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.
- Book Title Geometry: from Isometries to Special Relativity
- 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
Convex and Discrete Geometry
Theoretical, Mathematical and Computational Physics
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