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  • the convex hull of the <math>4</math>-gon is a quadrilateral, then at least If the convex hull of the <math>4</math>-gon is a triangle, let us say that <math>C</math
    6 KB (1,054 words) - 17:09, 11 December 2024
  • ...aight [[line segment]]s. There are two types of polygons: [[convex polygon|convex]] and [[concave polygon|concave]]. In any simple convex polygon, the sum of the [[exterior angle|exterior angles]] is equal to <mat
    2 KB (372 words) - 18:04, 30 May 2015
  • == Geometry == ...unity are connected in order (more technically, we would call this their [[convex hull]]), they form a regular '''n'''-sided polygon. This becomes even more
    3 KB (558 words) - 20:36, 11 December 2011
  • Let <math>ABCD </math> be a convex quadrilateral with <math>AB=BC=CD </math>, <math>AC \neq BD </math>, and le * [[Geometry]]
    4 KB (658 words) - 15:19, 28 April 2024
  • Let <math>P</math> be any [[convex]] [[polyhedron]], and let <math>V</math>, <math>E</math> and <math>F</math> A convex polyhedron has for its faces 12 squares, 8 regular hexagons, and 6 regular
    1,006 bytes (134 words) - 13:15, 6 March 2022
  • ...llest [[convex set]] containing them. Convex hulls are very important in [[geometry]] and [[combinatorics]]. [[Convex polygon]]
    202 bytes (29 words) - 18:06, 1 March 2008
  • A [[convex]] polyhedron <math> P </math> has <math>26</math> vertices, <math>60</math> [[Category:Intermediate Geometry Problems]]
    1 KB (156 words) - 16:56, 1 January 2016
  • Let <math> ABCDE </math> be a [[convex]] [[pentagon]] with <math> AB \parallel CE, BC \parallel AD, AC \parallel D [[Category:Intermediate Geometry Problems]]
    3 KB (486 words) - 21:15, 7 April 2023
  • ...[edge]]s, and <math>F</math> [[face]]s, <math>V-E+F=2</math>. A particular convex polyhedron has 32 faces, each of which is either a [[triangle]] or a [[pent The convex polyhedron of the problem can be easily visualized; it corresponds to a [[d
    4 KB (726 words) - 00:11, 12 January 2025
  • In [[convex]] [[quadrilateral]] <math> ABCD, \angle A \cong \angle C, AB = CD = 180, </ [[Category:Intermediate Geometry Problems]]
    3 KB (487 words) - 21:14, 24 November 2019
  • ...,2)</math> be points on the coordinate plane. Let <math>ABCDEF</math> be a convex equilateral hexagon such that <math>\angle FAB = 120^\circ,</math> <math>\o ...inate of <math>F</math> must be <math>4</math>. All other cases yield non-convex and/or degenerate hexagons, which violate the problem statement.
    9 KB (1,472 words) - 14:24, 29 December 2024
  • ...ircle, but in general polygons with 4 or more sides (such as non-[[square (geometry) | square]] [[rectangle]]s) do not have an incircle. A quadrilateral that d [[Category:Geometry]]
    2 KB (384 words) - 17:38, 9 March 2023
  • [[Triangle]]s have no diagonals, while [[convex polygon|convex]] [[quadrilateral]]s have two interior diagonals, and [[concave]] quadrilat ...on|Octahedra]] have no face diagonals but have 3 space diagonals. [[Cube (geometry) | Cube]]s have 12 face diagonals (2 on each face) and 4 space diagonals.
    2 KB (374 words) - 23:37, 24 January 2015
  • ...under which the centroid must be inside the figure is when the figure is [[convex]].) Of particular interest to students of olympiad geometry is the '''centroid''' of a [[triangle]]. This is the [[point]] of [[interse
    3 KB (612 words) - 16:21, 11 September 2024
  • ...set. The [[interior]]s of [[circle]]s and of all [[regular polygon]]s are convex, but a circle itself is not because every segment joining two points on the ...] by [[real number]]s (such as any real [[vector space]]) is said to be '''convex''' if for any <math>a,b\in S</math> and <math>0\le t\le 1</math>, <math>ta+
    1 KB (227 words) - 21:47, 1 March 2008
  • ...nt will be outside the polygon. For example, every [[regular polygon]] is convex. ...polygon is <math>360^\circ</math> and the sum of the internal angles of a convex <math>n</math>-gon is <math>(n - 2)180^\circ</math>.
    948 bytes (147 words) - 21:10, 27 February 2020
  • ...ne intersects a curve in a single point. However, if a curve is neither [[convex]] nor [[concave]], it is possible for a tangent line to intersect a curve i Within the realm of differential geometry, the generalization of a tangent is a tangent space. Generally, the tangent
    2 KB (332 words) - 20:54, 11 March 2024
  • ..., a [[cube (geometry) | cube]] has six faces, each of which is a [[square (geometry) | square]]. The polygons that bound higher-dimensional [[polytope]]s are * [[Convex geometry]]
    507 bytes (70 words) - 18:15, 4 April 2008
  • Polyhedra can be [[convex polyhedron | convex]] or [[concave polyhedron | concave]]. [[Category:geometry]]
    1 KB (193 words) - 22:15, 6 December 2016
  • ...polygon <math> \mathcal{P} </math> in the plane is dissected into smaller convex polygons by drawing all of its diagonals. The lengths of all sides and all ...n be <math>AC </math> and <math>BD </math>. Since <math>ABCD </math> is a convex quadrilateral with sides and diagonals of rational length, we consider it i
    2 KB (335 words) - 19:50, 29 April 2014

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