Squaring the Plane

Henle and Henle show how to square the plane. Their research was inspired by two lovely pieces of mathematics: the discovery by William T. Tutte, A. H. Stone, R. L. Brooks, and C. A. B. Smith of squares with integral sides that can be tiled by smaller squares with integral sides; and the well-known...

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Bibliographic Details
Published in:The American mathematical monthly 2008-01, Vol.115 (1), p.3-12
Main Authors: Henle, Frederick V., Henle, James M.
Format: Article
Language:English
Subjects:
Discrete mathematics
Geometric planes
Geometry
Mathematical integrals
Mathematical procedures
Mathematical theorems
Mathematics education
Rectangles
Tessellations
Theorems
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Summary:Henle and Henle show how to square the plane. Their research was inspired by two lovely pieces of mathematics: the discovery by William T. Tutte, A. H. Stone, R. L. Brooks, and C. A. B. Smith of squares with integral sides that can be tiled by smaller squares with integral sides; and the well-known tiling of plane by squares whose sides are the Fibonacci numbers. Their approach focus on rectangles and ells to show that the plane admits a tiling that uses exactly one square of side-length n.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2008.11920491