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arXiv · 0704.2716

Constructing a quadrilateral inside another one

J. M. Ash·M. A. Ash·P. F. Ash
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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.

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J. M. Ash, M. A. Ash, P. F. Ash. 2007-09-17. Constructing a quadrilateral inside another one. https://arxiv.org/abs/0704.2716

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