Foundations of Geometry and the Non-Euclidean Plane

ISBN-10: 0387906940
ISBN-13: 9780387906942
Edition: 1975
Authors: G. E. Martin
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Description: 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  More...

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Book details

List price: $79.95
Copyright year: 1975
Publisher: Springer
Publication date: 12/19/1997
Binding: Hardcover
Pages: 512
Size: 6.25" wide x 9.75" long x 1.25" tall
Weight: 1.980
Language: English

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.

Preface
Foreword to the Student
Introduction
Equivalence Relations
Mappings
The Real Numbers
Axiom Systems
Absolute Geometry
Models
Incidence Axiom and Ruler Postulate
Betweenness
Segments, Rays, and Convex Sets
Angles and Triangles
The Golden Age of Greek Mathematics (Optional)
Euclid's Elements (Optional)
Pasch's Postulate and Plane Separation Postulate
Crossbar and Quadrilaterals
Measuring Angles and the Protractor Postulate
Alternative Axiom Systems (Optional)
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
Non-Euclidean Geometry
Parallels and the Ultimate Axiom
Brushes and Cycles
Rotations, Translations, and Horolations
The Classification of Isometries
Symmetry
Horocircles
The Fundamental Formula
Categoricalness and Area
Quadrature of the Circle
Hints and Answers
Notation Index
Index

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