- 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
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- About this Textbook
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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.
- About the authors
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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.
- Table of contents (6 chapters)
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Euclidean Plane
Pages 1-22
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Sphere
Pages 23-45
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Stereographic Projection and Inversions
Pages 47-85
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Hyperbolic Plane
Pages 87-127
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Lorentz–Minkowski Plane
Pages 129-182
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Geometry: from Isometries to Special Relativity
- Authors
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- Nam-Hoon Lee
- Series Title
- Undergraduate Texts in Mathematics
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-42101-4
- DOI
- 10.1007/978-3-030-42101-4
- Hardcover ISBN
- 978-3-030-42100-7
- Softcover ISBN
- 978-3-030-42103-8
- Series ISSN
- 0172-6056
- Edition Number
- 1
- Number of Pages
- XIII, 258
- Number of Illustrations
- 74 b/w illustrations, 18 illustrations in colour
- Topics
