An extensively illustrated introduction to Euclidean and hyperbolic geometry in the plane, designed for undergraduate courses in geometry.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Matthew Harvey is an Associate Professor of Mathematics at the University of Virginia's College at Wise, where he has taught since 2006. He graduated from the University of Virginia in 1995 with a BA in Mathematics, and from Johns Hopkins University in 2002 with a PhD in Mathematics.
Inhaltsangabe
Axioms and models Part I. Neutral Geometry: 1. The axioms of incidence and order 2. Angles and triangles 3. Congruence verse I: SAS and ASA 4. Congruence verse II: AAS 5. Congruence verse III: SSS 6. Distance, length and the axioms of continuity 7. Angle measure 8. Triangles in neutral geometry 9. Polygons 10. Quadrilateral congruence theorems Part II. Euclidean Geometry: 11. The axiom on parallels 12. Parallel projection 13. Similarity 14. Circles 15. Circumference 16. Euclidean constructions 17. Concurrence I 18. Concurrence II 19. Concurrence III 20. Trilinear coordinates Part III. Euclidean Transformations: 21. Analytic geometry 22. Isometries 23. Reflections 24. Translations and rotations 25. Orientation 26. Glide reflections 27. Change of coordinates 28. Dilation 29. Applications of transformations 30. Area I 31. Area II 32. Barycentric coordinates 33. Inversion I 34. Inversion II 35. Applications of inversion Part IV. Hyperbolic Geometry: 36. The search for a rectangle 37. Non-Euclidean parallels 38. The pseudosphere 39. Geodesics on the pseudosphere 40. The upper half-plane 41. The Poincaré disk 42. Hyperbolic reflections 43. Orientation preserving hyperbolic isometries 44. The six hyperbolic trigonometric functions 45. Hyperbolic trigonometry 46. Hyperbolic area 47. Tiling Bibliography Index.
Axioms and models Part I. Neutral Geometry: 1. The axioms of incidence and order 2. Angles and triangles 3. Congruence verse I: SAS and ASA 4. Congruence verse II: AAS 5. Congruence verse III: SSS 6. Distance, length and the axioms of continuity 7. Angle measure 8. Triangles in neutral geometry 9. Polygons 10. Quadrilateral congruence theorems Part II. Euclidean Geometry: 11. The axiom on parallels 12. Parallel projection 13. Similarity 14. Circles 15. Circumference 16. Euclidean constructions 17. Concurrence I 18. Concurrence II 19. Concurrence III 20. Trilinear coordinates Part III. Euclidean Transformations: 21. Analytic geometry 22. Isometries 23. Reflections 24. Translations and rotations 25. Orientation 26. Glide reflections 27. Change of coordinates 28. Dilation 29. Applications of transformations 30. Area I 31. Area II 32. Barycentric coordinates 33. Inversion I 34. Inversion II 35. Applications of inversion Part IV. Hyperbolic Geometry: 36. The search for a rectangle 37. Non-Euclidean parallels 38. The pseudosphere 39. Geodesics on the pseudosphere 40. The upper half-plane 41. The Poincaré disk 42. Hyperbolic reflections 43. Orientation preserving hyperbolic isometries 44. The six hyperbolic trigonometric functions 45. Hyperbolic trigonometry 46. Hyperbolic area 47. Tiling Bibliography Index.
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