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An Unexpected Maximum in a Family of Rectangles

An ordered triple of distances from a point P to three consecutive
vertices of a rectangle uniquely determines the distance from P to the
fourth vertex, but does not uniquely determine the rectangle. We investigate
several questions which arise in this setting, including the question of
which rectangle has maximum area for a given triple of distances. *The
Geometer's Sketchpad* and *Mathematica* were both helpful in the
work on this paper. A reprint
is available in pdf format, and you should be able to get it if you have
Adobe Acrobat Reader, but no promises.

Leon Hall lmhall@umr.edu
Revised July 104, 2009