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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Editorial Reviews

School Library Journal
Gr 10-Up-In uniform but independent volumes, Tabak offers sustained, meaty historical and methodological studies of the major branches of mathematics. Beginning, in some cases, with prehistoric evidence, he traces: developments in our very idea of what algebra is; the nature of ancient, projective (including non-Euclidian), and coordinate geometry; the uses of mathematics in finding precise ways to describe natural laws; the "invention" of rational, irrational and imaginary numbers, and the idea of infinity; and advances in probability theory and statistics. In each volume he analyzes the insights and accomplishments of many thinkers, ancient and modern, providing a generous array of illuminating demonstrations and examples while keeping extraneous biographical details-and, for that matter, illustrations-to a minimum, then closes with a time line, a specialized glossary, and annotated, multimedia reading lists. General readers may prefer to start with such single-volume histories as William Berlinghoff and Fernando Gouvea's Math through the Ages (Oxton House, 2002) or Ivor Grattan-Guinness's Rainbow of Mathematics (Norton, 2000), but for serious students of the subject, and collections supporting strong science programs, these make appropriate additions to both reference and circulating shelves.-John Peters, New York Public Library Copyright 2004 Reed Business Information.
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Product Details

  • ISBN-13: 9780816049530
  • Publisher: Facts on File, Incorporated
  • Publication date: 4/28/2004
  • Series: Facts on File Math Library
  • Pages: 240
  • Age range: 11 - 17 Years
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.80 (d)

Table of Contents

Pt. 1 Geometry in antiquity 1
1 Geometry before the Greeks 3
2 Early Greek geometry 10
3 Major mathematical works of Greek geometry 24
Pt. 2 Projective geometry 51
4 Mathematics and art during the renaissance 52
5 The first theorems 66
6 Projective geometry rediscovered 75
7 A non-Euclidean geometry 92
Pt. 3 Coordinate geometry 101
8 The beginnings of analytic geometry 102
9 Calculus and analytic geometry 120
10 Differential geometry 140
11 The shape of space and time 153
12 Infinite-dimensional geometry 170
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