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

Bjorn Poonen; Michael Rubinstein

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

Metric Geometry 2008-02-03 v3

Authors: 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 $V-E+F=2$ .

Keywords

regular polygon diagonals intersection points euler's formula regions

Cite

@article{arxiv.math/9508209,
  title  = {The Number of Intersection Points Made by the Diagonals of a Regular Polygon},
  author = {Bjorn Poonen and Michael Rubinstein},
  journal= {arXiv preprint arXiv:math/9508209},
  year   = {2008}
}

Comments

This 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')

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

Abstract

Keywords

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