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圆周长动画演示

圆周长动画演示
几何画板及绘图内容加载中，请稍等……
2015-11-27 10:33
圆函数几何作图
①本范例通过动画演示圆的周长计算与相关几何变换；②涉及核心数学概念包括圆、线性函数、多项式函数、勾股定理、线性变换；③作图要点：运用了Center（中心点）、Rotate（旋转）、Angle（角度）、CircleArc（圆弧）、Dilate（缩放）、Segment（线段）、Point（点）等GeoGebra命令；④适合高中数学教学，用于理解圆周长公式及几何变换应用。

GeoGebra 命令及参数

  1. Center(c) → B
  2. Rotate(A, 1, B) → A'
  3. Angle(A, B, A') → α
  4. Rotate(A', 1, B) → A''
  5. Angle(A', B, A'') → β
  6. Rotate(A'', 1, B) → A'''
  7. Angle(A'', B, A''') → γ
  8. Rotate(A''', 1, B) → C
  9. Angle(A''', B, C) → δ
  10. Rotate(C, 1, B) → C'
  11. Angle(C, B, C') → ε
  12. Rotate(C', 1, B) → C''
  13. Angle(C', B, C'') → ζ
  14. CircleArc(B, A, A') → d
  15. CircleArc(B, A', A'') → e
  16. CircleArc(B, A'', A''') → f
  17. CircleArc(B, A''', C) → g
  18. CircleArc(B, C, C') → h
  19. CircleArc(B, C', C'') → k
  20. Rotate(A, If[0 ≤ a ≤ 1, (a * α), α], B) → A'_1
  21. CircleArc(B, A, A'_1) → p
  22. Dilate(B, If[0 ≤ a ≤ 1, 1 - a, 0], A) → B'
  23. Segment(B', A) → b
  24. CircleArc(B, C'', A) → q
  25. CircleArc(B, A'_1, A') → s
  26. Segment(B, B') → j
  27. Segment(B, A') → l
  28. Point(h) → D
  29. Segment(B, D) → Radius
  30. Rotate(B', If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → B''
  31. Rotate(d, If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → d'
  32. CircleArc(B, A, B'') → t
  33. Dilate(B, If[1.2 ≤ a ≤ 2.2, 2.2 - a, 0], A) → B'_1
  34. Segment(B'_1, A) → m
  35. Segment(B, B'_1) → n
  36. Dilate(B, If[2.4 ≤ a ≤ 3.4, 3.4 - a, 0], A) → B'_2
  37. Segment(B, B'_2) → a_1
  38. Segment(B'_2, A) → b_1
  39. Rotate(d', If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → d''
  40. Rotate(t, If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → t'
  41. Rotate(A, If[2.4 < a < 3.4, ((a - 2.4) * β), β], B) → A'_2
  42. CircleArc(B, A, A'_2) → c_1
  43. Dilate(B, If[3.6 ≤ a ≤ 4.6, 4.6 - a, 0], A) → B'_3
  44. Segment(B'_3, A) → d_1
  45. Segment(B, B'_3) → e_1
  46. Rotate(A, If[3.6 < a < 4.6, ((a - 3.6) * β), β], B) → A'_3
  47. CircleArc(B, A, A'_3) → f_1
  48. Rotate(d'', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → d'''
  49. Rotate(t', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → t''
  50. Rotate(c_1, If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → g_1
  51. Dilate(B, If[4.8 ≤ a ≤ 5.8, 5.8 - a, 0], A) → B'_4
  52. Segment(B, B'_4) → h_1
  53. Segment(B'_4, A) → i_1
  54. Rotate(d''', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → k_1
  55. Rotate(t'', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → t'''
  56. Rotate(g_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → p_1
  57. Rotate(f_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → q_1
  58. Rotate(A, If[4.8 < a < 5.8, ((a - 4.8) * β), β], B) → A'_4
  59. CircleArc(B, A, A'_4) → r_1
  60. Dilate(B, If[6 ≤ a ≤ 7, 7 - a, 0], A) → B'_5
  61. Segment(B'_5, A) → j_1
  62. Segment(B, B'_5) → l_1
  63. Rotate(A, If[6 < a < 7, ((a - 6) * β), β], B) → A'_5
  64. CircleArc(B, A, A'_5) → s_1
  65. Rotate(k_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → t_1
  66. Rotate(t''', If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → c_2
  67. Rotate(p_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → d_2
  68. Rotate(q_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → e_2
  69. Rotate(r_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → f_2
  70. CircleArc(B, C'', A) → g_2