Cutting polygons composed of equal rectangles into similar rectangles (Q2063655)

\textit{M. Dehn} [Math. Ann. 57, 314--332 (1903; JFM 34.0547.02)] proved his famous result that a rectangle can be cut into squares if and only if the ratio of the sides of the rectangle is a rational number. One can consider the general and very complicated problem of cutting a polygon into similar rectangles. The author treats the particular case of cutting a polygon all of whose sides belong to \(\mathbb Q[\sqrt{p}]=\{a+b\sqrt{p}:a, b \in\mathbb Q\}\), where \(p\) is a quadratic irrationality.