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EspañolEQUIANGULAR 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.''
★ Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, 1979. p. 32
★
★ A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.
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.''
| Contents |
| References |
| External links |
References
★ Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, 1979. p. 32
External links
★
★ A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.
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