• Thumbnail for Convex polygon
    geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained...
    6 KB (881 words) - 09:02, 13 March 2025
  • Thumbnail for Convex hull
    In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...
    58 KB (7,173 words) - 01:04, 1 July 2025
  • passes outside the polygon. Simple: the boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. There...
    37 KB (4,236 words) - 14:28, 13 January 2025
  • Thumbnail for Concave polygon
    A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that...
    3 KB (337 words) - 07:05, 22 May 2025
  • Thumbnail for Simple polygon
    These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons. The sum of external angles of a simple polygon is...
    31 KB (3,206 words) - 07:42, 13 March 2025
  • length, or at least one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition...
    9 KB (1,100 words) - 22:45, 4 April 2025
  • Thumbnail for Polygon triangulation
    algorithms have been proposed to triangulate a polygon. It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding...
    13 KB (1,386 words) - 18:20, 13 April 2025
  • Thumbnail for Star polygon
    In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not...
    17 KB (1,633 words) - 00:46, 16 April 2025
  • same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates...
    31 KB (3,061 words) - 23:46, 28 April 2025
  • Thumbnail for Convex hull of a simple polygon
    computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon. It is a special case of...
    9 KB (1,141 words) - 03:36, 2 June 2025
  • fundamental domain for Γ is given by a convex polygon for the hyperbolic metric on H. These can be defined by Dirichlet polygons and have an even number of sides...
    43 KB (6,002 words) - 10:21, 3 May 2025
  • Thumbnail for Point in polygon
    available for some special polygons. Simpler algorithms are possible for monotone polygons, star-shaped polygons, convex polygons and triangles. The triangle...
    12 KB (1,530 words) - 23:08, 6 July 2025
  • Thumbnail for Polyhedron
    Polyhedron (redirect from Convex polyhedra)
    of such a surface is not itself a convex polygon, O'Rourke requires it to be subdivided into smaller convex polygons, with flat dihedral angles between...
    96 KB (10,656 words) - 22:12, 1 July 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 Convex curve
    Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...
    37 KB (4,174 words) - 06:39, 27 September 2024
  • then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need to be a convex polygon: it could be concave...
    5 KB (547 words) - 19:22, 28 June 2024
  • polygon's boundary, is described later in a separate subsection. If not all points are on the same line, then their convex hull is a convex polygon whose...
    17 KB (2,326 words) - 04:22, 2 May 2025
  • Thumbnail for Diagonal
    Diagonal (section Polygons)
    convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon. Any n-sided polygon...
    10 KB (1,333 words) - 11:18, 13 February 2025
  • Thumbnail for Convex polytope
    shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon. Special cases of an unbounded convex polytope are a slab...
    23 KB (3,262 words) - 04:00, 7 July 2025
  • Thumbnail for Gerrymandering
    to convex polygon ratio.[definition needed] To use this method, every proposed district is circumscribed by the smallest possible convex polygon (its...
    170 KB (18,726 words) - 20:56, 6 July 2025
  • Thumbnail for Rectilinear polygon
    Corollary: every rectilinear polygon has at least 4 convex corners. The number of knobs (sides connecting two convex corners) is four more than the...
    11 KB (1,571 words) - 22:36, 30 May 2025
  • Thumbnail for Convex set
    non-convex sets. A set that is not convex is called a non-convex set. A polygon that is not a convex polygon is sometimes called a concave polygon, and...
    27 KB (3,429 words) - 17:52, 10 May 2025
  • Thumbnail for Tangential polygon
    In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called...
    6 KB (719 words) - 19:25, 11 April 2025
  • Thumbnail for Internal and external angles
    angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle...
    6 KB (698 words) - 16:22, 17 April 2025
  • Thumbnail for Viviani's theorem
    of an equiangular polygon does not depend on the location of the point. A necessary and sufficient condition for a convex polygon to have a constant...
    8 KB (912 words) - 00:14, 6 December 2024
  • Thumbnail for Rectangle
    In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular...
    20 KB (2,193 words) - 00:35, 20 June 2025
  • Thumbnail for Triangle
    given convex polygon, one with maximal area can be found in linear time; its vertices may be chosen as three of the vertices of the given polygon. A circular...
    55 KB (6,518 words) - 21:25, 19 June 2025
  • Thumbnail for Voronoi diagram
    all of these n − 1 {\displaystyle n-1} half-spaces, and hence it is a convex polygon. When two cells in the Voronoi diagram share a boundary, it is a line...
    46 KB (5,504 words) - 09:37, 24 June 2025
  • Thumbnail for Reuleaux polygon
    accurately approximated by Reuleaux polygons. They have been applied in coinage shapes. If P {\displaystyle P} is a convex polygon with an odd number of sides...
    7 KB (669 words) - 07:07, 2 April 2025
  • Thumbnail for Polygon mesh
    convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon...
    26 KB (2,618 words) - 06:27, 12 June 2025