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Truchet 3x3 图形演示

Truchet 3x3 图形演示
几何画板及绘图内容加载中，请稍等……
2018-11-03 02:33
概率统计变换几何作图
①本范例演示了 Truchet 图形的三种组合模式，通过随机变量生成不同的几何图案；②涉及的核心数学概念包括概率统计、几何变换和逻辑判断；③作图要点使用了 GeoGebra 命令 Polygon（多边形）、Midpoint（中点）、Circle（圆）、Point（点）、Rotate（旋转）、CircleSector（圆扇形）；④适合高中数学教学，用于理解随机变量与几何图形的关联，以及几何变换的应用。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, b, f_1, g_1, h_1, G_1, H_1
  2. Midpoint(A, G_1) → O_1
  3. Circle(O_1, A) → c_1
  4. Point(c_1) → P_1
  5. Rotate(P_1, 90°, O_1) → P_2
  6. Rotate(P_2, 90°, O_1) → P_3
  7. Rotate(P_3, 90°, O_1) → P_4
  8. Midpoint(P_4, P_1) → M_1
  9. Midpoint(P_1, P_2) → M_2
  10. Midpoint(P_2, P_3) → M_3
  11. Midpoint(P_3, P_4) → M_4
  12. CircleSector(P_1, M_2, M_1) → cb_1
  13. CircleSector(P_4, M_1, M_4) → cw_1
  14. CircleSector(P_3, M_4, M_3) → cb_2
  15. CircleSector(P_2, M_3, M_2) → cw_2
  16. Polygon(C, D, 4) → poly2, f, g, h, i, E_1, F_1
  17. Midpoint(C, E_1) → O_2
  18. Circle(O_2, C) → c_2
  19. Point(c_2) → P_5
  20. Rotate(P_5, 90°, O_2) → P_6
  21. Rotate(P_6, 90°, O_2) → P_7
  22. Rotate(P_7, 90°, O_2) → P_8
  23. Midpoint(P_6, P_7) → M_6
  24. Midpoint(P_5, P_6) → M_5
  25. Midpoint(P_5, P_8) → M_8
  26. Midpoint(P_8, P_7) → M_7
  27. CircleSector(P_6, M_6, M_5) → cw_3
  28. CircleSector(P_7, M_7, M_6) → cb_3
  29. CircleSector(P_8, M_8, M_7) → cw_4
  30. CircleSector(P_5, M_5, M_8) → cb_4
  31. Polygon(E, F, 4) → poly3, j, k, l, m, I_1, J_1
  32. Midpoint(E, I_1) → O_4
  33. Circle(O_4, E) → c_3
  34. Point(c_3) → P_9
  35. Rotate(P_9, 90°, O_4) → P_{10}
  36. Rotate(P_{10}, 90°, O_4) → P_{11}
  37. Rotate(P_{11}, 90°, O_4) → P_{12}
  38. Midpoint(P_9, P_{10}) → M_9
  39. Midpoint(P_{10}, P_{11}) → M_{10}
  40. Midpoint(P_{11}, P_{12}) → M_{11}
  41. Midpoint(P_{12}, P_9) → M_{12}
  42. CircleSector(P_{10}, M_{10}, M_9) → cb_5
  43. CircleSector(P_{11}, M_{11}, M_{10}) → cw_5
  44. CircleSector(P_{12}, M_{12}, M_{11}) → cb_6
  45. CircleSector(P_9, M_9, M_{12}) → cw_6
  46. Polygon(G, H, 4) → poly4, n, p, q, s, K_1, L_1
  47. Midpoint(G, K_1) → O_3
  48. Circle(O_3, G) → c_4
  49. Point(c_4) → P_{13}
  50. Rotate(P_{13}, 90°, O_3) → P_{14}
  51. Rotate(P_{14}, 90°, O_3) → P_{15}
  52. Rotate(P_{15}, 90°, O_3) → P_{16}
  53. Midpoint(P_{13}, P_{14}) → M_{13}
  54. Midpoint(P_{14}, P_{15}) → M_{14}
  55. Midpoint(P_{15}, P_{16}) → M_{15}
  56. Midpoint(P_{16}, P_{13}) → M_{16}
  57. CircleSector(P_{13}, M_{13}, M_{16}) → cb_7
  58. CircleSector(P_{14}, M_{14}, M_{13}) → cw_8
  59. CircleSector(P_{15}, M_{15}, M_{14}) → cb_8
  60. CircleSector(P_{16}, M_{16}, M_{15}) → cw_7
  61. Polygon(I, J, 4) → poly5, t, a, d, e, M_{37}, N_1
  62. Midpoint(I, M_{37}) → O_5
  63. Circle(O_5, I) → c_5
  64. Point(c_5) → P_{17}
  65. Rotate(P_{17}, 90°, O_5) → P_{18}
  66. Rotate(P_{18}, 90°, O_5) → P_{19}
  67. Rotate(P_{19}, 90°, O_5) → P_{20}
  68. Midpoint(P_{17}, P_{18}) → M_{17}
  69. Midpoint(P_{18}, P_{19}) → M_{18}
  70. Midpoint(P_{19}, P_{20}) → M_{19}
  71. Midpoint(P_{20}, P_{17}) → M_{20}
  72. CircleSector(P_{18}, M_{18}, M_{17}) → cw_9
  73. CircleSector(P_{19}, M_{19}, M_{18}) → cb_9
  74. CircleSector(P_{20}, M_{20}, M_{19}) → cw_{10}
  75. CircleSector(P_{17}, M_{17}, M_{20}) → cb_{10}
  76. Polygon(K, L, 4) → poly6, c, i_1, j_1, k_1, O_{10}, P_{37}
  77. Midpoint(K, O_{10}) → O_6
  78. Circle(O_6, K) → c_6
  79. Point(c_6) → P_{21}
  80. Rotate(P_{21}, 90°, O_6) → P_{22}
  81. Rotate(P_{22}, 90°, O_6) → P_{23}
  82. Rotate(P_{23}, 90°, O_6) → P_{24}
  83. Midpoint(P_{21}, P_{22}) → M_{21}
  84. Midpoint(P_{22}, P_{23}) → M_{22}
  85. Midpoint(P_{23}, P_{24}) → M_{23}
  86. Midpoint(P_{24}, P_{21}) → M_{24}
  87. CircleSector(P_{22}, M_{22}, M_{21}) → cb_{11}
  88. CircleSector(P_{21}, M_{21}, M_{24}) → cw_{11}
  89. CircleSector(P_{24}, M_{24}, M_{23}) → cb_{12}
  90. CircleSector(P_{23}, M_{23}, M_{22}) → cw_{12}
  91. Polygon(M, N, 4) → poly7, l_1, m_1, n_1, p_1, Q_{10}, R_1
  92. Midpoint(M, Q_{10}) → O_7
  93. Circle(O_7, M) → c_7
  94. Point(c_7) → P_{25}
  95. Rotate(P_{25}, 90°, O_7) → P_{26}
  96. Rotate(P_{26}, 90°, O_7) → P_{27}
  97. Rotate(P_{27}, 90°, O_7) → P_{28}
  98. Midpoint(P_{25}, P_{26}) → M_{25}
  99. Midpoint(P_{26}, P_{27}) → M_{26}
  100. Midpoint(P_{27}, P_{28}) → M_{27}
  101. Midpoint(P_{28}, P_{25}) → M_{28}
  102. CircleSector(P_{25}, M_{25}, M_{28}) → cw_{13}
  103. CircleSector(P_{26}, M_{26}, M_{25}) → cb_{13}
  104. CircleSector(P_{27}, M_{27}, M_{26}) → cw_{14}
  105. CircleSector(P_{28}, M_{28}, M_{27}) → cb_{14}
  106. Polygon(O, P, 4) → poly8, q_1, r_1, s_1, t_1, S, T
  107. Polygon(Q, R, 4) → poly9, a_1, b_1, d_1, e_1, U, V
  108. Midpoint(O, S) → O_8
  109. Midpoint(Q, U) → O_9
  110. Circle(O_8, O) → c_8
  111. Circle(O_9, Q) → c_9
  112. Point(c_8) → P_{29}
  113. Point(c_9) → P_{33}
  114. Rotate(P_{29}, 90°, O_8) → P_{30}
  115. Rotate(P_{30}, 90°, O_8) → P_{31}
  116. Rotate(P_{31}, 90°, O_8) → P_{32}
  117. Rotate(P_{33}, 90°, O_9) → P_{34}
  118. Rotate(P_{34}, 90°, O_9) → P_{35}
  119. Rotate(P_{35}, 90°, O_9) → P_{36}
  120. Midpoint(P_{29}, P_{30}) → M_{29}
  121. Midpoint(P_{30}, P_{31}) → M_{30}
  122. Midpoint(P_{31}, P_{32}) → M_{31}
  123. Midpoint(P_{32}, P_{29}) → M_{32}
  124. Midpoint(P_{33}, P_{34}) → M_{33}
  125. Midpoint(P_{34}, P_{35}) → M_{34}
  126. Midpoint(P_{35}, P_{36}) → M_{35}
  127. Midpoint(P_{36}, P_{33}) → M_{36}
  128. CircleSector(P_{34}, M_{34}, M_{33}) → cw_{17}
  129. CircleSector(P_{33}, M_{33}, M_{36}) → cb_{17}
  130. CircleSector(P_{36}, M_{36}, M_{35}) → cw_{18}
  131. CircleSector(P_{35}, M_{35}, M_{34}) → cb_{18}
  132. CircleSector(P_{29}, M_{29}, M_{32}) → cw_{15}
  133. CircleSector(P_{32}, M_{32}, M_{31}) → cb_{15}
  134. CircleSector(P_{31}, M_{31}, M_{30}) → cw_{16}
  135. CircleSector(P_{30}, M_{30}, M_{29}) → cb_{16}