Constructing a quadrilateral inside another one

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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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General Mathematics, 51N20 (Primary); 51A20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/137967

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.2716
 http://arxiv.org/abs/0704.2716

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arXiv