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Fourteen Proofs of a Result about Tiling a Rectangle

Year of Award: 1988

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 94, 1987, pp. 601-617

Summary: This paper recounts several proofs of the theorem, "Whenever a rectangle is tiled by rectangles each of which has at least one integer side, then the tiled rectangle also must have at least one integer side."  The proof techniques range from double integrals to graph theory.  Generalizations of the theorem are discussed, and the proof techniques are scrutinized for applicability to the more general problems.

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About the Author: (from The American Mathematical Monthly, vol. 94 (1987)) Stan Wagon: I received my undergraduate degree at McGill and my doctorate at Dartmouth, in set theory under James Baumgartner. Recently my work has centered around expository writing: The Banach-Tarski Paradox was published in 1985 (Cambridge), and a series of eight articles on numerical evidence for various conjectures appeared in The Mathematical Intelligencer in 1985-6.

 

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Stan Wagon
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Stan Wagon
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Publication Date: 
Tuesday, September 23, 2008
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Summary: 
This paper recounts several proofs of the theorem, "Whenever a rectangle is tiled by rectangles each of which has at least one integer side, then the tiled rectangle also must have at least one integer side." The proof techniques range from double integrals to graph theory. Generalizations of the theorem are discussed, and the proof techniques are scrutinized for applicability to the more general problems.

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