Geometric Symmetry In Patterns And Tilings
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Geometric Symmetry in Patterns and Tilings
This book covers a wide range of mathematical concepts as they are applied to regularly repeating surface decoration for textiles and other decorated materials such as wallpapers and wrappings. Starting with basic principles of symmetry it moves on to cover more complex issues of graph theory, group theory and topology. All these concepts are extensively illustrated with over 1000 original illustrations. A complex area, previously best understood by mathematicians and crystallographers, is made accessible here to artists and designers.
Geometric Symmetry in Patterns and Tilings
This book encompasses a wide range of mathematical concepts relating to regularly repeating surface decoration from basic principles of symmetry to more complex issues of graph theory, group theory and topology. It presents a comprehensive means of classifying and constructing patterns and tilings. The classification of designs is investigated and discussed forming a broad basis upon which designers may build their own ideas. A wide range of original illustrative material is included.In a complex area previously best understood by mathematicians and crystallographers, the author develops and applies mathematical thinking to the context of regularly repeating surface-pattern design in a manner accessible to artists and designers. Design construction is covered from first principles through to methods appropriate for adaptation to large-scale screen-printing production. The book extends mathematical thinking beyond symmetry group classification. New ideas are developed involving motif orientation and positioning, including reference to a crystal structure, leading on to the classification and construction of discrete patterns and isohedral tilings.Designed to broaden the scope of surface-pattern designers by increasing their knowledge in otherwise impenetrable theory of geometry this 'designer friendly' book serves as a manual for all types of surface design including textiles, wallpapers and wrapping paper. It is also of value to crystallographers, mathematicians and architects.
Tilings and Patterns
Remarkable... It will surely remain the unique reference in this area for many years to come. Roger Penrose, Nature ... an outstanding achievement in mathematical education. Bulletin of The London Mathematical Society I am enormously impressed... Will be the definitive reference on tiling theory for many decades. Not only does the book bring together older results that have not been brought together before, but it contains a wealth of new material... I know of no comparable book. Martin Gardner