Aperiodic Tilings by Right Triangles

Abstract

Let ψ denote the square root of the golden ratio, $\psi=\sqrt{(\sqrt5-1)/2}$. A golden triangle is any right triangle with legs of lengths a,b where a/b = ψ. We consider tilings of the plane by two golden triangles: that with legs 1,ψ and that with legs ψ,ψ ². Under some natural constrains all such tilings are aperiodic.

The work was in part supported by the RFBR grant 14-01-93107.