Math and Art
portes grátis
Math and Art
An Introduction to Visual Mathematics
Kalajdzievski, Sasho
Taylor & Francis Ltd
09/2021
386
Dura
Inglês
9780367076139
15 a 20 dias
975
Descrição não disponível.
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Plane Symmetries;Julia Sets;Geometry;Tilings, Fractals;Topology;Mathematics and Art;Visual Math;Euclidean geometry;mathematics in art;Fibonacci numbers;Archimedes;Plato;Cellular Automata;Euclid;Line Segment AB;Hyperbolic Geometry;Euler Characteristic;Hyperbolic Plane;Regular Polygon;Hyperbolic Line;Julia Set;Frieze Pattern;Glide Reflections;Klein Bottle;Connected Sum;Torus Knot;Hyperbolic Length;Hyperbolic Distance;Drawing Plane;Perspective Images;Horizon Circle;Semiregular Polyhedra;Golden Rectangle;Stretching Factor;Golden Ratio;Translation Symmetries;Koch Snowflake
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Plane Symmetries;Julia Sets;Geometry;Tilings, Fractals;Topology;Mathematics and Art;Visual Math;Euclidean geometry;mathematics in art;Fibonacci numbers;Archimedes;Plato;Cellular Automata;Euclid;Line Segment AB;Hyperbolic Geometry;Euler Characteristic;Hyperbolic Plane;Regular Polygon;Hyperbolic Line;Julia Set;Frieze Pattern;Glide Reflections;Klein Bottle;Connected Sum;Torus Knot;Hyperbolic Length;Hyperbolic Distance;Drawing Plane;Perspective Images;Horizon Circle;Semiregular Polyhedra;Golden Rectangle;Stretching Factor;Golden Ratio;Translation Symmetries;Koch Snowflake
