Mathematical Research Letters

Volume 1 (1994)

Number 5

Tiling a square with silimar rectangles

Pages: 547 – 558



C. Freiling (California State University)

D. Rinne (California State University)


In 1903 M. Dehn proved that a rectangle can be tiled (or partitioned) into finitely many squares if and only if the ratio of its base and height is rational. In this article we show that a square can be tiled with finitely many similar rectangles of eccentricity $r$ if and only if $r$ is an algebraic number and each of its conjugate roots has positive real part.

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