Description

Motivated by questions in cosmology/ the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic/ elliptic/ and Euclidean geometry - three possibilities for the global geometry of the universe. The text/ written for students who have taken vector calculus/ also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study/ with over 200 exercises and several essays on topics including the history of geometry/ parallax and curvature/ and research aimed at determining the shape of the universe.