Meusnier's theorem (original) (raw)
In differential geometry, Meusnier's theorem states that all curves on a surface passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776, but not published until 1785.At least prior to 1912, several writers in English were in the habit of calling the result Meunier's theorem, although there is no evidence that Meusnier himself ever spelt his name in this way.This alternative spelling of Meusnier's name also appears on the Arc de Triomphe in Paris.
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| dbo:abstract | In differential geometry, Meusnier's theorem states that all curves on a surface passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776, but not published until 1785.At least prior to 1912, several writers in English were in the habit of calling the result Meunier's theorem, although there is no evidence that Meusnier himself ever spelt his name in this way.This alternative spelling of Meusnier's name also appears on the Arc de Triomphe in Paris. (en) In geometria differenziale, il teorema di Meusnier mette in relazione la curvatura di una superficie con la curvatura di una curva in essa contenuta. (it) ムーニエの定理(ムーニエのていり、Meusnier's theorem) とは1776年にフランスの数学者ジャン＝バティスト・ムーニエによって提唱され、1785年に論文発表された微分幾何学における定理である。 (ja) O Teorema de Meusnier, na geometria diferencial nos diz que todas as curvas em uma superfície passando por dado ponto p e tendo a mesma curva tangente em pe também a mesma curvatura normal estão em círculos osculadores e formam uma esfera. O teorema foi enunciado primeiramente por Jean Baptiste Meusnier em 1776, mas não foi publicado até 1785. (pt) Теоре́ма (или фо́рмула) Мёнье́ — даёт выражение для кривизны кривой, лежащей на поверхности. (ru) У диференційній геометрії теоремою Меньє називається твердження про властивості кривини на поверхні, яке було доведено у 1776 році (опубліковано 1785 році) французьким вченим Жаном Батістом Меньє. (uk) |
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| rdf:type | yago:WikicatTheoremsInDifferentialGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293 |
| rdfs:comment | In differential geometry, Meusnier's theorem states that all curves on a surface passing through a given point p and having the same tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste Meusnier in 1776, but not published until 1785.At least prior to 1912, several writers in English were in the habit of calling the result Meunier's theorem, although there is no evidence that Meusnier himself ever spelt his name in this way.This alternative spelling of Meusnier's name also appears on the Arc de Triomphe in Paris. (en) In geometria differenziale, il teorema di Meusnier mette in relazione la curvatura di una superficie con la curvatura di una curva in essa contenuta. (it) ムーニエの定理(ムーニエのていり、Meusnier's theorem) とは1776年にフランスの数学者ジャン＝バティスト・ムーニエによって提唱され、1785年に論文発表された微分幾何学における定理である。 (ja) O Teorema de Meusnier, na geometria diferencial nos diz que todas as curvas em uma superfície passando por dado ponto p e tendo a mesma curva tangente em pe também a mesma curvatura normal estão em círculos osculadores e formam uma esfera. O teorema foi enunciado primeiramente por Jean Baptiste Meusnier em 1776, mas não foi publicado até 1785. (pt) Теоре́ма (или фо́рмула) Мёнье́ — даёт выражение для кривизны кривой, лежащей на поверхности. (ru) У диференційній геометрії теоремою Меньє називається твердження про властивості кривини на поверхні, яке було доведено у 1776 році (опубліковано 1785 році) французьким вченим Жаном Батістом Меньє. (uk) |
| rdfs:label | Teorema di Meusnier (it) ムーニエの定理 (ja) Meusnier's theorem (en) Teorema de Meusnier (pt) Теорема Мёнье (ru) Теорема Меньє (uk) |
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