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维瓦尼亚定理动态演示

维瓦尼亚定理动态演示
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2017-12-03 10:35
测试改名0向量几何作图
所属专题 Geometry Review
本范例通过动态方式展示了维瓦尼亚定理，无需文字和数字说明。它利用GeoGebra中的Polygon, Dilate, Segment, Circle, Intersect, Rotate, Vector, Centroid, CircleArc, PointIn, Line, OrthogonalLine, Angle, Midpoint, Translate等命令构建，适合初中及以上学生学习几何变换和三角形性质。

GeoGebra 命令及参数

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
  3. Segment(A, A') → e
  4. Dilate(B, If[1 < d ≤ 2, 2 - d, 0], C) → B'
  5. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], A) → C'
  6. Segment(A, B) → h
  7. Segment(A, C) → i
  8. Segment(B, C) → j
  9. Circle(A, (0.15 * h)) → k
  10. Intersect(k, i, 1) → D
  11. Intersect(k, h, 1) → E
  12. Rotate(A, If[3.5 < d ≤ 4.5, ((d - 3.5) * pi / 3), 1.0471975511965976], A) → A'_1
  13. Rotate(A', If[3.5 < d ≤ 4.5, ((d - 3.5) * pi / 3), 1.0471975511965976], A) → A''
  14. Segment(A'_1, A'') → e'
  15. Rotate(A, If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * pi / 3), -1.0471975511965976], B) → A'_2
  16. Rotate(A', If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * pi / 3), -1.0471975511965976], B) → A''_1
  17. Segment(A'_2, A''_1) → e'_1
  18. Dilate(A, If[6 < d ≤ 7, 7 - d, 0], B) → A'_3
  19. Vector(A, A'_3) → u
  20. Circle(B, (0.15 * h)) → r
  21. Intersect(r, j, 1) → F
  22. Intersect(r, h, 1) → K
  23. Dilate(B, If[8 < d ≤ 9, 9 - d, 0], C) → B'_1
  24. Vector(B, B'_1) → v
  25. Centroid(poly1) → L
  26. Circle(L, B) → p
  27. CircleArc(L, B, A) → q
  28. CircleArc(L, A, B) → t
  29. Rotate(B, If[5.5 < d ≤ 6.5, (((d - 5.5) * 4) * pi / 3), (4 * pi / 3)], L) → B'_2
  30. Rotate(A, If[6.5 < d ≤ 7.5, (((d - 6.5) * 2) * pi / 3), (2 * pi / 3)], L) → A'_4
  31. PointIn(poly1) → R
  32. Line(A, B) → p_1
  33. Line(B, C) → q_1
  34. Line(C, A) → r_1
  35. OrthogonalLine(R, p_1) → s_1
  36. OrthogonalLine(R, q_1) → t_1
  37. OrthogonalLine(R, r_1) → a_1
  38. Intersect(r_1, a_1) → S
  39. Intersect(t_1, q_1) → T
  40. Intersect(p_1, s_1) → U
  41. Angle(B, U, R) → α
  42. Angle(C, T, R) → β
  43. Angle(R, S, A) → γ
  44. Midpoint(A, B) → V
  45. Segment(R, T) → l
  46. Segment(R, S) → m
  47. Segment(R, U) → n
  48. Line(C, V) → s
  49. Circle(C, m) → c_1
  50. Intersect(c_1, s) → M, N
  51. Circle(N, l) → d_1
  52. Intersect(d_1, s) → O, P
  53. Dilate(R, If[7 < d ≤ 8, 8 - d, 0], S) → R'
  54. Segment(R, R') → f_1
  55. Dilate(R, If[8 < d ≤ 9, 9 - d, 0], T) → R'_1
  56. Segment(R, R'_1) → g_1
  57. Angle(C, V, B) → δ
  58. Dilate(R, If[9 < d ≤ 10, 10 - d, 0], U) → R'_2
  59. Segment(R, R'_2) → h_1
  60. Dilate(C, If[11 < d ≤ 12, 12 - d, 0], N) → C'_1
  61. Dilate(N, If[12 < d ≤ 13, 13 - d, 0], P) → N'
  62. Dilate(P, If[13 < d ≤ 14, 14 - d, 0], V) → P'
  63. Segment(C, C'_1) → i_1
  64. Segment(N, N') → j_1
  65. Segment(P, P') → k_1
  66. Dilate(R, If[15 < d ≤ 16, 16 - d, 0], N) → R'_3
  67. Vector(R, R'_3) → w
  68. Translate(R, w) → R'_4
  69. Translate(R', w) → R''
  70. Rotate(R'_4, If[16 < d ≤ 17, ((-(d - 16)) * pi / 3), ((-pi)) / 3], N) → Q
  71. Dilate(R, If[17 < d ≤ 18, 18 - d, 0], P) → R'_5
  72. Vector(R, R'_5) → u_1
  73. Translate(R, u_1) → R'_6
  74. Translate(R'_1, u_1) → W
  75. Rotate(R'_6, If[18 < d ≤ 19, ((d - 18) * pi / 3), pi / 3], P) → Z
  76. Rotate(W, If[18 < d ≤ 19, ((d - 18) * pi / 3), pi / 3], P) → W'
  77. Dilate(R, If[19 < d ≤ 20, 20 - d, 0], P) → R'_7
  78. Vector(R, R'_7) → v_1
  79. Translate(R, v_1) → R'_8
  80. Translate(R'_2, v_1) → A_1
  81. Segment(R'_8, A_1) → e_1
  82. Dilate(R', If[15 < d ≤ 16, 16 - d, 0], C) → R''_{1}
  83. Vector(R', R''_{1}) → w_1
  84. Translate(R, w_1) → R'_{9}
  85. Translate(R', w_1) → R''_{2}
  86. Segment(R'_{9}, R''_{2}) → f_2
  87. Rotate(R'_{9}, If[16 < d ≤ 17, ((-(d - 16)) * pi / 3), ((-pi)) / 3], R''_{1}) → B_1
  88. Rotate(R''_{2}, If[16 < d ≤ 17, ((-(d - 16)) * pi / 3), ((-pi)) / 3], R''_{1}) → C_1
  89. Segment(B_1, C_1) → l_1
  90. Dilate(R'_1, If[17 < d ≤ 18, 18 - d, 0], N) → D_1
  91. Vector(R'_1, D_1) → b_1
  92. Translate(R, b_1) → R'_{10}
  93. Translate(R'_1, b_1) → E_1
  94. Segment(R'_{10}, E_1) → m_1
  95. Rotate(R'_{10}, If[18 < d ≤ 19, ((d - 18) * pi / 3), pi / 3], N) → F_1
  96. Rotate(E_1, If[18 < d ≤ 19, ((d - 18) * pi / 3), pi / 3], N) → G_1
  97. Segment(F_1, G_1) → n_1