Sasho Kalajdzievski

Math and Art (eBook, PDF)

An Introduction to Visual Mathematics

• Format: PDF

Produktbeschreibung

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.

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.

Features

• Provides an accessible introduction to mathematics in art
• Supports the narrative with a self-contained mathematical theory, with complete proofs of the main results (including the classification theorem for similarities)
• Presents hundreds of figures, illustrations, computer-generated graphics, designs, photographs, and art reproductions, mainly presented in full color
• Includes 21 projects and approximately 280 exercises, about half of which are fully solved
• Covers Euclidean geometry, golden section, Fibonacci numbers, symmetries, tilings, similarities, fractals, cellular automata, inversion, hyperbolic geometry, perspective drawing, Platonic and Archimedean solids, and topology

New to the Second Edition

• New exercises, projects and artworks
• Revised, reorganized and expanded chapters
• More use of color throughout

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 398
• Erscheinungstermin: 26. September 2021
• Englisch
• ISBN-13: 9780429667145
• Artikelnr.: 62587508

Autorenporträt

Sasho Kalajdzievski is the professor in the Mathematics department at University of Manitoba

Inhaltsangabe

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 Poincaré 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.