Aperiodic Tilings by Right Triangles
Let ψ denote the square root of the golden ratio, ψ = ( 5 − 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.