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Foundations of Geometry and the Non-Euclidean Plane

Foundations of Geometry and the Non-Euclidean Plane - 75 edition

ISBN13: 978-0387906942

Cover of Foundations of Geometry and the Non-Euclidean Plane 75 (ISBN 978-0387906942)
ISBN13: 978-0387906942
ISBN10: 0387906940
Cover type: Hardback
Edition/Copyright: 75
Publisher: IEP
Published: 1975
International: No

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Foundations of Geometry and the Non-Euclidean Plane - 75 edition

ISBN13: 978-0387906942

G.E. Martin

ISBN13: 978-0387906942
ISBN10: 0387906940
Cover type: Hardback
Edition/Copyright: 75
Publisher: IEP

Published: 1975
International: No
Summary

The Foundations of Geometry and the Non-Euclidean Plane is a self-contained text for junior, senior, and first-year graduate courses. Historical material is interwoven with a rigorous ruler- and protractor axiomatic development of the Euclidean and hyperbolic planes. Additional topics include the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry, and Pieri's system based on rigid motions. Models, such as Taxicab Geometry, are used extensively to illustrate theory.

Author Bio

Martin, G.E. : State University of New York at Albany, New York,

Table of Contents

Equivalence relations
Mappings
The real numbers
Axiom systems
Models
Incidence axiom and ruler postulate
Betweenness
Segments, rays, and convex sets
Angles and triangles
The golden age of greek mathematics
Euclid's elements
Pasch's postulate and plane separation postulate
Crossbar and Quadrilaterals
Measuring angles and the protractor postulate
Alternative axiom systems
Mirrors
Congruence and the penultimate postulate
Perpendiculars and inequalities
Reflections
Circles
Absolute geometry and Saccheri quadrilaterals
Saccheri's three hypotheses
Euclid's parallel postulate
Biangles
Excursions
Parallels and the ultimate axiom
Brushes and cycles
Rotations, translations, and horolations
The classification of isometries
ymmetry
Horocircles
The fundamental formula
Categoricalness and area
Quadrature of the circle
Hints and answers

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