Geometry Through History

Euclidean, Hyperbolic, and Projective Geometries

Authors: Dillon, Meighan I.

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  • Illuminates Euclid’s The Elements and traces the development of modern geometries
  • Enriches the geometry curriculum with extensions to algebraic curves and quaternions
  • Reinforces historical results with exercises that explore proof methods of the time
  • Illustrates results and proofs with full-color diagrams throughout
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  • ISBN 978-3-319-74135-2
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $59.99
price for USA in USD
  • ISBN 978-3-319-74134-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-08923-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises.

For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.


About the authors

Meighan Dillon is a Professor of Mathematics at Kennesaw State University. She is a life‐long educator, whose research in infinite-dimensional Lie algebras is complemented by explorations in pedagogy and the use of projective geometry in art.

Reviews

“While the book covers some advanced topics, it is also remarkably accessible: anyone with a year of college-level mathematics and a love of geometry will find value in this text, as Dillon (Kennesaw State Univ.) explores axioms, proofs, and an array of fascinating problems. … One of the most appealing aspects of this book is the author's way of introducing projective geometry to pique the reader's interest in modern algebra. … Summing Up: Recommended. Lower-division undergraduates and above.” (J. A. Bakal, Choice, Vol. 56 (03), November, 2018)​

“It discusses a lot of interesting topics in geometry, it is clearly written and should be accessible to its target audience of students … . it offers students an opportunity to see the relationship between geometry and other areas of mathematics, including abstract and linear algebra. If you are teaching a course in geometry at the college level and the topics discussed here are compatible with your course, this book certainly merits a serious look.” (Mark Hunacek, MAA Reviews, October, 2018)
“This is a wonderful new book that could be used as a textbook for geometry, but would be of interest to any mathematician whose work includes some geometry or who is interested in the history of mathematical developments. … The book offers a deep, thorough, and entertaining presentation of geometry through history.” (Tara D. Taylor, Mathematical Reviews, January, 2019)

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-74135-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA in USD
  • ISBN 978-3-319-74134-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA in USD
  • ISBN 978-3-030-08923-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry Through History
Book Subtitle
Euclidean, Hyperbolic, and Projective Geometries
Authors
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-74135-2
DOI
10.1007/978-3-319-74135-2
Hardcover ISBN
978-3-319-74134-5
Softcover ISBN
978-3-030-08923-8
Edition Number
1
Number of Pages
XII, 350
Number of Illustrations
233 illustrations in colour
Topics