Equiangular polygon

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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.

[edit] References

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

[edit] External links

• Eric W. Weisstein, Equiangular Polygon at MathWorld.
• A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.

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