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[[File:Intersecting planes.svg|thumb|Two intersecting planes in three-dimensional space]] In analytic [[geometry]], the '''intersection of two [[plane (mathematics)|planes]]''' in [[three-dimensional space]] is a [[line (mathematics)|line]]. ...

...lfilled by "ovoidal" Möbius planes only; thus, it is the analog for Möbius planes of [[Desargues' Theorem]] for [[projective plane]]s. ...bundle theorem should not be confused with [[möbius plane#Miquelian Möbius planes|Miquel's theorem]]. ...

...og of [[projective geometry]] in the setting of [[noncommutative algebraic geometry]]. ...8/31369741.pdf?sequence=1 |title=Modules over regular algebras and quantum planes |first=Kaushal |last=Ajitabh |year=1994 |type=Ph.D. thesis}} ...

...ional regular [[Near-field (mathematics)|nearfield]] planes are also André planes. ...itation | last1=Weibel | first1=Charles | title=Survey of Non-Desarguesian Planes | url=https://www.ams.org/notices/200710/ | year=2007 | journal= Notices o ...

In [[mathematics]], a '''Benz plane''' is a type of 2-[[dimension]]al [[Geometry|geometrical]] structure, named after the [[Germany|German]] [[mathematician <ref>F. Buekenhout (ed.), ''Handbook of [[Incidence (geometry)|Incidence Geometry]]'', [[Elsevier]] (1995) {{ISBN|0-444-88355-X}}</ref> ...

In [[geometry]], an '''affine plane''' is a [[two-dimensional]] [[affine space]]. ...d way occurs in [[incidence geometry]], where an [[affine plane (incidence geometry)|affine plane]] is defined as an abstract system of points and lines satisf ...

{{Short description|Region between parallel planes intersecting a sphere}} [[File:01sphere2planes.pdf|thumb|Pair of parallel planes intersecting a sphere forming a spherical segment (i.e., a spherical frustu ...

...m data concerning its projections (shadows) on planes or cross-sections by planes."<ref name="ref1"> [[Category:Projective geometry]] ...

...Euclidean plane]],<ref name="Preparata-Shamos"/> or between two parallel [[planes in three-dimensional Euclidean space]] or between two [[hyperplane]]s in [[ where <math>n</math> is the normal vector of the planes <math>n \cdot x = \alpha</math> and <math>n \cdot x = \beta</math>. ...

...1007/BF02413056}}</ref> In his proof he introduced the [[method of moving planes]], which was used after by many mathematicians successfully in geometric an ...io|last1=Ciraolo|first2=Alberto|last2=Roncoroni|title=The method of moving planes: a quantitative approach|date=2018|page=1}}</ref> ...

...the [[octonion]]s are smooth planes. However, these are not the only such planes. ...tion|first= R.|last=Löwen|year=1983|title=Topology and dimension of stable planes: On a conjecture of H. Freudenthal|journal= J. Reine Angew. Math.|volume=34 ...

...re the [[Möbius plane]], Laguerre plane and [[Minkowski plane]]. Laguerre planes are named after the [[France|French]] mathematician [[Edmond Nicolas Lague ...e plane geometry of the completed parabolas/lines is [[isomorphic]] to the geometry of the [[plane section]]s of a [[cylinder]] (see below). ...

...ptic geometry are [[geodesic]] curves and, unlike the lines of [[Euclidean geometry]], are of finite length. The algebra of [[quaternion]]s provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit. ...

...ce (such as an [[ellipsoid]] or [[hyperboloid]]). It is a special [[plane (geometry)|plane]] section of the quadric, as this circle is the intersection with th ...ce of revolution|quadric of revolution]] contains circles as sections with planes that are orthogonal to its axis; it does not contain any other circles, if ...

...geometry)|configuration]] of 12 [[Point (geometry)|points]] and 16 [[Line (geometry)|lines]]. ...ee dimensional space, with different radii, have two [[bitangent]] [[Cone (geometry)|double cones]], the apexes of which are called the centers of similitude. ...

..., '''Marsaglia's theorem''' connects [[modular arithmetic]] and [[analytic geometry]] to describe the flaws with the [[pseudorandom numbers]] resulting from a ...<math>k = 65539</math>, is much worse. All the points in fact fall into 15 planes. ...

...ematics)|surface]]s''. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infin ...f them are [[parallel lines|parallel]], meaning they never [[intersection (geometry)|intersect]] and stay at uniform distance from each-other. ...

...[[generalized circle]], and thus a natural setting for planar [[inversive geometry]]. ...he center of the circle exchanged with the point at infinity. In inversive geometry a straight line is considered to be a generalized circle containing the poi ...

...clidean]] 3D volume, where the base [[Cell (geometry)|cell]] has 6 [[Face (geometry)|faces]] ([[hexahedron]]). ...Bilinear interpolation|bilinear surfaces]] and the side faces are [[plane (geometry)|plane]]s. ...

For ''finite'' planes the following theorem provides a more simple definition. According to this theorem of [[Beniamino Segre]], for ''Pappian'' projective planes of ''odd'' order the ovals are just conics: ...