Product Description

The common thread throughout this book is aperiodic tilings; the best-known example is the "kite and dart" tiling. This tiling has been widely discussed, particularly since 1984 when it was adopted to model quasicrystals. The presentation uses many different areas of mathematics and physics to analyse the new features of such tilings. Although many people are aware of the existence of aperiodic tilings, and maybe even their origin in a question in logic, not everyone is familiar with their subtleties and the underlying rich mathematical theory. For the interested reader, this book fills that gap. Understanding this new type of tiling requires an unusual variety of specialties, including ergodic theory, functional analysis, group theory and ring theory from mathematics, and statistical mechanics and wave diffraction from physics. This interdisciplinary approach also leads to new mathematics seemingly unrelated to the tilings. Included are many problems (with solutions) and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.

Product Details

• Amazon Sales Rank: #878429 in Books
• Published on: 2000-01-13
• Original language: English
• Binding: Paperback
• 120 pages

Customer Reviews

Lovely book!
This book can't miss,--*not with a title like that!* And it *is* a hit!-- Perhaps few math books are hits in the corner-book store, or at amazon. In this case, my undergrad students, and the grad students too!,-- reacted very positively. And they aren't easy to please! This lovely little book also worked great when I tried it in an individual undergrad research project. --What does the old positional number system (the one we all learned in school)-- have to do with dynamics,-- or with various "mystery-tiles", pinwheel tilings...? Look!! It is in the book! (Hint: They all come about by clever manipulation of the letters in a finite alphabet, or the chosen 'digits' in our familiar number system.) These manipulations follow rules, and they come from specifying a matrix. Then the more abstract tools from mathematical analysis, and ergodic theory, enter when second generation dynamical systems, (abstractions if you will!)-- are built on "spaces" of all tilings in a given class,-- or on a specified varity of outcomes in symbolic dynamics. We then arrive at iterated matrix operations, and limits: We must solve associated eigenvalue problems. Take limits, and if you are careful, you find equilibrium states which represent solutions to otherwise intractable puzzles,-- from math (for example, familiar, or unfamiliar, completions of number systems),-- and from applications to real life problems, familiar,-- or perhaps unexpected, tilings. Useful ones!