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

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1. Let AC be a diameter on the unit circle and let OB be a perpendicular radius.
4π
17
The number 17 is a Fermat prime, which means it is of the form
n
2
2
+1
, with
n=2
. 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
16cos
2π
17
=-1+
17
+
34-2
17
+2
17+3
17
-
34-2
17
-2
34+2
17
.
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).

Details

External Links

Heptadecagon (Wolfram MathWorld)

Permanent Citation

S. M. Blinder
​
​"Constructing a Regular Heptadecagon (17-gon) with Ruler and Compass"​
​http://demonstrations.wolfram.com/ConstructingARegularHeptadecagon17GonWithRulerAndCompass/​
​Wolfram Demonstrations Project​
​Published: September 8, 2017