Raymond Aschheim – Classification of Quasicrystals by intersecting lattices and spheres
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We discover how successive shells of onion-like spheres intersecting square grids in high dimensional spaces will classify points of integral coordinates as solutions of Diophantine equations.
From this very simple construction emerges a deep link between the geometry of quasicrystals and the algebraic numbers, and also a link to number theory, from the sigma function counting the divisors, to more advanced Jacobi elliptic function and Dirichlet L-Series. Many applications to quasicrystals of icosahedral symmetry are presented, including the QSN.
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