动态几何图形演示 by Tim Brzezinski (5)

动态几何图形演示 by Tim Brzezinski (5)
几何画板及绘图内容加载中,请稍等……
2018-05-05 21:28
①本范例动态演示了圆、菱形、角度等几何图形的相互关系与变换;②涉及核心数学概念包括圆、菱形、角度、变换、比例等;③作图要点提炼自构造摘要,使用了Circle, Distance, PointIn, Semicircle, Intersect, Line, Angle, Dilate, Midpoint, Segment, Rotate, Vector, CircleArc, Point, Ray, CircleSector, Translate等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解几何变换与概率统计中的正态分布关系。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Distance(A, B) → a
  3. PointIn(b) → C_1
  4. Semicircle(A, C_1) → d
  5. Semicircle(C_1, A) → e
  6. Intersect(c, d, 1) → D_1
  7. Intersect(c, e, 1) → C
  8. Line(C_1, C) → f
  9. Line(C_1, D_1) → g
  10. Line(C, g) → h
  11. Intersect(c, h) → F, D
  12. Line(C_1, D) → i
  13. Intersect(c, i, 2) → E
  14. Line(C, E) → j
  15. Intersect(g, j) → G
  16. Angle(A, D_1, G) → α
  17. Angle(C_1, C, A) → β
  18. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], G) → H
  19. Midpoint(C, C_1) → I
  20. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], I) → J
  21. Segment(C_1, J) → l
  22. Segment(C_1, H) → m
  23. Dilate(G, If[0 < k ≤ 1, 1 - k, 0], G) → G'
  24. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], D_1) → A'
  25. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], C) → A'_1
  26. Segment(A, A') → n
  27. Segment(A, A'_1) → p
  28. Dilate(G, If[1 < k ≤ 2, 2 - k, 0], D_1) → G'_1
  29. Dilate(I, If[1 < k ≤ 2, 2 - k, 0], C) → I'
  30. Segment(G, G'_1) → q
  31. Segment(I, I') → r
  32. Rotate(A, 90°, C) → A'_2
  33. Angle(A, C, A'_2) → γ
  34. Circle(C_1, (0.4 * Distance[C_1, G])) → t
  35. Angle(G, C_1, C) → δ
  36. Intersect(t, m) → L,
  37. Rotate(L, If[4 < k ≤ 5, ((k - 4) * δ), δ], C_1) → L'
  38. Dilate(C_1, If[5.5 < k ≤ 6.5, 6.5 - k, 0], C) → M
  39. Vector(C_1, M) → u
  40. Dilate(E, If[7 < k ≤ 8, 8 - k, 0], C_1) → E'
  41. Segment(E, E') → h_1
  42. Dilate(C, If[8.5 < k ≤ 9.5, 9.5 - k, 0], E) → C'_1
  43. Dilate(E, If[9.5 < k ≤ 10.5, 10.5 - k, 0], G) → E'_1
  44. Rotate(C_1, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → N
  45. Rotate(G, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → G'_2
  46. CircleArc(A, D_1, C) → e_1
  47. Point(e_1) → O
  48. Line(O, C_1) → n_1
  49. Line(D_1, n_1) → p_1
  50. Intersect(e_1, p_1) → P, Q
  51. Line(O, Q) → f_1
  52. Midpoint(O, Q) → K
  53. Circle(O, (0.5 * Distance[O, K])) → s
  54. Intersect(s, n_1) → R, S
  55. Intersect(s, f_1, 1) → T
  56. Angle(R, O, T) → ε
  57. Line(C, Q) → g_1
  58. Intersect(n_1, g_1) → U
  59. Intersect(c, n_1) → V, W
  60. Dilate(O, If[4 < k ≤ 5, 5 - k, 0], U) → O'
  61. Segment(O, O') → q_1
  62. Dilate(U, If[5 < k ≤ 6, 6 - k, 0], W) → U'
  63. Segment(U, U') → r_1
  64. Ray(O, R) → s_1
  65. Dilate(W, If[6 < k ≤ 7, 7 - k, 0], C_1) → W'
  66. Segment(W, W') → t_1
  67. Circle(Q, 3) → c_1
  68. Intersect(c_1, p_1, 1) → Z
  69. Ray(Q, Z) → a_1
  70. Dilate(D_1, If[7 < k ≤ 8, 8 - k, 0], Q) → A_1
  71. Segment(D_1, A_1) → b_1
  72. Rotate(R, If[8.5 < k ≤ 9.5, ((k - 8.5) * ε), ε], O) → R'
  73. CircleSector(O, R, R') → d_1
  74. Dilate(O, If[10 < k ≤ 11, 11 - k, 0], Q) → O'_1
  75. Vector(O, O'_1) → v
  76. Translate(d_1, v) → c_2
  77. Dilate(C, If[11 < k ≤ 12, 12 - k, 0], U) → C'
  78. Segment(C, C') → i_1
  79. Dilate(U, If[12 < k ≤ 13, 13 - k, 0], Q) → U'_1
  80. Segment(U, U'_1) → j_1
  81. Angle(O, U, A) → ζ
  82. Dilate(A, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → A'_3
  83. Segment(A, A'_3) → k_1
  84. Dilate(O, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → O'_2
  85. Segment(O, O'_2) → l_1
  86. Rotate(O, If[15 < k ≤ 16, ((k - 15) * π), π], U) → O'_3
  87. Rotate(O'_2, If[15 < k ≤ 16, ((k - 15) * π), π], U) → B_1
  88. Segment(O'_3, B_1) → m_1
  89. Segment(O, O'_1) → f_2
  90. Circle(O, 1) → d_2
  91. Intersect(d_2, f_1, 1) → E_1
  92. Ray(O, E_1) → g_2

AI 绘图提示语参考

画一个动态几何图形,展示圆形、菱形和角之间的关系与变换。包含两个半圆相交形成交点,连接这些点形成菱形和直线。标记关键角,并展示菱形通过缩放和旋转与正态分布的关系。图形应动态变化,展示几何变换过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。