**by Michael P. Hitchman**

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Geometry with an Introduction to Cosmic Topology approaches geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big?

This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who have completed a multivariable calculus course and are ready for a course in which to practice the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study, with essays and discussions throughout.

Mathematicians and cosmologists have expended considerable amounts of effort investigating the shape of the universe, and this field of research is called cosmic topology. Geometry plays a fundamental role in this research. Under basic assumptions about the nature of space, there is a simple relationship between the geometry of the universe and its shape, and there are just three possibilities for the type of geometry: hyperbolic geometry, elliptic geometry, and Euclidean geometry. These are the geometries we study in this text. ### Table of Contents

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This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who have completed a multivariable calculus course and are ready for a course in which to practice the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study, with essays and discussions throughout.

Mathematicians and cosmologists have expended considerable amounts of effort investigating the shape of the universe, and this field of research is called cosmic topology. Geometry plays a fundamental role in this research. Under basic assumptions about the nature of space, there is a simple relationship between the geometry of the universe and its shape, and there are just three possibilities for the type of geometry: hyperbolic geometry, elliptic geometry, and Euclidean geometry. These are the geometries we study in this text.

This open book is licensed under a Creative Commons License (CC BY-SA). You can download Geometry with an Introduction to Cosmic Topology ebook for free in PDF format (3.2 MB).

Chapter 1

An Invitation to Geometry

Chapter 2

The Complex Plane

Chapter 3

Transformations

Chapter 4

Geometry

Chapter 5

Hyperbolic Geometry

Chapter 6

Elliptic Geometry

Chapter 7

Geometry on Surfaces

Chapter 8

Cosmic Topology

Title

Geometry with an Introduction to Cosmic Topology

Subject

Science and Mathematics

Publisher

Self-publishing

Published

2020

Pages

238

Edition

1

Language

English

ISBN13 Digital

9781717134813

ISBN10 Digital

1717134815

PDF Size

3.2 MB

License

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