• Thumbnail for Euclidean plane
    In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E}...
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  • Thumbnail for Euclidean geometry
    those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier, Euclid...
    60 KB (7,200 words) - 19:45, 6 July 2025
  • In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical...
    23 KB (3,411 words) - 05:58, 24 September 2024
  • Thumbnail for Euclidean planes in three-dimensional space
    In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional...
    17 KB (2,819 words) - 16:27, 10 June 2025
  • two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Several notions of a plane may be defined...
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  • Thumbnail for Euclidean distance
    distance from a point to a line, in the Euclidean plane The distance from a point to a plane in three-dimensional Euclidean space The distance between two lines...
    26 KB (3,288 words) - 16:41, 30 April 2025
  • Thumbnail for Hyperbolic geometry
    a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing...
    56 KB (6,970 words) - 13:36, 7 May 2025
  • geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras...
    45 KB (6,064 words) - 02:17, 9 July 2025
  • Thumbnail for Euclidean space
    commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that...
    47 KB (6,967 words) - 08:16, 28 June 2025
  • Thumbnail for Poincaré half-plane model
    non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically...
    24 KB (3,972 words) - 06:32, 7 December 2024
  • Thumbnail for Tessellation
    floors. More formally, a tessellation or tiling is a cover of the Euclidean plane by a countable number of closed sets, called tiles, such that the tiles...
    58 KB (6,055 words) - 17:49, 20 May 2025
  • Thumbnail for Conic section
    Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as...
    69 KB (9,174 words) - 17:05, 5 June 2025
  • Thumbnail for Real projective plane
    ⁠, is a two-dimensional projective space, similar to the familiar Euclidean plane in many respects but without the concepts of distance, circles, angle...
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  • a plane, then it is called a hyperbolic plane. q|U is degenerate. One of the most jarring properties (for a Euclidean intuition) of pseudo-Euclidean vectors...
    19 KB (2,367 words) - 07:09, 14 July 2024
  • the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles...
    27 KB (3,319 words) - 17:55, 18 May 2025
  • sphere geometry Non-Euclidean geometry Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective...
    13 KB (938 words) - 15:07, 19 June 2025
  • Thumbnail for Euclidean minimum spanning tree
    A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system...
    55 KB (6,676 words) - 19:53, 5 February 2025
  • Thumbnail for Euclidean group
    In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\displaystyle \mathbb {E} ^{n}} ; that is, the transformations...
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  • Thumbnail for Spherical geometry
    tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but also have some important differences...
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  • into a correlation, the Euclidean plane (which is not a projective plane) needs to be expanded to the extended euclidean plane by adding a line at infinity...
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  • Thumbnail for Real coordinate space
    coordinates of the points of a Euclidean space of dimension n, En (Euclidean line, E; Euclidean plane, E2; Euclidean three-dimensional space, E3) form...
    31 KB (4,248 words) - 16:09, 26 June 2025
  • Thumbnail for Euclidean tilings by convex regular polygons
    Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...
    32 KB (2,009 words) - 01:08, 16 April 2025
  • Thumbnail for Cartesian coordinate system
    three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n....
    41 KB (5,520 words) - 00:16, 1 June 2025
  • Thumbnail for Projective plane
    mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect...
    53 KB (6,933 words) - 22:59, 1 June 2025
  • geometry has a variety of properties that differ from those of classical Euclidean plane geometry. For example, the sum of the interior angles of any triangle...
    18 KB (2,656 words) - 19:30, 16 May 2025
  • In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...
    5 KB (670 words) - 00:49, 20 April 2024
  • Banach–Tarski paradox. In the Euclidean plane, two figures that are equidecomposable with respect to the group of Euclidean motions are necessarily of the...
    49 KB (6,938 words) - 10:18, 15 June 2025
  • groups and wallpaper groups of the Euclidean plane ( E 2 {\displaystyle E^{2}} ), and their analogues on the hyperbolic plane ( H 2 {\displaystyle H^{2}} )...
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  • Thumbnail for List of Euclidean uniform tilings
    semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings...
    15 KB (953 words) - 18:19, 31 March 2025
  • Thumbnail for Quadrant (plane geometry)
    The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. The axes...
    2 KB (194 words) - 15:05, 16 January 2025