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Revolutions of Geometry

ISBN-10: 0470167556
ISBN-13: 9780470167557
Edition: 2010
Authors: Michael O'Leary
List price: $212.95
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Description: Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for  More...

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Book details

List price: $212.95
Copyright year: 2010
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/26/2010
Binding: Hardcover
Pages: 608
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.398
Language: English

Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry's history to illustrate how crucial proof writing is to the job of a mathematician.

Preface
Acknowledgments
Foundations
The First Geometers
Egypt
Babylon
China
Thales
The Axiomatic System
Deductive Logic
Proof Writing
Plato and Aristotle
Form
Categorical Propositions
Categorical Syllogisms
Figures
The Golden Age
Pythagoras
Number Theory
The Pythagorean Theorem
Archytas
The Golden Ratio
Euclid
The Elements
Constructions
Triangles
Parallel Lines
Circles
The Pythagorean Theorem Revisited
Archimedes
The Archimedean Library
The Method of Exhaustion
The Method
Preliminaries to the Proof
The Volume of a Sphere
Enlightenment
The Analytic Art
Three Problems
Conic Sections
The Analytic Art in Two Variables
Compasses
Method
Analytic Geometry
Projections
Points at Infinity
Theorems of Desargues and Menelaus
Involutions
A Strange New World
The Question of Parallels
The Three Hypotheses
Conclusions for Two Hypotheses
Properties of Parallel Lines
Parallelism Redefined
The Three Hypotheses Revisited
Polygons
Omega Triangles
Pure Reason
Parallel Fundamentals
Horocycles
The Surface of a Sphere
Horospheres
Evaluating the Pi Function
New Directions
Metric Spaces
Topological Spaces
Stereographic Projection
Consistency of Non-Euclidean Geometry
The Projective Plane
Duality
Perspectivity
Homogeneous Coordinates
Group Theory
Transformation Groups
The Principal Group
Isometries of the Plane
Consistency of Euclidean Geometry
References
Index

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