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5.0
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This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non-Euclidean geometry and projective geometry form brief, self-contained treatments.
More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics education), and mathematically minded readers will appreciate this outstanding exploration of the role of geometry in the development of Western scientific thought.
Dover (2012) republication of the edition published by The John Day Company, Inc., New York, 1966. Introduction to the Dover edition by Peter Ruane.
Contents --- Introduction to the Dover Edition 5 *** 1 One Book and Three Metaphors 9 *** 2 Geometry Before Euclid 12 *** 3 Euclid's Geometry 63 *** 4 Geometry via Numbers 105 *** 5 Geometry via Arrows 137 *** 6 Geometry via Reflections 158 *** 7 Geometry in Newtonian Physics 187 *** 8 Non-Euclidean Geometry 195 *** 9 The Calculus and Geometry 261 *** 10 Projective Geometry 287 *** 11 Geometry in Relativity Physics 356 *** 12 Geometry Generalized 371 *** 13 Geometry and Algebra 382 *** Bibliography 389 *** Answers to Exercises 391 *** Index 405
