Miles of Tiles (Student Mathematical Library, Vol. 1) (Student Mathematical Library, V. 1)

'In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem...' - from the Preface. 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 analyze 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 worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience. “In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics—mathematics unforeseen from the motivating problem ...” —from the Preface 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 analyze 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 worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience. "Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative Tries to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem. This book focuses on aperiodic tilings; the best-known example is the 'kite and dart' tiling. With diagrams, explains the new mathematics and physics behind the jigsaw puzzle-modeled structures exemplified by Penrose's kit and dart tiling. For senior undergraduate math majors. Annotation c. Book News, Inc., Portland, OR (booknews.com)