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A Surprising but Easily Proved Geometric Decomposition Theorem

by Victor Klee and John R. Reay

Award: Carl B. Allendoerfer

Year of Award: 1999

Publication Information: Mathematics Magazine, Vol. 71(1998), pp. 3-11

Summary: Applications of homothetic transformations in the plane to a variety of set-theoretic results.

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About the Authors: (from Mathematics Magazine, Vol. 71 (1998)) Victor Klee 's 1949 Ph.D. is from the University of Virginia, which attracted him because of an initial interest in point-set topology. While there, he became interested also in functional analysis and convex geometry. After the move to Seattle, in 1953, his interests broadened to include combinatorics, optimization, and computational complexity. He is a co-author, with Stan Wagon, of the MAA book Old and New Unsolved Problems in Plane Geometry and Number Theory, and he was MAA President in 1971-73.  Victor Klee passed away on August 18, 2007 in Lakewood, Ohio.  To read the obituary from the MAA site:

John Reay studied music at Pacific Lutheran University and mathematics at the University of Washington, where Victor Klee directed his 1963 Ph.D. thesis. He now teaches at Western Washington University, and plays in the Whatcom Symphony Orchestra. This paper on 2-homothetic sets grew out of a talk he prepared for the Visiting Lecturer Program of the MAA, and the goading of friends who wanted a written version. The talk was based on earlier lectures of Klee.

Subject classification(s): Geometry and Topology | Analytic Geometry
Publication Date: 
Wednesday, February 7, 2007