Foundations of Geometry and the Non-Euclidean Plane

Name: Foundations of Geometry and the Non-Euclidean Plane
Price: 27.19 USD
Availability: InStock
ISBN: 9780387906942

ISBN-10: 0387906940

ISBN-13: 9780387906942

Edition: 1975

Authors: G. E. Martin

List price: $79.95

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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 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.

Book details

List price: $79.95
Copyright year: 1975
Publisher: Springer New York
Publication date: 3/22/1982
Binding: Hardcover
Pages: 512
Size: 6.14" wide x 9.21" long x 1.25" tall
Weight: 2.2
Language: English



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