Undergraduate Texts in Mathematics

The Foundations of Geometry and the Non-Euclidean Plane

Authors: Martin, G.E.

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  • ISBN 978-1-4612-5725-7
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  • ISBN 978-0-387-90694-2
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Softcover $79.95
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  • ISBN 978-1-4612-5727-1
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About this Textbook

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non­ Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap­ ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten­ sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three­ and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref­ erence if necessary.

Table of contents (34 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4612-5725-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA in USD
  • ISBN 978-0-387-90694-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA in USD
  • ISBN 978-1-4612-5727-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Foundations of Geometry and the Non-Euclidean Plane
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1975
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-5725-7
DOI
10.1007/978-1-4612-5725-7
Hardcover ISBN
978-0-387-90694-2
Softcover ISBN
978-1-4612-5727-1
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XVI, 512
Additional Information
Originally published by Intext Educational Publishers, New York, 1972
Topics