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Geometry through historyEuclidean, h...

Dillon, Meighan I.

Geometry through historyEuclidean, hyperbolic, and projective geometries /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry through historyby Meighan I. Dillon.
Reminder of title:	Euclidean, hyperbolic, and projective geometries /
Author:	Dillon, Meighan I.
Published:	Cham :Springer International Publishing :2018.
Description:	xii, 350 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	GeometryHistory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-74135-2
ISBN:	9783319741352$q(electronic bk.)

Geometry through historyEuclidean, hyperbolic, and projective geometries /
Dillon, Meighan I.

Geometry through historyEuclidean, hyperbolic, and projective geometries /[electronic resource] :by Meighan I. Dillon. - Cham :Springer International Publishing :2018. - xii, 350 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783319741352$q(electronic bk.)

Standard No.: 10.1007/978-3-319-74135-2doiSubjects--Topical Terms:

561867
Geometry
--History.

LC Class. No.: QA443.5 / .D555 2018

Dewey Class. No.: 519.009

Geometry through historyEuclidean, hyperbolic, and projective geometries /
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300 $a xii, 350 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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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