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Euclidean Geometry and its Subgeometries

Authors: Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H.

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  • Provides a complete and rigorous axiomatic treatment of Euclidean geometryProofs for many theorems are worked out in detailTakes a modern approach by replacing congruence axioms with a transformational definition of congruence

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eBook $119.00
price for Mexico (gross)
  • ISBN 978-3-319-23775-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for Mexico
  • ISBN 978-3-319-23774-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for Mexico
  • ISBN 978-3-319-79533-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties.
There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem.
Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.

Reviews

“This is the most detailed undergraduate textbook on the axiomatic foundation of Euclidean geometry ever written.” (Victor V. Pambuccian, Mathematical Reviews, July, 2016)

“The authors do a commendable job of writing out proofs in detail and attempting to make the text accessible to undergraduates. … It makes a very useful reference source, and … there aren’t very many current textbooks that discuss geometry from this particular point of view. I commend this book to the attention of instructors with an interest in the foundations of geometry, and to university librarians.” (Mark Hunacek, MAA Reviews, maa.org, March, 2016)


Table of contents (21 chapters)

Table of contents (21 chapters)

Buy this book

eBook $119.00
price for Mexico (gross)
  • ISBN 978-3-319-23775-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for Mexico
  • ISBN 978-3-319-23774-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for Mexico
  • ISBN 978-3-319-79533-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Euclidean Geometry and its Subgeometries
Authors
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-23775-6
DOI
10.1007/978-3-319-23775-6
Hardcover ISBN
978-3-319-23774-9
Softcover ISBN
978-3-319-79533-1
Edition Number
1
Number of Pages
XIX, 527
Number of Illustrations
59 b/w illustrations
Topics