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整数除以分数的几何演示

整数除以分数的几何演示
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2016-06-06 12:15
圆角变换几何作图
所属专题 Fraction Book Fraction Book
该范例通过动态几何图形演示整数除以分数的运算过程与几何意义，帮助学习者直观理解“除以一个分数等于乘以该分数的倒数”这一核心法则。图中利用圆、圆扇形、旋转与角度等对象，构建了可交互的除法模型，直观展示被除数如何被除数所含的分数份数所划分。核心数学概念包括整数除以分数、分数的倒数、等价变换以及几何面积与角度的对应关系。作图要点主要调用了 GeoGebra 的 Circle（圆）、Rotate（旋转）、Angle（角）与 CircleSector（圆扇形）命令，并通过大量点对象（如 A、B、C、D、E、F、G 及其变换后的 O′、D′ 等）构建多层扇形与旋转对称结构，形成直观的除法演示动画。该范例适合初中阶段（约 7-9 年级）分数除法教学，也可用于小学高年级分数概念拓展或课堂互动演示，支持教师讲解与学生自主探索。

GeoGebra 命令及参数

  1. Circle(A, 2.5) → c
  2. Circle(B, 2.5) → d
  3. Circle(C, 2.5) → e
  4. Rotate(O, (360 / Denominator)°, A) → O'
  5. Angle(O, A, O') → α
  6. Rotate(O', (360 / Denominator)°, A) → O''
  7. Angle(O', A, O'') → β
  8. Rotate(O'', (360 / Denominator)°, A) → O'''
  9. Angle(O'', A, O''') → γ
  10. Rotate(O''', (360 / Denominator)°, A) → D
  11. Angle(O''', A, D) → δ
  12. Rotate(D, (360 / Denominator)°, A) → D'
  13. Angle(D, A, D') → ε
  14. Rotate(D', (360 / Denominator)°, A) → D''
  15. Angle(D', A, D'') → ζ
  16. Rotate(D'', (360 / Denominator)°, A) → D'''
  17. Angle(D'', A, D''') → η
  18. Rotate(D''', (360 / Denominator)°, A) → E
  19. Angle(D''', A, E) → θ
  20. Rotate(E, (360 / Denominator)°, A) → E'
  21. Angle(E, A, E') → ι
  22. Rotate(E', (360 / Denominator)°, A) → E''
  23. Angle(E', A, E'') → κ
  24. Rotate(F, (360 / Denominator)°, B) → F'
  25. Angle(F, B, F') → λ
  26. Rotate(F', (360 / Denominator)°, B) → F''
  27. Angle(F', B, F'') → μ
  28. Rotate(F'', (360 / Denominator)°, B) → F'''
  29. Angle(F'', B, F''') → ν
  30. Rotate(F''', (360 / Denominator)°, B) → G
  31. Angle(F''', B, G) → ξ
  32. Rotate(G, (360 / Denominator)°, B) → G'
  33. Angle(G, B, G') → ο
  34. Rotate(G', (360 / Denominator)°, B) → G''
  35. Angle(G', B, G'') → ρ
  36. Rotate(G'', (360 / Denominator)°, B) → G'''
  37. Angle(G'', B, G''') → σ
  38. Rotate(G''', (360 / Denominator)°, B) → H
  39. Angle(G''', B, H) → τ
  40. Rotate(H, (360 / Denominator)°, B) → H'
  41. Angle(H, B, H') → υ
  42. Rotate(H', (360 / Denominator)°, B) → H''
  43. Angle(H', B, H'') → ϕ
  44. Rotate(I, (360 / Denominator)°, C) → I'
  45. Angle(I, C, I') → χ
  46. Rotate(I', (360 / Denominator)°, C) → I''
  47. Angle(I', C, I'') → ψ
  48. Rotate(I'', (360 / Denominator)°, C) → I'''
  49. Angle(I'', C, I''') → ω
  50. Rotate(I''', (360 / Denominator)°, C) → J
  51. Angle(I''', C, J) → α_1
  52. Rotate(J, (360 / Denominator)°, C) → J'
  53. Angle(J, C, J') → β_1
  54. Rotate(J', (360 / Denominator)°, C) → J''
  55. Angle(J', C, J'') → γ_1
  56. Rotate(J'', (360 / Denominator)°, C) → J'''
  57. Angle(J'', C, J''') → δ_1
  58. Rotate(J''', (360 / Denominator)°, C) → K
  59. Angle(J''', C, K) → ε_1
  60. Rotate(K, (360 / Denominator)°, C) → K'
  61. Angle(K, C, K') → ζ_1
  62. Rotate(K', (360 / Denominator)°, C) → K''
  63. Angle(K', C, K'') → η_1
  64. CircleSector(A, O, O') → f
  65. CircleSector(A, O', O'') → g
  66. CircleSector(A, O'', O''') → h
  67. CircleSector(A, O''', D) → k
  68. CircleSector(A, D, D') → p
  69. CircleSector(A, D', D'') → q
  70. CircleSector(A, D'', D''') → r
  71. CircleSector(A, D''', E) → s
  72. CircleSector(A, E, E') → t
  73. CircleSector(A, E', O) → c_1
  74. CircleSector(B, F, F') → d_1
  75. CircleSector(B, F'', F''') → e_1
  76. CircleSector(B, F', F'') → f_1
  77. CircleSector(B, F''', G) → g_1
  78. CircleSector(B, G, G') → h_1
  79. CircleSector(B, G', G'') → k_1
  80. CircleSector(B, G'', G''') → p_1
  81. CircleSector(B, G''', H) → q_1
  82. CircleSector(B, H, H') → r_1
  83. CircleSector(B, H', F) → s_1
  84. CircleSector(C, I, I') → t_1
  85. CircleSector(C, I', I'') → c_2
  86. CircleSector(C, I'', I''') → d_2
  87. CircleSector(C, I''', J) → e_2
  88. CircleSector(C, J, J') → f_2
  89. CircleSector(C, J', J'') → g_2
  90. CircleSector(C, J'', J''') → h_2
  91. CircleSector(C, J''', K) → k_2
  92. CircleSector(C, K, K') → p_2
  93. CircleSector(C, K', I) → q_2

AI 绘图提示语参考

画三个半径相同的圆，圆心分别位于三个不同位置。每个圆按给定的分母将整圆等分为若干扇形，通过依次绕圆心旋转相同角度生成一系列顶点，并标出相邻顶点与圆心形成的角。整体呈现三组同心旋转对称的扇形排列，直观展示整数除以分数等于乘以倒数的几何模型。
以上提示语为根据原始绘图命令整理而来，仅供参考。