Geometry: the language of space and form

John Tabak081604953X, 9780816049530, 9780816068760

Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. Projective geometry began its development in the Renaissance as artists like da Vinci and Durer explored methods for representing 3-dimensional objects on 2-dimensional surfaces. These ideas were refined and made increasingly abstract in the 19th and 20th centuries. Late in the 20th century, ideas from projective geometry found widespread application in the area of computer graphics. Similarly, Descartes’s ideas about coordinate geometry led to progress in finding mathematical representations for shapes of increasing complexity, including the shape of the universe and other areas considered by mathematicians today. Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed. Biographical information on key figures, a look at different applications of geometry over time, and the groundbreaking discoveries related to geometry are comprehensively covered.

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Table of contents :
Cover……Page 1
Front Matter……Page 4
Table of Contents……Page 8
Acknowledgments……Page 12
Introduction……Page 14
Part One: Geometry in Antiquity……Page 20
1. Geometry Before the Greeks……Page 22
2. Early Greek Geometry……Page 29
3. Major Mathematical Works of Greek Geometry……Page 43
Part Two: Projective Geometry……Page 70
4. Mathematics and Art During the Renaissance……Page 71
5. The First Theorems……Page 85
6. Projective Geometry Rediscovered……Page 94
7. A Non-Euclidean Geometry……Page 111
Part Three: Coordinate Geometry……Page 120
8. The Beginnings of Analytic Geometry……Page 121
9. Calculus and Analytic Geometry……Page 139
10. Differential Geometry……Page 160
11. The Shape of Space and Time……Page 173
12. Infinite-Dimensional Geometry……Page 190
Chronology……Page 197
Glossary……Page 215
Further Reading……Page 220
Index……Page 230