Constructing a Regular Heptadecagon (17-gon) with Ruler and Compass

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The number 17 is a Fermat prime, which means it is of the form , with . In 1796, Gauss discovered that regular polygons with a Fermat number of sides can be constructed using only a straight edge and compass [1]. Gauss showed, in particular, that

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This is derived in [1, 2]. An explicit construction of a regular heptadecagon was given by H. W. Richmond in 1893 [3]. This Demonstration is based on his method. A reproduction of Richmond's paper is shown in the Details. Alternative constructions have since been proposed (see, for example, the MathWorld article).

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Contributed by: S. M. Blinder (September 2017)
Open content licensed under CC BY-NC-SA


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