Undergraduate Texts in Mathematics

Geometry: Euclid and Beyond

Authors: Hartshorne, Robin

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  • ISBN 978-0-387-22676-7
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About this Textbook

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.

Table of contents (9 chapters)

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-0-387-22676-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $64.95
price for USA
  • ISBN 978-0-387-98650-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $64.95
price for USA
  • ISBN 978-1-4419-3145-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry: Euclid and Beyond
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2000
Publisher
Springer-Verlag New York
Copyright Holder
Robin Hartshorne
eBook ISBN
978-0-387-22676-7
DOI
10.1007/978-0-387-22676-7
Hardcover ISBN
978-0-387-98650-0
Softcover ISBN
978-1-4419-3145-0
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XII, 528
Topics