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...l tiling''' is a [[tessellation]] of the [[Euclidean plane]], [[hyperbolic plane]], or some other two-dimensional space by [[apeirogon]]s. Tilings of this t *[[Order-2 apeirogonal tiling]], Euclidean tiling of two half-spaces ...

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

...35, 273 </ref> It is primarily used for calculating distances (see [[point-plane distance]] and [[point-line distance]]). ...<math>d \ge 0</math> is the shortest distance from the origin ''O'' to the plane or line. ...

...description|Undirected graph with graph distances linearly bounded w.r.t. Euclidean distances}} ...[[shortest path]] has a length that is within a constant factor of their [[Euclidean distance]]. ...

...ck-S-Woods-Plane/bams/1183414982.full Review of ''Plane and Solid Analytic geometry''] via [[Project Euclid]]</ref> ...[[curvature of Riemannian manifolds]]. In 1903 he spoke on [[non-Euclidean geometry]]. ...

...oduced separately: [[Möbius plane]]s, [[Laguerre plane]]s, and [[Minkowski plane]]s.<ref>W. Benz, ''Vorlesungen über Geomerie der Algebren'', [[Springer Sci <ref>F. Buekenhout (ed.), ''Handbook of [[Incidence (geometry)|Incidence Geometry]]'', [[Elsevier]] (1995) {{ISBN|0-444-88355-X}}</ref> ...

...ions.com/TeichmullerVol1.html|title=Teichmüller Theory and Applications to Geometry, Topology, and Dynamics|date=|publisher=Matrix Editions|last=Hubbard|first= ...s parallel to the boundaries of the band within the band are [[hypercycle (geometry)|hypercycles]] whose common axis is the line through the middle of the band ...

...is the analog for Möbius planes of [[Desargues' Theorem]] for [[projective plane]]s. The bundle theorem should not be confused with [[möbius plane#Miquelian Möbius planes|Miquel's theorem]]. ...

...parallel lines which extend infinitely while remaining equidistant. In non-Euclidean spaces, lines perpendicular to a traversal either converge or diverge.]] ...sed to represent physical positions, like an [[affine plane]] or [[complex plane]]. ...

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

..."Preparata-Shamos"/> or between two parallel [[planes in three-dimensional Euclidean space]] or between two [[hyperplane]]s in [[higher dimensions]].<ref name=" * [[Half-plane]] ...

{{Short description|Axiom in the foundations of geometry}} ...hese lines).]] '''Aristotle's axiom''' is an axiom in the [[foundations of geometry]], proposed by [[Aristotle]] in ''[[On the Heavens]]'' that states: ...

In the [[mathematics|mathematical]] field of [[differential geometry]], '''Euler's theorem''' is a result on the [[curvature]] of [[curve]]s on ...vector|unit]]) [[tangent vector]] to ''M'' at ''p'', there passes a normal plane ''P''_''X'' which cuts out a curve in ''M''. That curve has a ce ...

In analytic [[geometry]], the '''intersection of two [[plane (mathematics)|planes]]''' in [[three-dimensional space]] is a [[line (mathe This is found by noticing that the line must be perpendicular to both plane normals, and so parallel to their cross product <math>\boldsymbol {n}_1 \ti ...

...ry]], the '''midpoint theorem''' describes a property of parallel [[Chord (geometry)|chord]]s in a [[Conic section|conic]]. It states that the midpoints of par ...le]], [[ellipse]] or [[hyperbola]] the diameter goes through its [[centre (geometry)#Projective conics|center]]. For a [[parabola]] the diameter is always perp ...

...through a point <math>P</math> not on line <math>R</math>; however, in the plane, two parallels may be closer to <math>l</math> than all others (one in each Thus it is useful to make a new definition concerning parallels in neutral geometry. If there are closest parallels to a given line they are known as the '''li ...

{{Short description|Problem in coordinate geometry}} ...eometry)|parallel]] [[Line (geometry)|lines]]''' in the [[plane (geometry)|plane]] is the minimum distance between any two points. ...

In [[plane geometry]], a '''Jacobi point''' is a point in the [[Euclidean plane]] determined by a [[triangle]] {{math|△''ABC''}} and a triple of angles {{m ...te book|first=Michael |last=de Villiers|title=Some Adventures in Euclidean Geometry|year=2009|publisher=Dynamic Mathematics Learning|isbn=9780557102952|pages=1 ...

...ional [[linear space|linear]], [[affine geometry|affine]], or [[projective geometry|projective]] space into connected [[abstract cell complex|cell]]s of differ ...object. For instance the cells of an arrangement of lines in the Euclidean plane are of three types: ...

'''Maxwell's theorem''' is the following statement about triangles in the plane. * [[Daniel Pedoe]]: ''Geometry: A Comprehensive Course''. Dover, 1970, pp. 35–36, 114–115 ...