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.


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