UID:
almahu_9948336508002882
Format:
XIII, 258 p. 92 illus., 18 illus. in color.
,
online resource.
Edition:
1st ed. 2020.
ISBN:
9783030421014
Series Statement:
Undergraduate Texts in Mathematics,
Content:
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.
Note:
Euclidean Plane -- Sphere -- Stereographic Projection and Inversions -- Hyperbolic Plane -- Lorentz-Minkowski Plane -- Geometry of Special Relativity -- Answers to Selected Exercises -- Index.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783030421007
Additional Edition:
Printed edition: ISBN 9783030421021
Additional Edition:
Printed edition: ISBN 9783030421038
Language:
English
DOI:
10.1007/978-3-030-42101-4
URL:
https://doi.org/10.1007/978-3-030-42101-4
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