95-37 Radin Charles, Sadun Lorenzo

THE ISOPERIMETRIC PROBLEM FOR PINWHEEL TILINGS (389K, plain TeX) Jan 31, 95

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Abstract. In aperiodic ``pinwheel'' tilings of the plane there exist unions of tiles with ratio (area)/(perimeter)${}^2$ arbitrarily close to that of a circle. Such approximate circles can be constructed with arbitrary center and any sufficiently large radius. The existence of such circles follows from the metric on pinwheel space being almost Euclidean at large distances; if $P$ and $Q$ are points separated by large Euclidean distance $R$, then the shortest path along tile edges from $P$ to $Q$ has length $R + o(R)$.

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