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一个奇怪的三角谜题。你能解释吗？

一个奇怪的三角谜题。你能解释吗？
几何画板及绘图内容加载中，请稍等……
2020-05-12 15:14
测试改名0三角函数几何作图
这是一个展示三角形性质的谜题。涉及的核心数学概念包括不等边三角形、相似三角形和三角函数。通过使用GeoGebra命令如Midpoint、Polygon、Intersect等进行几何作图。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Midpoint(A, B) → G
  2. Polygon(A, B, C) → t1, h, e, f
  3. Line(I, h) → g
  4. Intersect(g, t1) → J, K
  5. Segment(C, G) → i
  6. Line(J, i) → j
  7. Line(K, i) → k
  8. Line(L, h) → l
  9. Line(M, l) → m
  10. Intersect(h, j) → N
  11. Intersect(k, h) → O
  12. Intersect(k, t1) → P, Q
  13. Intersect(k, l) → R
  14. Intersect(m, j) → S
  15. Polygon(S, M, L, R, O, N) → poly1, s, m_1, l_1, r, o, n
  16. Polygon(J, K, R, L, M, S) → poly2, j_1, k_1, r_1, l_2, m_2, s_1
  17. Polygon(J, A + (0, 0), N) → t2, b, c, d
  18. Polygon(K, O, B + (0, 0)) → t3, f_1, g_1, h_1
  19. Polygon(C, I, J) → t4, p, q, t
  20. Polygon(C + (0, 0), I, K) → t5, i_1, n_1, p_1
  21. Translate(I, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, A])]) → I'
  22. Translate(I, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, B])]) → I'_1
  23. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, B])]) → K'
  24. Translate(C, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, C])]) → H'_2
  25. Translate(N, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, C])]) → N'
  26. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, C])]) → K'_1
  27. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, C])]) → O'
  28. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → S'
  29. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → M'
  30. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → L'
  31. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → R'
  32. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → O'_1
  33. Translate(N, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-0.75, 0)])]) → N'_1
  34. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (0.75, 0)])]) → K'_2
  35. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (0.75, 0)])]) → R'_1
  36. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (0.75, 0)])]) → L'_1
  37. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (0.75, 0)])]) → M'_1
  38. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (0.75, 0)])]) → S'_1
  39. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → S'_2
  40. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → M'_2
  41. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → L'_2
  42. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → R'_2
  43. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → O'_2
  44. Translate(N, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1, 0)])]) → N'_2
  45. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → K'_3
  46. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → R'_3
  47. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → L'_3
  48. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → M'_3
  49. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → S'_3
  50. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, C])]) → J'
  51. Translate(A, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, C])]) → E'
  52. Translate(N, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, C])]) → N'_3
  53. Polygon(J', E' + (-0.05, 0), N'_3) → t2', e_1, f_2, g_2
  54. Translate(C, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, B])]) → H'
  55. Translate(I, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, B])]) → I'_2
  56. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, B])]) → K'_4
  57. Polygon(H' + (0.025, 0), I'_2, K'_4) → t5', a, q_1, t_1
  58. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[B])]) → K'_5
  59. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[B])]) → O'_3
  60. Translate(B, Vector[(If[Change < 10, Change / 10, 1] * Vector[B])]) → F'
  61. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, C])]) → K'_6
  62. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, C])]) → O'_4
  63. Translate(B, Vector[(If[Change < 10, Change / 10, 1] * Vector[P, C])]) → F'_1
  64. Polygon(K'_6, O'_4, F'_1 + (0.05, 0)) → t3', h_2, i_2, j_2
  65. Translate(C, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, A])]) → H'_1
  66. Translate(I, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, A])]) → I'_3
  67. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[J, A])]) → J'_1
  68. Polygon(H'_1 + (-0.025, 0), I'_3, J'_1) → t4', a_1, b_1, c_1
  69. Segment(C, A) → k_2
  70. Segment(C, B) → n_2
  71. Segment(A, B) → p_2
  72. Midpoint(k_2) → E
  73. Midpoint(n_2) → F
  74. CircumcircleArc(A, H, C) → c_2
  75. CircumcircleArc(C, T, B) → d_2
  76. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → J'_3
  77. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → K'_7
  78. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → R'_4
  79. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → L'_4
  80. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → M'_4
  81. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.125, 0)])]) → S'_4
  82. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → J'_4
  83. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → K'_8
  84. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → R'_5
  85. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → L'_5
  86. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → M'_5
  87. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.1, 0)])]) → S'_5
  88. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → J'_5
  89. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → K'_9
  90. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → R'_6
  91. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → L'_6
  92. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → M'_6
  93. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1, 0)])]) → S'_6
  94. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → S'_7
  95. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → M'_7
  96. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → L'_7
  97. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → R'_7
  98. Translate(O, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → O'_5
  99. Translate(N, Vector[(If[Change < 10, Change / 10, 1] * Vector[N, N + (-1.04, 0)])]) → N'_4
  100. Polygon(S'_7, M'_7, L'_7, R'_7, O'_5, N'_4) → poly1', s'_7, m'_7, l'_7, r'_7, o'_5, n'_4
  101. Translate(J, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → J'_2
  102. Translate(K, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → K'_{10}
  103. Translate(R, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → R'_8
  104. Translate(L, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → L'_8
  105. Translate(M, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → M'_8
  106. Translate(S, Vector[(If[Change < 10, Change / 10, 1] * Vector[R, Q + (1.04, 0)])]) → S'_8
  107. Polygon(J'_2, K'_{10}, R'_8, L'_8, M'_8, S'_8) → poly2'_1, j'_2, k'_{10}, r'_8, l'_8, m'_8, s'_8

AI 绘图提示语参考

绘制一个三角形ABC，然后在三角形内部构造一系列三角形和线段，包括中点G、线段t1、h、e、f、线段g、线段j、线段k、线段l、线段m、线段i、线段n、线段r、线段o、线段s，以及多个交点J、K、N、O、P、Q、R、S、M、L。通过平移操作，使这些线段和三角形在特定方向上移动，形成一个复杂的三角形图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。