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Villarceau Circles Frame
Villarceau or Villarceaux may refer to: * Yvon Villarceau, a 19th-century French astronomer, mathematician, and engineer * Villarceau circles In geometry, Villarceau circles () are a pair of circles produced by cutting a torus obliquely through the center at a special angle. Given an arbitrary point on a torus, four circles can be drawn through it. One is in a plane parallel to the e ..., a pair of circles found in an obliquely cut torus, which are named after him * Domaine of Villarceaux, a château, water garden, and park in the commune of Chaussy in the Val d'Oise Department of France {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yvon Villarceau
Antoine-Joseph Yvon Villarceau (15 January 1813 – 23 December 1883) was a French astronomer, mathematician, and engineer. He constructed an equatorial meridian-instrument and an isochronometric regulator for the Paris Observatory. He wrote ''Mécanique Céleste. Expose des Méthodes de Wronski et Composantes des Forces Perturbatrices suivant les Axes Mobiles'' (Paris: Gauthier-Villars, 1881) and ''Sur l'établissement des arches de pont, envisagé au point de vue de la plus grande stabilité'' (Paris: Imprimerie Impériale, 1853). He is the eponym of Villarceau circles, which are two circular sections of a torus other than the two trivial ones. A short street in the 16th arrondissement of Paris The 16th arrondissement of Paris (''XVIe arrondissement'') is one of the 20 arrondissements of the capital city of France. In spoken French, this arrondissement is referred to as ''seizième''. The arrondissement includes part of the Arc de T ... is named after Villarceau. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Villarceau Circles
In geometry, Villarceau circles () are a pair of circles produced by cutting a torus obliquely through the center at a special angle. Given an arbitrary point on a torus, four circles can be drawn through it. One is in a plane parallel to the equatorial plane of the torus and another perpendicular to that plane (these are analogous to lines of latitude and longitude on the Earth). The other two are Villarceau circles. They are obtained as the intersection of the torus with a plane that passes through the center of the torus and touches it tangentially at two antipodal points. If one considers all these planes, one obtains two families of circles on the torus. Each of these families consists of disjoint circles that cover each point of the torus exactly once and thus forms a 1-dimensional foliation of the torus. The Villarceau circles are named after the French astronomer and mathematician Yvon Villarceau (1813–1883) who wrote about them in 1848. Mannheim (1903) showed that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
