Equiangular polygon

Equiangular polygon

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal then it is a regular polygon.

The only equiangular triangle is the equilateral triangle. Rectangles, including the square, are the only equiangular four-sided figures.

For an equiangular n-gon each angle is 180° - 360°/n; this is the "equiangular polygon theorem".

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

References

*Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, 1979. p. 32

External links

*MathWorld|title=Equiangular Polygon|urlname=EquiangularPolygon
* [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.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Equiangular — In geometry equiangular relates to having equal angles. In particular: *Equiangular polygon a polygon with equal angles. *The Logarithmic spiral or equiangular spiral a type of spiral. *Equiangular lines a set of lines where every pair of lines… …   Wikipedia

  • 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

  • equiangular — adjective Of a polygon, having all interior angles equal. This is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square …   Wiktionary

  • equiangular triangle — noun a three sided regular polygon • Syn: ↑equilateral triangle • Hypernyms: ↑triangle, ↑trigon, ↑trilateral, ↑regular polygon • Hyponyms: ↑delta …   Useful english dictionary

  • Star polygon — Set of regular star polygons {5/2} {7/2} …   Wikipedia

  • Regular polygon — A regular polygon is a polygon which is equiangular (all angles are congruent) and equilateral (all sides have the same length). Regular polygons may be convex or star.General propertiesThese properties apply to both convex and star regular… …   Wikipedia

  • 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… …   Wikipedia

  • Regular polygon — Regular Reg u*lar ( l?r), a. [L. regularis, fr. regula a rule, fr. regere to guide, to rule: cf. F. r[ e]gulier. See {Rule}.] [1913 Webster] 1. Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established… …   The Collaborative International Dictionary of English

  • regular polygon — noun A polygon which is both equiangular and equilateral (i.e. having all sides the same length and all interior angles the same). Ant: irregular, polygon …   Wiktionary

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”