Tiling a square with silimar rectangles

1994/01/01 by C. Freiling, D. Rinne · 1 citation
Materials Science · Computer Science · Mathematics · #Quasicrystal Structures and Properties #semigroups and automata theory #Mathematics and Applications #Mathematics #Square tiling #Square (algebra) #Combinatorics #Geometry #Grid

paper · doi:10.4310/mrl.1994.v1.n5.a3

openalex publication_date 1994/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

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.

Citations

• Eine Basis aller Zahlen und die unstetigen L�sungen der Funktionalgleichung:f(x+y)=f(x)+f(y)
• On the zeros of polynomials with complex coefficients
• The dissection of rectangles into squares
• On Hilbert’s third problem

Cited by

• Plastic ratio [wikipedia]