Geometry: from Isometries to Special Relativity (Undergraduate Texts in Mathematics)
Explores Euclidean and non-Euclidean geometries, culminating ina mathematical model for special relativityIntroduces students familiar with calculus to the rigorousfoundations of plane geometry: Euclidean, spherical, hyperbolic,and relativisticOffers a pathway from classical to abstract geometries byfocusing on isometries——————————This textbook offers a geometric perspective on specialrelativity, bridging Euclidean space, hyperbolic space, andEinstein’s spacetime in one accessible, self-contained volume.Using tools tailored to undergraduates, the author exploresEuclidean and non-Euclidean geometries, gradually building fromintuitive to abstract spaces. By the end, readers will haveencountered a range of topics, from isometries to theLorentz–Minkowski plane, building an understanding of how geometrycan be used to model special relativity.Beginning with intuitive spaces, such as the Euclidean plane andthe sphere, a structure theorem for isometries is introduced thatserves as a foundation for increasingly sophisticated topics, suchas the hyperbolic plane and the Lorentz–Minkowski plane. Bygradually introducing tools throughout, the author offers readersan accessible pathway to visualizing increasingly abstractgeometric concepts. Numerous exercises are also included withselected solutions provided.Geometry: from Isometries to Special Relativity offersa unique approach to non-Euclidean geometries, culminating in amathematical model for special relativity. The focus on isometriesoffers undergraduates an accessible progression from the intuitiveto abstract; instructors will appreciate the complete instructorsolutions manual available online. A background in elementarycalculus is assumed.