Modern Geometries

Non-Euclidean, Projective, and Discrete

Michael Henle

390 pages, parution le 01/09/2001 (2^eme édition)

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Résumé

Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

Contents

Dependency Chart.
Introduction.

I. BACKGROUND.

1. Some History.
2. Complex Numbers.
3. Geometric Transformations.
4. The Erlanger Program.

II. PLANE GEOMETRY.

5. Möbius Geometry.
6. Steiner Circles.
7. Hyperbolic Geometry.
8. Cycles.
9. Hyperbolic Length.
10. Area.
11. Elliptic Geometry.
12. Absolute Geometry.

III. PROJECTIVE GEOMETRY.

13. The Real Projective Plane.
14. Projective Transformations.
15. Multidimensional Projective Geometry.
16. Universal Projective Geometry.

IV. SOLID GEOMETRY.

17. Quaternions.
18. Euclidean and Pseudo-Euclidean Solid Geometry.
19. Hyperbolic and Elliptic Solid Geometry.

V. DISCRETE GEOMETRY.

20. Matroids.
21. Reflections.
22. Discrete Symmetry.
23. Non-Euclidean Symmetry.

VI. AXIOM SYSTEMS.

24. Hilbert's Axioms.
25. Bachmann's Axioms.
26. Metric Absolute Geometry.

VII. CONCLUSION.

27. The Cultural Impact of Non-Euclidean Geometry.
28. The Geometric Idea of Space.
Bibliography.
Index.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Prentice Hall
Auteur(s)	Michael Henle
Parution	01/09/2001
Édition	2^eme édition
Nb. de pages	390
Format	15,5 x 23,5
Couverture	Relié
Poids	632g
Intérieur	Noir et Blanc
EAN13	9780130323132

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Modern Geometries

Résumé

Caractéristiques techniques

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