Foundations of Geometry and the Non-Euclidean Plane
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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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $79.95
Copyright year: 1975
Publication date: 12/19/1997
Size: 6.25" wide x 9.75" long x 1.25" tall
|Foreword to the Student|
|The Real Numbers|
|Incidence Axiom and Ruler Postulate|
|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)|
|Congruence and the Penultimate Postulate|
|Perpendiculars and Inequalities|
|Absolute Geometry and Saccheri Quadrilaterals|
|Saccheri's Three Hypotheses|
|Euclid's Parallel Postulate|
|Parallels and the Ultimate Axiom|
|Brushes and Cycles|
|Rotations, Translations, and Horolations|
|The Classification of Isometries|
|The Fundamental Formula|
|Categoricalness and Area|
|Quadrature of the Circle|
|Hints and Answers|