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 (and also holds for equilateral ones):
- The sum of distances from a point to the side lines of an equiangular [or equilateral] 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 Publications, 1979. p. 32
External links
- Weisstein, Eric W., "Equiangular Polygon" from MathWorld.
- A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.
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