This text brings together 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 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. In this
monograph, Marjorie Senechal gives us insight into what happened
when established ideas had to be re-examined, modified or
overturned.
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