# Geometry: from Isometries to Special Relativity

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xiii
2. Nam-Hoon Lee
Pages 1-22
3. Nam-Hoon Lee
Pages 23-45
4. Nam-Hoon Lee
Pages 47-85
5. Nam-Hoon Lee
Pages 87-127
6. Nam-Hoon Lee
Pages 129-182
7. Nam-Hoon Lee
Pages 183-223
8. Back Matter
Pages 225-258

### Introduction

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

1. 1.Department of Mathematics EducationHongik UniversitySeoulKorea (Republic of)

Nam-Hoon Lee received his Ph.D. in mathematics from the University of Michigan in Ann Arbor after studying physics at Seoul National University as an undergraduate. His research interests include algebraic geometry, differential geometry, and the theory of relativity. He is now Professor of Mathematics Education at Hongik University in Seoul, South Korea.

### Bibliographic information

• Book Title Geometry: from Isometries to Special Relativity
• Authors Nam-Hoon Lee
• Series Title Undergraduate Texts in Mathematics
• Series Abbreviated Title Undergraduate Texts Mathematics
• DOI https://doi.org/10.1007/978-3-030-42101-4
• Copyright Information Springer Nature Switzerland AG 2020
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-030-42100-7
• Softcover ISBN 978-3-030-42103-8
• eBook ISBN 978-3-030-42101-4
• 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
• Buy this book on publisher's site