Author | Martin, George E. author |
---|---|
Title | The Foundations of Geometry and the Non-Euclidean Plane [electronic resource] / by George E. Martin |
Imprint | New York, NY : Springer New York, 1975 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5725-7 |
Descript | XVI, 512 p. online resource |
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 EuclidโS Elements (Optional) -- 12 Paschโs 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 Euclidโs 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