Symmetry, Shape, and Space: An Introduction to Mathematics Through Geometry
June 2008, ©2002
To the Reader.
1. The Basics.
2.2. Celtic Knots.
3.1. Ruler and Compass Constructions.
3.2. The Pentagon and the Golden Ratio.
3.3. Theoretical Origami.
3.4. Knots and Stars.
4.1. Regular and Semiregular Tilings.
4.2. Irregular Tilings.
4.3. Penrose Tilings.
5. Two-Dimensional Symmetry.
5.2. Rosette Groups: Point Symmetry.
5.3. Frieze Patterns: Line Symmetry.
5.4. Wallpaper Patterns: Plane Symmetry.
5.5. Islamic Lattice Patterns.
6. Other Dimensions, Other Worlds.
6.2. The Fourth Dimension.
7.1. Pyramids, Prisms, and Antiprisms.
7.2. The Platonic Solids.
7.3. The Archimedean Solids.
7.4. Polyhedral Transformations.
7.5. Models of Polyhedra.
7.6. Infinite Polyhedra.
8. Three-Dimensional Symmetry.
8.1. Symmetries of Polyhedra.
8.2. Three-Dimensional Kaleidoscopes.
9. Spiral Growth.
9.1. Spirals and Helices.
9.2. Fibonacci Numbers and Phyllotaxis.
10. Drawing Three Dimensions in Two.
10.2. Optical Illusions.
11.1. Noneuclidean Geometry.
11.2. Map Projections.
11.3. Curvature of Curves.
11.4. Curvature of Surfaces.
11.5. Soap Bubbles.
12. Graph Theory.
13.3. More About Surfaces.
13.4. Map Coloring Problems.
Hints and Solutions to Selected Problems.
Exercises and activities link students' intuitive and analytical capabilities
Each chapter essentially independent of the others, allowing flexibility in course design
Unique Table of Contents assured to intrigue and delight readers
Available bundled with The Geometer's Sketchpad
Perfect for students in the arts or pre-service education
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