图书简介
Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. It includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire or generate art._x000D_
Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions._x000D_
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Provides an accessible introduction to mathematics in art_x000D_
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Supports the narrative with a self-contained mathematical theory, with complete proofs of the main results (including the classification theorem for similarities) _x000D_
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Presents hundreds of figures, illustrations, computer-generated graphics, designs, photographs, and art reproductions, mainly presented in full color_x000D_
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Includes 21 projects and about 280 exercises, about half of which are fully solved_x000D_
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Covers Euclidean geometry, golden section, Fibonacci numbers, symmetries, tilings, similarities, fractals, cellular automata, inversion, hyperbolic geometry, perspective drawing, Platonic and Archimedean solids, and topology_x000D_
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New to the Second Edition_x000D_
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New exercises, projects and artworks_x000D_
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Revised, reorganised and expanded chapters_x000D_
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Chapter 1. Euclidean Geometry. 1.0. Introduction. 1.1. The Five Axioms of Euclidean Geometry. 1.2. Ruler and Compass Constructions. 1.3. The Golden Ratio. 1.4. Fibonacci Numbers. Chapter 2. Plane Transformations. 2.1. Plane Symmetries. 2.2.* Plane Symmetries, Vectors, and Matrices (Optional). 2.3. Groups of Symmetries Of Planar Objects. 2.4. Frieze Patterns. 2.5. Wallpaper Designs and Tilings of the Plane. 2.6. Tilings and Art. Chapter 3. Similarities, Fractals, and Cellular Automata. 3.1. Similarities and some other Planar Transformations. 3.2.* Complex Numbers (Optional). 3.3. Fractals: Definition and Some Examples. 3.4. Julia Sets. 3.5. Cellular Automata. Chapter 4. Hyperbolic Geometry. 4.1. Non-Euclidean Geometries: Background and Some History. 4.2. Inversion. 4.3. Hyperbolic Geometry. 4.4. Some Basic Constructions in the Poincare Model. 4.5. Tilings of the Hyperbolic Plane. Chapter 5. Perspective. 5.1. Perspective: A brief overview of the Evolution of the rules of perspective. 5.2. Perspective Drawing and Constructions of Some Two-Dimensional (Planar) Objects. 5.3. Perspective Images of Three-Dimensional Objects. 5.4.* Mathematics of Perspective Drawing: A Brief Overview (Optional). Chapter 6. Some Three-Dimensional Objects. 6.1. Regular and Other Polyhedra. 6.2. Sphere, Cylinder, Cone, and Conic Sections. 6.3. Geometry, Tilings, Fractals, and Cellular Automata in Three Dimensions. Chapter 7. Topology. 7.1. Homotopy of Spaces: An Informal Introduction. 7.2. Two-Manifolds and The Euler Characteristic. 7.3. Non-Orientable Two-Manifolds and Three-Manifolds. Appendix: Classification Theorem for Similarities. Solutions.
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