About: Petr–Douglas–Neumann theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Petr–Douglas–Neumann theorem Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatQuadrilaterals, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/5ADFWCbE3Y

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.

Attributes	Values
rdf:type	yago:WikicatTheoremsInGeometry yago:Abstraction100002137 yago:Attribute100024264 yago:Communication100033020 yago:Figure113862780 yago:Message106598915 yago:PlaneFigure113863186 yago:Polygon113866144 yago:Proposition106750804 yago:Quadrilateral113879126 yago:Shape100027807 yago:Statement106722453 yago:Theorem106752293 yago:WikicatQuadrilaterals
rdfs:label	Petr–Douglas–Neumann theorem (en) 佩特諾-伊曼-道格拉斯定理 (zh)
rdfs:comment	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)
foaf:depiction
dcterms:subject	Theorems about quadrilaterals
Wikipage page ID	35762367 (xsd:integer)
Wikipage revision ID	1123725464 (xsd:integer)
Link from a Wikipage to another Wikipage	Prague Quadrilateral Midpoint Bernhard Neumann Algorithm Theorems about quadrilaterals Perpendicular Regular pentagon Regular polygon Generalisation Geometry Pentagon Plane (geometry) Polygon Diagonal Isosceles triangle Karel Petr Jesse Douglas Triangle Square (geometry) Vertex (geometry) Napoleon's theorem Van Aubel's theorem
sameAs	Petr–Douglas–Neumann theorem Petr–Douglas–Neumann theorem Petr–Douglas–Neumann theorem Petr–Douglas–Neumann theorem
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/PDNTheoremForTriangle.svg?width=300
has abstract	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)
gold:hypernym	Result
prov:wasDerivedFrom	wikipedia-en:Petr–Douglas–Neumann_theorem?oldid=1123725464&ns=0
page length (characters) of wiki page	12841 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Petr–Douglas–Neumann_theorem
is Link from a Wikipage to another Wikipage of	Bernhard Neumann Karel Petr Jesse Douglas Petr-Douglas-Neumann theorem Van Aubel's theorem Douglas-Neumann theorem Douglas–Neumann theorem
is Wikipage redirect of	Petr-Douglas-Neumann theorem Douglas-Neumann theorem Douglas–Neumann theorem
is known for of	Bernhard Neumann
is known for of	Bernhard Neumann
is foaf:primaryTopic of	wikipedia-en:Petr–Douglas–Neumann_theorem

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 59 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software