A New Look at Geometry

Overview


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 ...
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A New Look at Geometry

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Overview


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.
Introduction to the Dover edition by Peter Ruane.
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Product Details

  • ISBN-13: 9780486498515
  • Publisher: Dover Publications
  • Publication date: 10/17/2012
  • Series: Dover Books on Mathematics Series
  • Edition description: Reprint
  • Pages: 416
  • Sales rank: 1,381,994
  • Product dimensions: 5.30 (w) x 8.40 (h) x 1.10 (d)

Table of Contents


1. One Book and Three Metaphors
2. Geometry Before Euclid
3. Euclid's Geometry
4. Geometry via Numbers
5. Geometry via Arrows
6. Geometry via Reflections
7. Geometry in Newtonian Physics
8. Non-Euclidean Geometry
9. The Calculus and Geometry
10. Projective Geometry
11. Geometry in Relativity Physics
12. Geometry Generalized
13. Geometry and Algebra
Bibliography
Answers to Exercises
Index
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