91-12 Charles Radin

GLOBAL ORDER FROM LOCAL SOURCES (70K, TeX) Jul 15, 91

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Abstract. This article contains introductions to three open problems of significant research interest, the sphere packing problem from number theory, the tiling problem from logic, and the crystal problem from condensed matter physics. All three problems will be shown to have at their core special cases of one simply-stated optimization problem. Our goal is to use the intuition gained from these three perspectives to direct attention to this common core. We will also show that some of the tools developed in the separate problems are of real value in the others.

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