English

Constructing a quadrilateral inside another one

General Mathematics 2007-09-17 v3

Abstract

Connect each vertex of a convex quadrilateral Q to the midpoint of the next (proceeding counterclockwise) side. The four connecting lines create an interior quadrilateral I. We study the ratio area(I)/area(Q). We also determine what happens to area(I)/area(Q) when the four midpoints are replaced by points which divide the sides in the ratio of rho to (1-rho) proceeding clockwise. Here rho is any fixed number satisfying 0 < rho < 1.

Cite

@article{arxiv.0704.2716,
  title  = {Constructing a quadrilateral inside another one},
  author = {J. M. Ash and M. A. Ash and P. F. Ash},
  journal= {arXiv preprint arXiv:0704.2716},
  year   = {2007}
}
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