EAN: 9783030421038

UNDERGRADUATE TEXTS IN MATHEMATICS GEOMETRY F...

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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