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Heptadecagon
From Wikipedia, the free encyclopedia
In geometry, a heptadecagon (or 17-gon) is a seventeen-sided polygon. A regular heptadecagon has internal angles each measuring 
degrees.
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The regular heptadecagon is a constructible polygon, as was shown by Carl Friedrich Gauss in 1796. Gauss was so pleased by this that he asked for one to be inscribed on his tombstone. The stonemason declined, stating that the difficult construction would essentially look like a circle. So it was later decided that a star would be used instead.
Constructibility implies that trigonometric functions of 2π/17 can be expressed with basic arithmetic and square roots alone. Gauss' book Disquisitiones Arithmeticae contains the following equation, given here in modern notation:
The first actual method of construction was devised by Johannes Erchinger, a few years after Gauss' work, as shown step-by-step in the animation below. It takes 64 steps.
- F. Klein et al. Famous Problems and Other Monographs. - Describes the algebraic aspect, by Gauss.
- Heptadecagon at MathWorld contains a description of the construction.
| Polygons |
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| Triangle • Quadrilateral • Pentagon •Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon |