Tiling a square with silimar rectangles

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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Published 1 January 1994