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Geometry: The Language of Space and Form

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Geometry is a compelling look not only at how this branch of mathematics arose and flourished in different cultures at different times but also at its useful applications in science and in society. Author John Tabak pinpoints the beginnings of geometry to ancient Egypt and Mesopotamia and traces its extraordinary progress in Greece. Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. Geometry continued its evolution with projective geometry, an area born through the work of Renaissance artists, such as da Vinci and Durer, and their exploration of methods for representing three-dimensional objects on two-dimensional surfaces. Over centuries, mathematicians refined these concepts to the extent that projective geometry found application in the area of computer graphics. Tabak explores geometry as an indispensable part of mathematics and a widely utilized tool in the scientific community.Geometry includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources for further research. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics.

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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

Language

English

Format

PDF

size

1.29 MB

Author(s)

John Tabak

ISBN

9780816049530, 0-8160-4953-X

Publisher

Facts on File, Year: 2004

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