Elementary geometry from an advanced standpoint
著者
書誌事項
Elementary geometry from an advanced standpoint
Addison-Wesley, c1990
3rd ed
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内容説明・目次
内容説明
Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.
目次
1. The Algebra of the Real Numbers.
2. Incidence Geometry in Planes and Space.
3. Distance and Congruence.
4. Separation in Planes and Space.
5. Angular Measure.
6. Congruences between Triangles.
7. Geometric Inequalities.
8. The Euclidean Program: Congruence without Distance.
9. Three Geometries.
10. Absolute Plane Geometry.
11. The Parallel Postulate and Parallel Projection.
12. Similarities Between Triangles.
13. Polygonal Regions and Their Areas.
14. The Construction of an Area Function.
15. Perpendicular Lines and Planes in Space.
16. Circles and Spheres.
17. Cartesian Coordinate Systems.
18. Rigid Motion.
19. Constructions with Ruler and Compass.
20. From Eudoxus to Dedekind.
21. Length and Plane Area.
22. Jordan Measure in the Plane.
23. Solid Mensuration: The Elementary Theory.
24. Hyperbolic Geometry.
25. The Consistency of the Hyperbolic Postulates.
26. The Consistency of Euclidean Geometry.
27. The Postulation Method.
28. The Theory of Numbers.
29. The Theory of Equations.
30. Limits of Sequences.
31. Countable and Uncountable Sets.
32. An Ordered Field Which Is Euclidean But Not Archimedean.
Index.
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