Sasho Kalajdzievski

Math and Art (eBook, PDF)

An Introduction to Visual Mathematics

• Format: PDF

Produktbeschreibung

This introduction explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With color figures and animations on an accompanying downloadable resources, plus a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductio

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Produktdetails

• Verlag: Taylor & Francis
• 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.