Quasicrystals and Geometry

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CUP Archive, Sep 26, 1996 - Mathematics - 286 pages
Quasicrystals and Geometry brings together for the first time the many strands of contemporary research in quasicrystal geometry and weaves them into a coherent whole. The author describes the historical and scientific context of this work, and carefully explains what has been proved and what is conjectured. This, together with a bibliography of over 250 references, provides a solid background for further study. The discovery in 1984 of crystals with 'forbidden' symmetry posed fascinating and challenging problems in many fields of mathematics, as well as in the solid state sciences. Increasingly, mathematicians and physicists are becoming intrigued by the quasicrystal phenomenon, and the result has been an exponential growth in the literature on the geometry of diffraction patterns, the behaviour of the Fibonacci and other nonperiodic sequences, and the fascinating properties of the Penrose tilings and their many relatives.
 

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Contents

Lattices Voronoi cells and quasicrystals
34
Introduction to diffraction geometry
74
Order on the line
106
Tiles and tilings
135
Penrose tilings of the plane
170
The aperiodic zoo
207
An atlas of tiling transforms
238
A mathematical toolbag
259
De Bruijns generalized functions
267
Index
283
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