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately . In 1799, the metre was redefined in terms of a prototype metre bar. The bar used was changed in 1889, and in 1960 the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Marie De La Condamine
Charles Marie de La Condamine (; 28 January 1701 – 4 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in territory which is now Ecuador, measuring the length of a degree of latitude at the equator and preparing the first map of the Amazon region based on astro-geodetic observations. Furthermore he was a contributor to the ''Encyclopédie''. Biography Charles Marie de La Condamine was born in Paris as a son of well-to-do parents, Charles de La Condamine and Louise Marguerite Chourses. He studied at the Collège Louis-le-Grand in Paris, where he was trained in humanities as well as in mathematics. After finishing his studies, he enlisted in the army and fought in the war against Spain (1719). After returning from the war, he became acquainted with scientific circles in Paris. On 12 December 1730 he became a member of the Académie des Sciences and was appointed Assistant Chemist at the Academy. In 1729 La Condamine and his friend Volta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Geodesic Mission
The French Geodesic Mission to the Equator (), also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission, was an 18th-century expedition to what is now Ecuador carried out for the purpose of performing an arc measurement, measuring the length of a degree of latitude near the Equator, by which the Earth's radius can be inferred. The mission was one of the first geodesic (or ''geodetic'') missions carried out under modern scientific principles, and the first major international scientific expedition. Background In the 18th century, there was significant debate in the scientific community, specifically in the French Academy of Sciences (''Académie des sciences''), as to whether the circumference of the Earth was greater around the Equator or around the poles. French astronomer Jacques Cassini held to the view that the polar circumference was greater. Louis XV of France and the academy sent two expeditions to determine the answer: a northern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Jean Baptiste Joseph Delambre, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
