Tilings and patterns

Tilings and Patterns stands as a comprehensive mathematical text exploring the theory and applications of tilings - partitions of planes into regions - and patterns that form through regular repetition of motifs. Published in 1987 after a decade of development, this 700-page volume represents a collaboration between mathematicians Branko Grünbaum and Geoffrey Colin Shephard. The first section establishes foundational concepts through seven chapters, covering general tiling theory, regular polygons, and pattern analysis. The work includes detailed illustrations, proofs, and examples throughout its systematic examination of tiling principles and their mathematical properties. The final five chapters move into advanced territory, examining colored patterns, polygonal tilings, aperiodic arrangements, Wang tiles, and unconventional tiling methods. Each chapter contains exercises and extensive historical notes that document the field's development, including unsolved problems and potential applications. The text serves as a bridge between pure mathematical theory and practical applications, connecting abstract geometric concepts to real-world uses in science, mathematics, and arts. Its thorough bibliography and comprehensive index have made it a key reference work in the field of geometric pattern study.

Readers describe this as a comprehensive reference text on tilings, with detailed mathematical treatment and thorough historical background. Mathematics professors and graduate students make up most reviewers. Likes: - Extensive illustrations and diagrams - Rigorous mathematical proofs - Coverage of both classical and modern tiling theory - Historical development of key concepts - Useful as both textbook and reference Dislikes: - Dense mathematical notation challenges non-experts - High price ($200+ for hardcover) - Some readers note minor printing quality issues in diagrams - Limited coverage of 3D tilings Ratings: Goodreads: 4.5/5 (12 ratings) Amazon: 4.7/5 (6 ratings) One professor wrote: "Contains material I haven't found anywhere else, especially on color symmetry and marked motifs." A graduate student noted: "The proofs are elegant but require significant mathematical maturity." The book remains in print but high costs limit accessibility for individual buyers.

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🔷 The book's publication in 1987 marked a turning point in the study of tilings, consolidating centuries of scattered research into one comprehensive volume. 🔷 Author Branko Grünbaum's contributions to geometry earned him the Leroy P. Steele Prize for Mathematical Exposition in 2005, recognizing his exceptional clarity in mathematical writing. 🔷 The work features over 700 illustrations, making it one of the most visually detailed mathematical texts of its time. 🔷 The book's coverage of Wang tiles influenced early computer graphics and continues to impact modern procedural texture generation in video games. 🔷 The original manuscript took over a decade to complete, with Grünbaum and co-author G.C. Shephard corresponding entirely by mail between continents before email existed.