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动态可调的几何问题演示 by Tim Brzezinski

动态可调的几何问题演示 by Tim Brzezinski
几何画板及绘图内容加载中，请稍等……
2018-02-04 11:16
圆向量几何作图
①本范例动态演示了Antonio Gutierrez提出的一个几何问题，涉及二维向量、棱柱、外接圆等元素；②核心数学概念包括二维向量、外接圆、定积分、方程等；③作图要点运用了Circle（圆）、Point（点）、Line（线）、OrthogonalLine（垂线）、Intersect（交点）、Ray（射线）、Angle（角）、Radius（半径）、Dilate（缩放）、Segment（线段）、Rotate（旋转）、Polygon（多边形）、Midpoint（中点）、CircleSector（扇形）、Vector（向量）、Translate（平移）等GeoGebra命令/对象；④适合高中及以上数学学习者，用于理解向量、几何变换及积分应用。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Circle(C, A) → d
  4. Line(A, C) → f
  5. OrthogonalLine(C, f) → g
  6. Intersect(d, g, 2) → D
  7. Intersect(d, g, 1) → E
  8. Line(D, A) → h
  9. Intersect(c, h, 1) → F
  10. Intersect(c, d, 2) → G
  11. Ray(F, G) → i
  12. Angle(A, F, G) → α
  13. Radius(c) → b
  14. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], C) → A'
  15. Segment(A, A') → j
  16. Rotate(A, If[1 < e ≤ 2, ((e - 1) * π / 3), π / 3], C) → A'_1
  17. Rotate(A', If[1 < e ≤ 2, ((e - 1) * π / 3), π / 3], C) → A''
  18. Segment(A'_1, A'') → j'
  19. Rotate(A'_1, If[2 < e ≤ 3, ((e - 2) * π / 3), π / 3], G) → I
  20. Rotate(A'', If[2 < e ≤ 3, ((e - 2) * π / 3), π / 3], G) → A'''
  21. Segment(I, A''') → j''
  22. Polygon(A, G, C) → t1, c_1, a_1, g_1
  23. Rotate(G, If[3 < e ≤ 4, ((e - 2) * π / 3), π / 3], G) → G'
  24. Midpoint(C, G) → J
  25. Dilate(A, If[4 < e ≤ 5, 5 - e, 0], J) → A'_2
  26. Segment(A, A'_2) → l
  27. Circle(A, (0.3 * b)) → p
  28. Line(A, C) → m
  29. Intersect(p, m) → K, L
  30. Rotate(L, If[5 < e ≤ 6, ((-(e - 5)) * π / 6), ((-π)) / 6], A) → L'
  31. CircleSector(A, L', L) → q
  32. Rotate(q, If[7 < e ≤ 8, ((-(e - 7)) * π / 6), ((-π)) / 6], A) → q'
  33. Line(H, j'') → n
  34. Line(H, l) → r
  35. Circle(H, 2) → s
  36. Intersect(s, n, 1) → M
  37. Intersect(s, k) → N, O
  38. Angle(M, H, O) → β
  39. Dilate(A, If[9 < e ≤ 10, 10 - e, 0], H) → A'_3
  40. Vector(A, A'_3) → u
  41. Translate(q', u) → q''
  42. Rotate(q'', If[9 < e ≤ 10, ((e - 9) * β), β], A'_3) → q'''
  43. Circle(H, (0.55 * b)) → t
  44. Intersect(t, k) → P, Q
  45. Rotate(Q, π / 6, H) → Q'
  46. Segment(H, Q') → f_1
  47. Rotate(Q', (5 * π / 24), H) → Q''
  48. Rotate(Q'', (5 * π / 24), H) → Q'''
  49. Rotate(Q''', (5 * π / 24), H) → R
  50. Circle(H, (0.3 * b)) → d_1
  51. Ray(H, Q') → h_1
  52. Intersect(d_1, h_1) → S,
  53. Dilate(H, If[10 < e ≤ 11, 11 - e, 0], Q') → H'
  54. Dilate(H, If[10 < e ≤ 11, 11 - e, 0], Q'') → H'_1
  55. Dilate(H, If[10 < e ≤ 11, 11 - e, 0], Q''') → H'_2
  56. Dilate(H, If[10 < e ≤ 11, 11 - e, 0], R) → H'_3
  57. Segment(H, H') → i_1
  58. Segment(H, H'_1) → j_1
  59. Segment(H, H'_2) → k_1
  60. Segment(H, H'_3) → l_1
  61. Rotate(S, If[11 < e ≤ 12, (((e - 11) * 5) * π / 24), (5 * π / 24)], H) → S'
  62. CircleSector(H, S, S') → e_1
  63. Rotate(e_1, If[13 < e ≤ 14, (((e - 13) * 5) * π / 24), (5 * π / 24)], H) → p_1
  64. Rotate(p_1, If[15 < e ≤ 16, (((e - 15) * 5) * π / 24), (5 * π / 24)], H) → q_1
  65. Rotate(q_1, If[17 < e ≤ 18, (((e - 17) * 5) * π / 24), (5 * π / 24)], H) → r_1
  66. Dilate(C, If[20 < e ≤ 21, 21 - e, 0], E) → C'
  67. Dilate(C, If[20 < e ≤ 21, 21 - e, 0], D) → C'_1
  68. Segment(C, C'_1) → m_1
  69. Segment(C, C') → n_1
  70. Angle(D, C, A) → γ
  71. Dilate(D, If[21 < e ≤ 22, 22 - e, 0], F) → D'
  72. Segment(D, D') → s_1
  73. Dilate(F, If[22 < e ≤ 23, 23 - e, 0], A) → F'
  74. Segment(F, F') → t_1
  75. Dilate(F, If[23 < e ≤ 24, 24 - e, 0], G') → F'_1
  76. Segment(F, F'_1) → b_1
  77. Line(F, k) → f_2
  78. Point(f_2) → T
  79. Angle(T, F, G) → δ
  80. Dilate(H, If[25 < e ≤ 26, 26 - e, 0], F) → H'_4
  81. Vector(H, H'_4) → v
  82. Translate(r_1, v) → c_2
  83. Rotate(c_2, If[25 < e ≤ 26, ((e - 25) * δ), δ], H'_4) → d_2