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- In geometry, the Petr–Douglas–Neumann theorem (or the PDN-theorem) is a result concerning arbitrary planar polygons. The theorem asserts that a certain procedure when applied to an arbitrary polygon always yields a regular polygon having the same number of sides as the initial polygon. The theorem was first published by Karel Petr (1868–1950) of Prague in 1908. The theorem was independently rediscovered by Jesse Douglas (1897–1965) in 1940 and also by B H Neumann (1909–2002) in 1941. The naming of the theorem as Petr–Douglas–Neumann theorem, or as the PDN-theorem for short, is due to Stephen B Gray. This theorem has also been called Douglas's theorem, the Douglas–Neumann theorem, the Napoleon–Douglas–Neumann theorem and Petr's theorem. The PDN-theorem is a generalisation of the Napoleon's theorem which is concerned about arbitrary triangles and of the van Aubel's theorem which is related to arbitrary quadrilaterals. (en)
- 佩特-諾伊曼-道格拉斯定理（Petr–Douglas–Neumann theorem）也稱為PDN定理，是幾何學中有關平面多邊形的定理。此定理證明，對於任何多邊形，都可以依定理中的作法找到一正多邊形，其邊數恰和原來的多邊形相同。佩特諾-伊曼-道格拉斯定理最早是由（1868–1950）1908年在布拉格提出。1940年及1941年時也分別被傑西·道格拉斯（1897–1965）和（1909–2002）獨立證明。此定理由Stephen B Gray命名為佩特-諾伊曼-道格拉斯定理，或簡稱為PDN定理，有時也被稱為道格拉斯定理、道格拉斯-諾伊曼定理、諾伊曼-道格拉斯-佩特定理或佩特定理。 (zh)
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- 佩特-諾伊曼-道格拉斯定理（Petr–Douglas–Neumann theorem）也稱為PDN定理，是幾何學中有關平面多邊形的定理。此定理證明，對於任何多邊形，都可以依定理中的作法找到一正多邊形，其邊數恰和原來的多邊形相同。佩特諾-伊曼-道格拉斯定理最早是由（1868–1950）1908年在布拉格提出。1940年及1941年時也分別被傑西·道格拉斯（1897–1965）和（1909–2002）獨立證明。此定理由Stephen B Gray命名為佩特-諾伊曼-道格拉斯定理，或簡稱為PDN定理，有時也被稱為道格拉斯定理、道格拉斯-諾伊曼定理、諾伊曼-道格拉斯-佩特定理或佩特定理。 (zh)
- In geometry, the Petr–Douglas–Neumann theorem (or the PDN-theorem) is a result concerning arbitrary planar polygons. The theorem asserts that a certain procedure when applied to an arbitrary polygon always yields a regular polygon having the same number of sides as the initial polygon. The theorem was first published by Karel Petr (1868–1950) of Prague in 1908. The theorem was independently rediscovered by Jesse Douglas (1897–1965) in 1940 and also by B H Neumann (1909–2002) in 1941. The naming of the theorem as Petr–Douglas–Neumann theorem, or as the PDN-theorem for short, is due to Stephen B Gray. This theorem has also been called Douglas's theorem, the Douglas–Neumann theorem, the Napoleon–Douglas–Neumann theorem and Petr's theorem. (en)
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- Petr–Douglas–Neumann theorem (en)
- 佩特諾-伊曼-道格拉斯定理 (zh)
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