Authors:
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
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
About this book
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.
Reviews
“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)
Authors and Affiliations
-
Department of Mathematics, Kennesaw State University, Marietta, USA
Meighan I. Dillon
About the author
Bibliographic Information
Book Title: Geometry Through History
Book Subtitle: Euclidean, Hyperbolic, and Projective Geometries
Authors: Meighan I. Dillon
DOI: https://doi.org/10.1007/978-3-319-74135-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-74134-5Published: 05 April 2018
Softcover ISBN: 978-3-030-08923-8Published: 26 January 2019
eBook ISBN: 978-3-319-74135-2Published: 21 March 2018
Edition Number: 1
Number of Pages: XII, 350
Number of Illustrations: 233 illustrations in colour
Topics: Convex and Discrete Geometry, History of Mathematical Sciences, Hyperbolic Geometry, Projective Geometry