The Number of Intersection Points Made by the Diagonals of a Regular Polygon

Abstract

We give a formula for the number of interior intersection points made by the diagonals of a regular $n$-gon. The answer is a polynomial on each residue class modulo 2520. We also compute the number of regions formed by the diagonals, by using Euler's formula $V-E+F=2$.

arXiv commentThis version corrects a typo that appeared in the 1995 arxiv version and also in the SIAM version (specifically coefficient '262' in theorem 1 appeared incorrectly as '232')

Cited by in corpus (1)

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