An Unexpected Maximum in a Family of Rectangles

L. M. Hall and R. P. Roe

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 Revised July 104, 2009