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Geometry through history : Euclidean, hyperbolic, and projective geometries

Author: Meighan Dillon
Publisher: Cham, Switzerland : Springer, [2018] ©2018
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: History
Additional Physical Format: Electronic version:
Dillon, Meighan, 1956-
Geometry through history.
Cham, Switzerland : Springer, 2018
(OCoLC)1029870899
Document Type: Book
All Authors / Contributors: Meighan Dillon
ISBN: 9783319741345 3319741349 9783030089238 3030089231
OCLC Number: 1016048184
Description: xii, 350 pages : illustrations ; 24 cm
Contents: Preface --
1. The Elements of Euclid --
2. Neutral Geometry --
3. The Hyperbolic Plane --
4. Hilbert's Grundlagen --
5. More Euclidean Geometry --
6. Models for the Hyperbolic Plane --
7. Affine Geometry --
8. An Introduction to Projective Geometry --
9. Algebraic Curves --
10. Rotations and Quaternions --
Index.
Responsibility: Meighan I. Dillon.

Abstract:

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.--

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"While the book covers some advanced topics, it is also remarkably accessible: anyone with a year of college-level mathematics and a love of geometry will find value in this text, as Dillon (Kennesaw Read more...

 
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