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Mathematics > General Mathematics

arXiv:0704.2716 (math)
[Submitted on 20 Apr 2007 (v1), last revised 17 Sep 2007 (this version, v3)]

Title:Constructing a quadrilateral inside another one

Authors: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.
Subjects: General Mathematics (math.GM)
MSC classes: 51N20 (Primary); 51A20 (Secondary)
Cite as: arXiv:0704.2716 [math.GM]
  (or arXiv:0704.2716v3 [math.GM] for this version)
  https://doi.org/10.48550/arXiv.0704.2716

Submission history

From: J. Marshall Ash [view email]
[v1] Fri, 20 Apr 2007 14:21:42 UTC (7 KB)
[v2] Tue, 1 May 2007 13:19:58 UTC (94 KB)
[v3] Mon, 17 Sep 2007 15:24:19 UTC (15 KB)
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