|aThe symmetries of things /|cJohn H. Conway, Heidi Burgiel, Chaim Goodman-Strauss.
260
|aWellesley, Mass. :|bA.K. Peters,|cc2008.
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|axviii, 426 p. :|bill. (chiefly col.) ;|c25 cm.
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|atext|btxt|2rdacontent
337
|aunmediated|bn|2rdamedia
338
|avolume|bnc|2rdacarrier
504
|aIncludes bibliographical references (p. 419-421) and index.
505
0
|aSymmetries -- Planar patterns -- The magic theorem -- The spherical patterns -- Frieze patterns -- Why the magic theorems work -- Euler's map theorem -- Classification of surfaces -- Orbifolds -- Presenting presentations -- Twofold colorations -- Threefold colorings of plane patterns -- Other primefold colorings -- Searching for relations -- Types of tilings -- Abstract groups -- Introducing hyperbolic groups -- More on hyperbolic groups -- Archimedean tilings -- Generalized Schläfli symbols -- Naming Archimedian and Catalan polyhedra and tilings -- The 35 "prime" space groups -- Objects with prime symmetry -- Flat universes -- The 184 composite space groups -- Higher still.
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|a"Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, together with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers."--Jacket.
內容簡介top The Symmetries of Things 簡介 Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, together with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.