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Quasicrystals and Geometry

  • Date Published: September 1996
  • availability: Available
  • format: Paperback
  • isbn: 9780521575416

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  • 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.

    • Quasicrystals are one of the hottest topics in both mathematics (geometry) and condensed matter physics
    • The first-ever single-author account of what is known about these systems and the mathematics behind them
    • Beautiful graphics, well written and carefully compiled
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    Reviews & endorsements

    'In this excellent monograph, Marjorie Senechal … gives us insight into what happened when established ideas had to be reexamined, modified or overturned … Her several published reports and this book convey both the searches for new directions and the excitement of new results and are worthwhile narratives of ten exciting years.' Science

    'This is a little gem of a book, with a quasicrystalline elegance to it.' American Scientist

    '… this is a nice, timely and valuable book and is recommended to anyone interested in learning about this subject.' European Mathematical Society Newsletter

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    Product details

    • Date Published: September 1996
    • format: Paperback
    • isbn: 9780521575416
    • length: 308 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.46kg
    • availability: Available
  • Table of Contents

    Preface
    1. Past as prologue
    2. Lattices, Voronoi cells, and quasicrystals
    3. Introduction to diffraction geometry
    4. Order on the line
    5. Tiles and tilings
    6. Penrose tilings of the plane
    7. The aperiodic zoo
    8. An atlas of tiling transforms
    Appendix I. A mathematician's toolbag
    Appendix II. De Bruijn's generalized functions
    References.

  • Author

    Marjorie Senechal, Smith College, Massachusetts

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