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Truchet 3x3 Pattern Demo

Truchet 3x3 Pattern Demo
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2018-11-03 02:33
Probability & StatisticsTransformationGeometric Construction
This example demonstrates the three possible combinations of Truchet patterns using random variables to generate distinct geometric figures. It involves core math concepts like probability & statistics, geometric transformations, and logic. The construction uses GeoGebra commands such as Polygon, Midpoint, Circle, Point, Rotate, and CircleSector. Suitable for high school mathematics education to understand the relationship between random variables and geometric shapes, as well as the application of geometric transformations.

GeoGebra Commands & Parameters

  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}