In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection. The problem was posed by Fred Richman in the American Mathematical Monthly in 1965, and was proved by Paul Monsky in 1970.
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| - Teorema di Monsky (it)
- Théorème de Monsky (fr)
- Monsky's theorem (en)
- Teorema de Monsky (pt)
- Теорема о разрезании квадрата на равновеликие треугольники (ru)
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| - En mathématiques, et plus précisément en géométrie, le théorème de Monsky affirme qu'il est impossible de partitionner un carré en un nombre impair de triangles de même aire.Autrement dit, un carré n'admet pas d'équidissection impaire. La question fut posée par Fred Richman dans l'American Mathematical Monthly en 1965, et le résultat démontré par (en) en 1970. (fr)
- In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection. The problem was posed by Fred Richman in the American Mathematical Monthly in 1965, and was proved by Paul Monsky in 1970. (en)
- Il teorema di Monsky stabilisce che non è possibile scomporre un quadrato in un numero dispari di triangoli equivalenti. Il problema fu proposto da sulla rivista American Mathematical Monthly nel 1965 e dimostrato da nel 1970. La dimostrazione di Monsky utilizza tecniche di algebra e di combinatoria, come la valutazione 2-adica sui razionali e una sua estensione al campo reale . (it)
- Теорема о разрезании квадрата на равновеликие треугольники гласит, что квадрат невозможно разрезать на нечётное число треугольников одинаковой площади. Теорема знаменита своим неожиданным доказательством, использующим 2-адическую норму. (ru)
- Na geometria, o teorema de Monsky afirma que é impossível dividir um quadrado em um número ímpar de triângulos de mesma área. Isso foi conjecturado por Fred Richman em 1965, e foi provado por Paul Monsky em 1970, valendo-se de sofisticadas técnicas algébricas. (pt)
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| - En mathématiques, et plus précisément en géométrie, le théorème de Monsky affirme qu'il est impossible de partitionner un carré en un nombre impair de triangles de même aire.Autrement dit, un carré n'admet pas d'équidissection impaire. La question fut posée par Fred Richman dans l'American Mathematical Monthly en 1965, et le résultat démontré par (en) en 1970. (fr)
- In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection. The problem was posed by Fred Richman in the American Mathematical Monthly in 1965, and was proved by Paul Monsky in 1970. (en)
- Il teorema di Monsky stabilisce che non è possibile scomporre un quadrato in un numero dispari di triangoli equivalenti. Il problema fu proposto da sulla rivista American Mathematical Monthly nel 1965 e dimostrato da nel 1970. La dimostrazione di Monsky utilizza tecniche di algebra e di combinatoria, come la valutazione 2-adica sui razionali e una sua estensione al campo reale . (it)
- Теорема о разрезании квадрата на равновеликие треугольники гласит, что квадрат невозможно разрезать на нечётное число треугольников одинаковой площади. Теорема знаменита своим неожиданным доказательством, использующим 2-адическую норму. (ru)
- Na geometria, o teorema de Monsky afirma que é impossível dividir um quadrado em um número ímpar de triângulos de mesma área. Isso foi conjecturado por Fred Richman em 1965, e foi provado por Paul Monsky em 1970, valendo-se de sofisticadas técnicas algébricas. (pt)
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