Authors:
- Explores Euclidean and non-Euclidean geometries, culminating in a mathematical model for special relativity
- Introduces students familiar with calculus to the rigorous foundations of plane geometry: Euclidean, spherical, hyperbolic, and relativistic
- Offers a pathway from classical to abstract geometries by focusing on isometries
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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 (6 chapters)
-
Front Matter
-
Back Matter
About this book
This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity.
Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided.Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.
Keywords
- Euclidean geometry and relativity
- Non-Euclidean geometry and relativity
- Undergraduate geometry and relativity
- Euclidean plane
- Special relativity undergraduate
- Special relativity via geometry
- Stereographic projection
- Hyperbolic plane
- Hyperbolic plane geodesics
- Hyperbolic plan isometries
- Hyperbolic geometry for undergraduates
- Geometry via isometries
- Isometries of the plane
- Poincaré disk
- Three reflections theorem
Authors and Affiliations
-
Department of Mathematics Education, Hongik University, Seoul, Korea (Republic of)
Nam-Hoon Lee
About the author
Bibliographic Information
Book Title: Geometry: from Isometries to Special Relativity
Authors: Nam-Hoon Lee
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-42101-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-42100-7Published: 29 April 2020
Softcover ISBN: 978-3-030-42103-8Published: 29 April 2021
eBook ISBN: 978-3-030-42101-4Published: 28 April 2020
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XIII, 258
Number of Illustrations: 74 b/w illustrations, 18 illustrations in colour
Topics: Hyperbolic Geometry, Convex and Discrete Geometry, Theoretical, Mathematical and Computational Physics