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动画205

动画205
几何画板及绘图内容加载中，请稍等……
2017-02-21 12:49
圆变换几何作图
该范例演示了一个圆与矩形的动画。核心数学概念包括圆、矩形、相似性、距离和斜率。通过使用GeoGebra命令如Circle、Point、Segment、Intersect等，可以构造出动态的几何图形。适合初中及以上学生学习几何变换和动态几何。

GeoGebra 命令及参数

  1. Circle(A_1, A) → c
  2. Circle(C, A) → d
  3. Semicircle(A, D_1) → e
  4. Semicircle(D_1, A) → f
  5. Point(e) → D
  6. Segment(A, D) → g
  7. Intersect(d, g, 2) → P
  8. OrthogonalLine(D, h) → i
  9. Intersect(d, i, 2) → F
  10. Intersect(h, i) → E
  11. Ray(A, F) → j
  12. Intersect(e, j, 2) → G
  13. OrthogonalLine(G, h) → k
  14. Intersect(d, k, 2) → M
  15. Segment(A, M) → l
  16. Intersect(i, l) → N
  17. Distance(A, g) → distanceAg
  18. Distance(A, N) → distanceAN
  19. Distance(P, A) → distancePA
  20. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], P) → A'
  21. Segment(A, A') → n
  22. Dilate(P, If[1 < m ≤ 2, 2 - m, 0], D) → P'
  23. Segment(P, P') → p
  24. Dilate(D, If[2 < m ≤ 3, 3 - m, 0], F) → D'
  25. Segment(D, D') → q
  26. Intersect(k, xAxis) → B
  27. Angle(G, B, A) → β
  28. Angle(D, E, A) → α
  29. Dilate(F, If[3 < m ≤ 4, 4 - m, 0], E) → F'
  30. Segment(F, F') → r
  31. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], F) → A'_1
  32. Segment(A, A'_1) → s
  33. Dilate(F, If[5 < m ≤ 6, 6 - m, 0], G) → F'_1
  34. Segment(F, F'_1) → t
  35. Dilate(G, If[6 < m ≤ 7, 7 - m, 0], M) → G'
  36. Segment(G, G') → f_1
  37. Dilate(M, If[7 < m ≤ 8, 8 - m, 0], B) → M'
  38. Segment(M, M') → g_1
  39. Dilate(A, If[8 < m ≤ 9, 9 - m, 0], N) → A'_2
  40. Segment(A, A'_2) → h_1
  41. Dilate(N, If[9 < m ≤ 10, 10 - m, 0], M) → N'
  42. Segment(N, N') → i_1
  43. Intersect(e, j_1, 1) → I
  44. Angle(N, A, P) → γ
  45. Rotate(A, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → A'_3
  46. Rotate(A'_2, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → J
  47. Segment(A'_3, J) → k_1
  48. Semicircle(A, H) → c_1
  49. Line(P, N) → l_1
  50. Line(D, M) → m_1
  51. Line(P, D) → n_1
  52. Circle(D, 2) → d_1
  53. Intersect(d_1, n_1, 2) → K
  54. Ray(D, K) → p_1
  55. Intersect(l_1, s) → L
  56. Circle(P, (0.5 * Distance[P, L])) → e_1
  57. Intersect(e_1, k_1, 1) → O
  58. Intersect(e_1, l_1, 2) → Q
  59. Intersect(e_1, l_1, 1) → R
  60. Ray(P, R) → q_1
  61. Circle(D, 2) → r_1
  62. Intersect(r_1, m_1, 1) → S
  63. Ray(D, S) → s_1
  64. Dilate(N, If[12 < m ≤ 13, 13 - m, 0], P) → N'_1
  65. Dilate(M, If[12 < m ≤ 13, 13 - m, 0], D) → M'_1
  66. Segment(N, N'_1) → t_1
  67. Segment(M, M'_1) → a_1
  68. Angle(R, P, O) → δ
  69. Rotate(R, If[13 < m ≤ 14, ((m - 13) * δ), δ], P) → R'
  70. CircleSector(P, R, R') → c_2
  71. Dilate(P, If[14 < m ≤ 15, 15 - m, 0], D) → P'_1
  72. Vector(P, P'_1) → u
  73. Translate(c_2, u) → d_2
  74. Segment(A, D_1) → b_1