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

Bjorn Poonen·Michael Rubinstein
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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 $V-E+F=2$.

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Bjorn Poonen, Michael Rubinstein. 2006-03-18. The Number of Intersection Points Made by the Diagonals of a Regular Polygon. https://arxiv.org/abs/math/9508209

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