Equilateral polygon

Equilateral polygon

In geometry, an equilateral polygon is a polygon which has all sides of the same length.

For instance, an equilateral triangle is a triangle of equal edge lengths. All equilateral triangles are similar to each other, and have 60 degree internal angles.:

Any equilateral quadrilateral is a rhombus, which includes the square.:

An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon.Not all equilateral polygons are convex: all equilateral polygons with more than four sides, such as the pentagon, can be concave.

Viviani's Theorem holds for equilateral polygons::"The sum of distances from a point to the side lines of an equilateral polygon does not depend on the point and is that polygon's invariant."

External links

* [http://www.mathopenref.com/equilateral.html Equilateral triangle] With interactive animation
* [http://www.cut-the-knot.org/Curriculum/Geometry/EquiangularPoly.shtml A Property of Equiangular Polygons: What Is It About?] a discussion of Viviani's theorem at Cut-the-knot.
* [http://www.geocities.com/jorgeluismireles/equilaterals/ Equilateral Pentagons] With Java animations.
* [http://www.geocities.com/jorgeluismireles/lenses/ Equilateral Hexagons] A family of pieces resembling lenses tiling the plane.


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  • Equilateral — E qui*lat er*al, a. [L. aequilateralis; aequus equal + latus, lateris, side: cf. F. [ e]quilat[ e]ral.] Having all the sides equal; as, an equilateral triangle; an equilateral polygon. [1913 Webster] {Equilateral hyperbola} (Geom.), one whose… …   The Collaborative International Dictionary of English

  • Equilateral hyperbola — Equilateral E qui*lat er*al, a. [L. aequilateralis; aequus equal + latus, lateris, side: cf. F. [ e]quilat[ e]ral.] Having all the sides equal; as, an equilateral triangle; an equilateral polygon. [1913 Webster] {Equilateral hyperbola} (Geom.),… …   The Collaborative International Dictionary of English

  • Equilateral shell — Equilateral E qui*lat er*al, a. [L. aequilateralis; aequus equal + latus, lateris, side: cf. F. [ e]quilat[ e]ral.] Having all the sides equal; as, an equilateral triangle; an equilateral polygon. [1913 Webster] {Equilateral hyperbola} (Geom.),… …   The Collaborative International Dictionary of English

  • equilateral — adjective Etymology: Late Latin aequilateralis, from Latin aequi + later , latus side more at lateral Date: 1570 1. having all sides equal < an equilateral triangle > < an equilateral polygon > see triangle illustration 2. having all the faces… …   New Collegiate Dictionary

  • Polygon — For other uses, see Polygon (disambiguation). Some polygons of different kinds In geometry a polygon (   …   Wikipedia

  • polygon — polygonal /peuh lig euh nl/, adj. polygonally, adv. /pol ee gon /, n. a figure, esp. a closed plane figure, having three or more, usually straight, sides. See illus. under heptagon, hexagon, octagon, pentagon, quadrilateral, triangle …   Universalium

  • Equilateral triangle — In geometry, an equilateral triangle is a triangle in which all three sides have equal lengths. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also equal to each other and… …   Wikipedia

  • Mutually equilateral — Equilateral E qui*lat er*al, a. [L. aequilateralis; aequus equal + latus, lateris, side: cf. F. [ e]quilat[ e]ral.] Having all the sides equal; as, an equilateral triangle; an equilateral polygon. [1913 Webster] {Equilateral hyperbola} (Geom.),… …   The Collaborative International Dictionary of English

  • equilateral — 1. adjective Referring to a polygon all of whose sides are of equal length. Not necessarily a regular polygon since the angles can still differ (a regular polygon would also be equiangular). 2. noun An equilateral triangle …   Wiktionary

  • equilateral —    When every side of a polygon is of the same length. A square, for instance, must be equilateral in order to be a square. Also see mathematics, regular, and shape …   Glossary of Art Terms

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