Symmetry, Shape, and Space : An Introduction to Mathematics Through Geometry

by Kinsey, L. Christine; Moore, Teresa E.

• ISBN13: 9781930190092
• ISBN10: 1930190093
• Format: Hardcover
• Copyright: 2001-06-01
• Publisher: Wiley

Summary

This text is suitable for introductory students, perhaps in programs such as education, art and architecture. The text contains some traditional material from geometry as well as more innovative topics. Throughout the text, the authors place strong emphasis on pedagogy, hands-on model building, a guided discovery method of learning, etc. Much of the material is written in such a way that it can be used in the classroom for enrichment projects, by prospective mathematics teachers.

Table of Contents

Preface	vii
To the Reader	xiii
The Basics	1	(19)
Measurement	1	(12)
Polygons	13	(7)
Grids	20	(20)
Billiards	20	(10)
Celtic Knots	30	(10)
Constructions	40	(45)
Ruler and Compass Constructions	40	(11)
The Pentagon and the Golden Ratio	51	(10)
Theoretical Origami	61	(11)
Knots and Stars	72	(6)
Linkages	78	(7)
Tesselations	85	(42)
Regular and Semiregular Tilings	85	(9)
Irregular Tilings	94	(21)
Penrose Tilings	115	(12)
Two-Dimensional Symmetry	127	(53)
Kaleidoscopes	127	(11)
Rosette Groups: Point Symmetry	138	(9)
Frieze Patterns: Line Symmetry	147	(9)
Wallpaper Patterns: Plane Symmetry	156	(15)
Islamic Lattice Patterns	171	(9)
Other Dimensions, Other Worlds	180	(28)
Flatlands	180	(14)
The Fourth Dimension	194	(14)
Polyhedra	208	(55)
Pyramids, Prisms, and Antiprisms	208	(8)
The Platonic Solids	216	(8)
The Archimedean Solids	224	(6)
Polyhedral Transformations	230	(5)
Models of Polyhedra	235	(18)
Infinite Polyhedra	253	(10)
Three-Dimensional Symmetry	263	(16)
Symmetries of Polyhedra	263	(7)
Three-Dimensional Kaleidoscopes	270	(9)
Spiral Growth	279	(21)
Spirals and Helices	279	(11)
Fibonacci Numbers and Phyllotaxis	290	(10)
Drawing Three Dimensions in two	300	(29)
Perspective	300	(15)
Optical Illusions	315	(14)
Shape	329	(54)
Noneuclidean Geometry	329	(7)
Map Projections	336	(13)
Curvature of Curves	349	(10)
Curvature of Surfaces	359	(13)
Soap Bubbles	372	(11)
Graph Theory	383	(28)
Graphs	383	(10)
Trees	393	(8)
Mazes	401	(10)
Topology	411	(38)
Dimension	411	(10)
Surfaces	421	(10)
More About Surfaces	431	(8)
Map Coloring Problems	439	(10)
Hints and Solutions to Selected Problems	449	(32)
Bibliography	481	(8)
Index	489	(4)
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