Desarguesian plane

In projective geometry a Desarguesian plane, named after Gérard Desargues, is a plane in which Desargues' theorem holds. The ordinary real projective plane is a Desarguesian plane. More generally any projective plane over a division ring is Desarguesian, and conversely Hilbert showed that any Desarguesan projective plane is the projective plane over some division ring. The division ring is commutative if and only if the projective plane satisfies Pappus's hexagon theorem. In particular all finite Desarguesian planes satisfy Pappus's theorem, but there are some infinite ones that do not. There are many examples of non-Desarguesian planes where Desargues's theorem does not hold, such as the Moulton plane.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · edit] References Ch. Weibel: Survey of Nondesarguesian planes Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Canadian Screenwriting Awards Ken Brown (footballer) Look at other dictionaries: Non-Desarguesian plane — In mathematics, a non Desarguesian plane, named after Gérard Desargues, is a projective plane that does not satisfy Desargues s theorem, or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is valid in all… …   Wikipedia Oval (projective plane) — In mathematics, an oval in a projective plane is a set of points, no three collinear, such that there is a unique tangent line at each point (a tangent line is defined as a line meeting the point set at only one point, also known as a 1 secant).… …   Wikipedia Moufang plane — In mathematics, a Moufang plane, named for Ruth Moufang, is a type of projective plane, characterised by the property that the group of automorphisms fixing all points of any given line acts transitively on the points not on the line. In other… …   Wikipedia Moulton plane — The Moulton plane. Lines sloping down and to the right are bent where they cross the y axis. In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues theorem does not hold. It is named after the American… …   Wikipedia Projective plane — See real projective plane and complex projective plane, for the cases met as manifolds of respective dimension 2 and 4 In mathematics, a projective plane has two possible definitions, one of them coming from linear algebra, and another (which is… …   Wikipedia Gérard Desargues — Girard Desargues Girard Desargues (February 21 1591–October 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues theorem, the Desargues graph, and the crater Desargues on the Moon… …   Wikipedia Moulton-Ebene — Geraden in der Moulton Ebene Die Moulton Ebene ist ein oft benutztes Beispiel für eine affine Ebene, in der der Satz von Desargues nicht gilt, also einer nichtdesargueschen Ebene. Damit liefern ihre Koordinaten zugleich ein Beispiel eines… …   Deutsch Wikipedia Projective geometry — is a non metrical form of geometry, notable for its principle of duality. Projective geometry grew out of the principles of perspective art established during the Renaissance period, and was first systematically developed by Desargues in the 17th …   Wikipedia List of geometry topics — This is list of geometry topics, by Wikipedia page.*Geometric shape covers standard terms for plane shapes *List of mathematical shapes covers all dimensions *List of differential geometry topics *List of geometers *See also list of curves, list… …   Wikipedia Moulton — is a word that may refer to various things. Contents 1 Places in the United Kingdom 2 Places in the U.S. 3 Places in Antarctica …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”