Authors:
Provides a complete and rigorous axiomatic treatment of Euclidean geometry.
Proofs for many theorems are worked out in detail.
Takes a modern approach by replacing congruence axioms with a transformational definition of congruence
Includes supplementary material: sn.pub/extras
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Table of contents (21 chapters)
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Front Matter
About this book
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)
Authors and Affiliations
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Indiana University South Bend, SOUTH BEND, USA
Edward John Specht
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Andrews University, Berrien Springs, USA
Harold Trainer Jones, Keith G. Calkins
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Andrews University, Bloomington, USA
Donald H. Rhoads
Bibliographic Information
Book Title: Euclidean Geometry and its Subgeometries
Authors: Edward John Specht, Harold Trainer Jones, Keith G. Calkins, Donald H. Rhoads
DOI: https://doi.org/10.1007/978-3-319-23775-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-23774-9Published: 12 January 2016
Softcover ISBN: 978-3-319-79533-1Published: 30 March 2018
eBook ISBN: 978-3-319-23775-6Published: 31 December 2015
Edition Number: 1
Number of Pages: XIX, 527
Number of Illustrations: 59 b/w illustrations
Topics: Geometry, History of Mathematical Sciences