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Geometry: from Isometries to Special Relativity

  • Textbook
  • © 2020

Overview

Authors:
  1. Nam-Hoon Lee

    1. Department of Mathematics Education, Hongik University, Seoul, Korea (Republic of)

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  • 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)

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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.

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Euclidean Plane

    • Nam-Hoon Lee
    Pages 1-22

  3. Sphere

    • Nam-Hoon Lee
    Pages 23-45

  4. Stereographic Projection and Inversions

    • Nam-Hoon Lee
    Pages 47-85

  5. Hyperbolic Plane

    • Nam-Hoon Lee
    Pages 87-127

  6. Lorentz–Minkowski Plane

    • Nam-Hoon Lee
    Pages 129-182

  7. Geometry of Special Relativity

    • Nam-Hoon Lee
    Pages 183-223

  8. Back Matter

    Pages 225-258
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Authors and Affiliations

  • Department of Mathematics Education, Hongik University, Seoul, Korea (Republic of)

    Nam-Hoon Lee

About the author

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.

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