Geometry illuminated : an illustrated introduction to Euclidean and hyperbolic plane geometry
著者
書誌事項
Geometry illuminated : an illustrated introduction to Euclidean and hyperbolic plane geometry
(MAA textbooks)
The Mathematical Association of America, c2015
大学図書館所蔵 全2件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes biliographical references (p. 537-538) and index
内容説明・目次
内容説明
An introduction to geometry in the plane, both Euclidean and hyperbolic, this book is designed for an undergraduate course in geometry. With its patient approach, and plentiful illustrations, it will also be a stimulating read for anyone comfortable with the language of mathematical proof. While the material within is classical, it brings together topics that are not generally found together in books at this level, such as: parametric equations for the pseudosphere and its geodesics; trilinear and barycentric coordinates; Euclidean and hyperbolic tilings; and theorems proved using inversion. The book is divided into four parts, and begins by developing neutral geometry in the spirit of Hilbert, leading to the Saccheri-Legendre Theorem. Subsequent sections explore classical Euclidean geometry, with an emphasis on concurrence results, followed by transformations in the Euclidean plane, and the geometry of the Poincare disk model.
目次
- 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 Poincare 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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