WOLFRAM|DEMONSTRATIONS PROJECT

Cyclogons

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n-gon
2
3
4
5
6
7
8
9
10
20
50
time
0
vertex
footprints
cyclogon
cycloid
circumcircle
spokes
A vertex of a rolling regular polygon traces out a cyclogon. Roll the polygon to see the alternating circular sectors and triangular "footprints" that form the polygon. Vary the number of sides of the polygon, showing visually that the cyclogon becomes a cycloid in the limit as the number of sides increases.