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.
By:
G. E. Martin
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 1st Corrected ed. 1975. Corr. 3rd printing 1997
Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 28mm
Weight: 2.030kg
ISBN: 9780387906942
ISBN 10: 0387906940
Series: Undergraduate Texts in Mathematics
Pages: 512
Publication Date: 22 March 1982
Audience:
College/higher education
,
Professional and scholarly
,
Professional & Vocational
,
A / AS level
,
Further / Higher Education
Format: Hardback
Publisher's Status: Active
1. Equivalence Relations.- 2 Mappings.- 3 The Real Numbers.- 4 Axiom Systems.- One Absolute Geometry.- 5 Models.- 6 Incidence Axiom and Ruler Postulate.- 7 Betweenness.- 8 Segments, Rays, and Convex Sets.- 9 Angles and Triangles.- 10 The Golden Age of Greek Mathematics (Optional).- 11 Euclid’S Elements (Optional).- 12 Pasch’s Postulate and Plane Separation Postulate.- 13 Crossbar and Quadrilaterals.- 14 Measuring Angles and the Protractor Postulate.- 15 Alternative Axiom Systems (Optional).- 16 Mirrors.- 17 Congruence and the Penultimate Postulate.- 18 Perpendiculars and Inequalities.- 19 Reflections.- 20 Circles.- 21 Absolute Geometry and Saccheri Quadrilaterals.- 22 Saccherfs Three Hypotheses.- 23 Euclid’s Parallel Postulate.- 24 Biangles.- 25 Excursions.- Two Non-Euclidean Geometry.- 26 Parallels and the Ultimate Axiom.- 27 Brushes and Cycles.- 28 Rotations, Translations, and Horolations.- 29 The Classification of Isometries.- 30 Symmetry.- 31 HOrocircles.- 32 The Fundamental Formula.- 33 Categoricalness and Area.- 34 Quadrature of the Circle.- Hints and Answers.- Notation Index.
