# Geometry Through History

## Euclidean, Hyperbolic, and Projective Geometries

• Meighan I. Dillon
Textbook

1. Front Matter
Pages i-xii
2. Meighan I. Dillon
Pages 1-50
3. Meighan I. Dillon
Pages 51-76
4. Meighan I. Dillon
Pages 77-95
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Pages 97-121
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Pages 123-166
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Pages 167-186
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Pages 187-240
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Pages 241-271
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Pages 273-311
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Pages 313-332
12. Back Matter
Pages 333-350

### Introduction

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises.

For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.

### Keywords

Euclidean geometry neutral geometry hyperbolic planes projective geometry affine geometry algebraic curves quaternions Euclid's 'The Elements' history of geometry development of modern geometries historical development of geometry

#### Authors and affiliations

• Meighan I. Dillon
• 1
1. 1.Department of MathematicsKennesaw State UniversityMariettaUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-74135-2
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-74134-5
• Online ISBN 978-3-319-74135-2
• Buy this book on publisher's site