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The foundations of geometry and the non-Euclidean plane

Author: George Edward Martin
Publisher: New York : Springer, 1998, ©1975.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : English : Corr. 4th printView all editions and formats
Database:WorldCat
Summary:

Suitable for junior, senior, and first-year graduate courses. This work interweaves historical material with a rigorous ruler - and protractor axiomatic development of the Euclidean and hyperbolic  Read more...

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Details

Document Type: Book
All Authors / Contributors: George Edward Martin
ISBN: 0387906940 9780387906942 3540906940 9783540906940
OCLC Number: 40738901
Notes: Reprint. Originally published: New York : Intext Educational Publishers, ©1975. (Intext series in mathematics).
Includes indexes.
Description: xvi, 509 p. : ill. ; 25 cm.
Contents: Introduction: --
1. Equivalence relations --
2. Mappings --
3. The real numbers --
4. Axiom systems --
Part 1. 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 Green mathematics --
11. Euclid's elements --
12. Pasch's postulate and plane separation postulate --
13. Crossbar and quadrilaterals --
14. Measuring angles and the protractor postulate --
15. Alternative axiom systems --
16. Mirrors --
17. Congruence and the penultimate postulate --
18. Perpendiculars and inequalities --
19. Reflections --
20. Circles --
21. Absolute geometry and Saccheri quadrilaterals --
22. Saccheri's three hypotheses --
23. Euclid's parallel postulate --
24. Biangles --
25. Excursions --
Part 2. 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.
Series Title: Undergraduate texts in mathematics.
Responsibility: George E. Martin.
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