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In geometry, a heptadecagon is a seventeen-sided polygon.
A regular heptadecagon has internal angles each measuring 158.823529411765 degrees.
The regular heptadecagon is a constructible polygon, as was shown by Carl Friedrich Gauss in 1796.
Constructibility implies that trigonometric functions of 2π/17 can be expressed with basic arithmetic and square roots alone. Gauss' book Disquisitiones contains the following equation, given here in modern notation:
- <math>16\,\operatorname{cos}{2\pi\over17}=-1+\sqrt{17}+\sqrt{34-2\sqrt{17}}+2\sqrt{17+3\sqrt{17}-\sqrt{34-2\sqrt{17}}-2\sqrt{34+2\sqrt{17}}}.<math>
See also
External links
You can see how to construct a regular 17-gon geometrically at either of
- http://www.showmath.co.kr/const/polygon/rpoly17.html (Korean, flash)
- http://www.geocities.com/RainForest/Vines/2977/gauss/formulae/heptadecagon.html
- http://mathworld.wolfram.com/Heptadecagon.html
And you can see the algebraic aspect (by Gauss) in this book :
'Famous Problems and Other Monographs' by F.Klein et al.
- http://www.mathlove.org/bbs/data/mathfb/alg17gon.ppt
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