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Wiley Module 2: Geometric Patterns and Theorems

Wiley Module 2: Geometric Patterns and Theorems
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2019-07-02 06:14
TrianglePolygonTrigonometryCoordinate GeometryGeometric Construction
In collections Virtual Manipulatives
This example demonstrates geometric patterns and theorems using interactive tools, focusing on hexagons, triangles, squares, and transformations. It involves core concepts like the Pythagorean theorem, scalene triangles, real numbers, centroid, and boxplots. GeoGebra commands such as Hexagon, Rotate, Midpoint, and Polygon are used in construction. Suitable for high school mathematics education, emphasizing geometric constructions and theorem verification.

GeoGebra Commands & Parameters

  1. Hexagon(A) → f, g, h, i, j, k, poly1, B
  2. Hexagon(C) → l, m, n, p, q, r, poly2, D
  3. Hexagon(E) → s, t, a, b, c, d, poly3, F
  4. Hexagon(G) → e, f_1, g_1, h_1, i_1, j_1, poly4, H
  5. Tool2(I) → poly5, k_1, l_1, m_1, n_1, J
  6. Tool2(K) → poly6, p_1, q_1, r_1, s_1, L
  7. Tool2(M) → poly7, t_1, a_1, b_1, c_1, N
  8. Tool2(O) → poly8, d_1, e_1, f_2, g_2, P
  9. Tool4(Q) → h_2, i_2, j_2, k_2, R, poly9
  10. Tool4(S) → l_2, m_2, n_2, p_2, T, poly10
  11. Tool4(U) → q_2, r_2, s_2, t_2, V, poly11
  12. Tool4(W) → a_2, b_2, c_2, d_2, Z, poly12
  13. Tool4(A_1) → e_2, f_3, g_3, h_3, B_1, poly13
  14. Tool4(C_1) → i_3, j_3, k_3, l_3, D_1, poly14
  15. Tool3(E_1) → m_3, n_3, p_3, F_1, poly15
  16. Tool3(G_1) → q_3, r_3, s_3, H_1, poly16
  17. Tool3(I_1) → t_3, a_3, b_3, J_1, poly17
  18. Tool3(K_1) → c_3, d_3, e_3, L_1, poly18
  19. Tool3(M_1) → f_4, g_4, h_4, N_1, poly19
  20. Tool3(O_1) → i_4, j_4, k_4, P_1, poly20
  21. Tool3(Q_1) → l_4, m_4, n_4, R_1, poly21
  22. Tool3(S_1) → p_4, q_4, r_4, T_1, poly22
  23. Tool3(U_1) → s_4, t_4, a_4, V_1, poly23
  24. Tool3(W_1) → b_4, c_4, d_4, Z_1, poly24
  25. Tool3(A_2) → e_4, f_5, g_5, B_2, poly25
  26. Tool3(C_2) → h_5, i_5, j_5, D_2, poly26
  27. Hexagon(A_3) → f_6, g_6, h_6, i_6, j_6, k_5, poly1_1, B_3
  28. Hexagon(C_3) → l_5, m_5, n_5, p_5, q_5, r_5, poly2_1, D_3
  29. Hexagon(E_2) → s_5, t_5, a_5, b_5, c_5, d_5, poly3_1, F_2
  30. Hexagon(G_2) → e_5, f_7, g_7, h_7, i_7, j_7, poly4_1, H_2
  31. Tool2(I_2) → poly5_1, k_6, l_6, m_6, n_6, J_2
  32. Tool2(K_2) → poly6_1, p_6, q_6, r_6, s_6, L_2
  33. Tool2(M_2) → poly7_1, t_6, a_6, b_6, c_6, N_2
  34. Tool2(O_2) → poly8_1, d_6, e_6, f_8, g_8, P_2
  35. Tool4(Q_2) → h_8, i_8, j_8, k_7, R_2, poly9_1
  36. Tool4(S_2) → l_7, m_7, n_7, p_7, T_2, poly10_1
  37. Tool4(U_2) → q_7, r_7, s_7, t_7, V_2, poly11_1
  38. Tool4(W_2) → a_7, b_7, c_7, d_7, Z_2, poly12_1
  39. Tool4(A_4) → e_7, f_9, g_9, h_9, B_4, poly13_1
  40. Tool4(C_4) → i_9, j_9, k_8, l_8, D_4, poly14_1
  41. Tool3(E_3) → m_8, n_8, p_8, F_3, poly15_1
  42. Tool3(G_3) → q_8, r_8, s_8, H_3, poly16_1
  43. Tool3(I_3) → t_8, a_8, b_8, J_3, poly17_1
  44. Tool3(K_3) → c_8, d_8, e_8, L_3, poly18_1
  45. Tool3(M_3) → f_{10}, g_{10}, h_{10}, N_3, poly19_1
  46. Tool3(O_3) → i_{10}, j_{10}, k_9, P_3, poly20_1
  47. Tool3(Q_3) → l_9, m_9, n_9, R_3, poly21_1
  48. Tool3(S_3) → p_9, q_9, r_9, T_3, poly22_1
  49. Tool3(U_3) → s_9, t_9, a_9, V_3, poly23_1
  50. Tool3(W_3) → b_9, c_9, d_9, Z_3, poly24_1
  51. Tool3(A_5) → e_9, f_{11}, g_{11}, B_5, poly25_1
  52. Tool3(C_5) → h_{11}, i_{11}, j_{11}, D_5, poly26_1
  53. Circle(A_6, 1) → c_{10}
  54. Point(c_{10}) → B_6
  55. Rotate(B_6, 90°, A_6) → B'_1
  56. Rotate(A_6, (-(90°)), B_6) → A'_1
  57. Square(C_6) → D_6, poly2_2, f_{12}, g_{12}, h_{12}, i_{12}
  58. Square(E_4) → F_4, poly3_2, j_{12}, k_{10}, l_{10}, m_{10}
  59. Square(G_4) → H_4, poly4_2, n_{10}, p_{10}, q_{10}, r_{10}
  60. Square(I_4) → J_4, poly5_2, s_{10}, t_{10}, d_{10}, e_{10}
  61. Square(K_4) → L_4, poly6_2, f_{13}, g_{13}, h_{13}, i_{13}
  62. Square(M_4) → N_4, poly7_2, j_{13}, k_{11}, l_{11}, m_{11}
  63. Square(O_4) → P_4, poly8_2, n_{11}, p_{11}, q_{11}, r_{11}
  64. Circle(A_7, 1) → c_{11}
  65. Point(c_{11}) → B_7
  66. Rotate(B_7, 150°, A_7) → B'_2
  67. Midpoint(B'_2, B_7) → C_7
  68. Mirror(A_7, C_7) → A'_2
  69. Polygon(A_7, B_7, A'_2, B'_2) → poly1_2, a_{10}, b_{10}, a'_1, b'_1
  70. TanRhombus(D_7) → E_5, poly2_3, f_{14}, g_{14}, h_{14}, i_{14}
  71. TanRhombus(F_5) → G_5, poly3_3, j_{14}, k_{12}, l_{12}, m_{12}
  72. TanRhombus(H_5) → I_5, poly4_3, n_{12}, p_{12}, q_{12}, r_{12}
  73. TanRhombus(J_5) → K_5, poly5_3, s_{11}, t_{11}, d_{11}, e_{11}
  74. TanRhombus(L_5) → M_5, poly6_3, f_{15}, g_{15}, h_{15}, i_{15}
  75. TanRhombus(N_5) → O_5, poly7_3, j_{15}, k_{13}, l_{13}, m_{13}
  76. TanRhombus(P_5) → Q_4, poly8_3, n_{13}, p_{13}, q_{13}, r_{13}
  77. Hexagon(A_8) → f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{14}, poly1_3, B_8
  78. Hexagon(C_8) → l_{14}, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, poly2_4, D_8
  79. Hexagon(E_6) → s_{12}, t_{12}, a_{11}, b_{11}, c_{12}, d_{12}, poly3_4, F_6
  80. Hexagon(G_6) → e_{12}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, poly4_4, H_6
  81. Hexagon(A_{11}) → f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, k_{15}, poly1_4, B_9
  82. Hexagon(C_{11}) → l_{15}, m_{15}, n_{15}, p_{15}, q_{15}, r_{15}, poly2_5, D_9
  83. Hexagon(E_8) → s_{13}, t_{13}, a_{12}, b_{12}, c_{13}, d_{13}, poly3_5, F_7
  84. Hexagon(G_8) → e_{13}, f_{19}, g_{19}, h_{19}, i_{19}, j_{19}, poly4_5, H_7
  85. Tool2(I_{10}) → poly5_4, k_{16}, l_{16}, m_{16}, n_{16}, J_6
  86. Tool2(K_{10}) → poly6_4, p_{16}, q_{16}, r_{16}, s_{14}, L_6
  87. Tool2(M_{10}) → poly7_4, t_{14}, a_{13}, b_{13}, c_{14}, N_6
  88. Tool2(O_{10}) → poly8_4, d_{14}, e_{14}, f_{20}, g_{20}, P_6
  89. Tool2(I_{12}) → poly5_5, k_{17}, l_{17}, m_{17}, n_{17}, J_7
  90. Tool2(K_{12}) → poly6_5, p_{17}, q_{17}, r_{17}, s_{15}, L_7
  91. Tool2(M_{12}) → poly7_5, t_{15}, a_{14}, b_{14}, c_{15}, N_7
  92. Tool2(O_{12}) → poly8_5, d_{15}, e_{15}, f_{21}, g_{21}, P_7
  93. Tool4(S_{12}) → l_{18}, m_{18}, n_{18}, p_{18}, T_4, poly10_2
  94. Tool4(U_{12}) → q_{18}, r_{18}, s_{16}, t_{16}, V_4, poly11_2
  95. Tool4(W_{12}) → a_{15}, b_{15}, c_{16}, d_{16}, Z_4, poly12_2
  96. Tool4(A_{21}) → e_{16}, f_{22}, g_{22}, h_{20}, B_{10}, poly13_2
  97. Circle(A_{26}, 1) → c_{17}
  98. Point(c_{17}) → B_{11}
  99. Rotate(B_{11}, 150°, A_{26}) → B'_3
  100. Midpoint(B'_3, B_{11}) → C_{26}
  101. Mirror(A_{26}, C_{26}) → A'_3
  102. Polygon(A_{26}, B_{11}, A'_3, B'_3) → poly1_5, a_{16}, b_{16}, a'_2, b'_2
  103. TanRhombus(D_{10}) → E_{18}, poly2_6, f_{23}, g_{23}, h_{21}, i_{20}
  104. TanRhombus(F_8) → G_{18}, poly3_6, j_{20}, k_{18}, l_{19}, m_{19}
  105. TanRhombus(H_8) → I_{18}, poly4_6, n_{19}, p_{19}, q_{19}, r_{19}
  106. TanRhombus(J_8) → K_{18}, poly5_6, s_{17}, t_{17}, d_{17}, e_{17}
  107. TanRhombus(L_8) → M_{18}, poly6_6, f_{24}, g_{24}, h_{22}, i_{21}
  108. TanRhombus(N_8) → O_{18}, poly7_6, j_{21}, k_{19}, l_{20}, m_{20}
  109. TanRhombus(P_8) → Q_{17}, poly8_6, n_{20}, p_{20}, q_{20}, r_{20}
  110. Sequence(Sequence[(3^(0.5) / 2, 0.5) + ((3^(0.5) * (i - 1)), k - 1), i, 1, 10], k, -10, 10) → IsoDots2
  111. Sequence(Sequence[(0, 0) + ((3^(0.5) * (i - 1)), k - 1), i, 1, 10], k, -10, 10) → IsoDots1

AI Drawing Prompt Reference

Create a symmetric geometric pattern composed of regular hexagons, triangles, and squares. Start by placing four hexagons near the corners, each containing a smaller hexagon inside. Then fill the gaps between hexagons with triangles and squares arranged in a circular pattern. The overall design is centrally symmetric, with multiple rotated polygons forming a repeating tessellation. All polygons share vertices and align edges to create a tightly packed planar mosaic.
The prompt above was compiled from the original drawing commands and is for reference only.