THE NUMBER OF INTERSECTION POINTS MADE

BY THE DIAGONALS OF A REGULAR POLYGON

Bjorn Poonen Michael Rubinstein

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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