10/3 and 10/4 Polygons

10/3 and 10/4 Polygons
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2019-12-31 16:23
This example demonstrates Islamic geometric patterns of 10/3 and 10/4 polygons. Core mathematical concepts include polygons, symmetry, quadrilaterals, quadratic equations, and logic. The construction uses GeoGebra commands such as ConstructionStep, Rotate, Polygon, Point, Midpoint, Segment, Intersect, PolyLine, etc. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Rotate(A, 36°) → A'
  3. Polygon(A, A', 10) → veelhoek1, f, p, B, C, D, E, F, G, H, I, g, h, i, j, k, l, m, n
  4. Point(xAxis) → J
  5. Rotate(K, 36°, J) → K'
  6. Polygon(K, K', 10) → veelhoek2, q, f_1, L, M, N, P, Q, R, S, T, r, s, t, a, b, c, d, e
  7. Midpoint(f) → U
  8. Midpoint(g) → V
  9. Midpoint(h) → W
  10. Midpoint(i) → Z
  11. Midpoint(j) → A_1
  12. Midpoint(k) → B_1
  13. Midpoint(l) → C_1
  14. Midpoint(m) → D_1
  15. Midpoint(n) → E_1
  16. Midpoint(p) → F_1
  17. Midpoint(q) → G_1
  18. Midpoint(r) → H_1
  19. Midpoint(s) → I_1
  20. Midpoint(t) → J_1
  21. Midpoint(a) → K_1
  22. Midpoint(b) → L_1
  23. Midpoint(c) → M_1
  24. Midpoint(d) → N_1
  25. Midpoint(e) → O_1
  26. Midpoint(f_1) → P_1
  27. Segment(U, Z) → g_1
  28. Segment(G_1, K_1) → h_1
  29. Segment(V, A_1) → i_1
  30. Segment(H_1, L_1) → j_1
  31. Segment(W, B_1) → k_1
  32. Segment(I_1, M_1) → l_1
  33. Segment(Z, C_1) → m_1
  34. Segment(J_1, N_1) → n_1
  35. Segment(A_1, D_1) → p_1
  36. Segment(K_1, O_1) → q_1
  37. Segment(B_1, E_1) → r_1
  38. Segment(L_1, P_1) → s_1
  39. Segment(C_1, F_1) → t_1
  40. Segment(M_1, G_1) → a_1
  41. Segment(D_1, U) → b_1
  42. Segment(N_1, H_1) → c_1
  43. Segment(E_1, V) → d_1
  44. Segment(O_1, I_1) → e_1
  45. Segment(F_1, W) → f_2
  46. Segment(P_1, J_1) → g_2
  47. Intersect(b_1, yAxis) → Q_1
  48. Intersect(d_1, f_2) → R_1
  49. Intersect(g_1, d_1) → S_1
  50. Intersect(g_1, f_2) → T_1
  51. Intersect(i_1, f_2) → U_1
  52. Intersect(g_1, xAxis) → V_1
  53. Intersect(g_1, k_1) → W_1
  54. Intersect(i_1, k_1) → Z_1
  55. Intersect(i_1, m_1) → A_2
  56. Intersect(k_1, m_1) → B_2
  57. Intersect(k_1, p_1) → C_2
  58. Intersect(p_1, m_1) → D_2
  59. Intersect(m_1, r_1) → E_2
  60. Intersect(p_1, r_1) → F_2
  61. Intersect(p_1, t_1) → G_2
  62. Intersect(r_1, t_1) → H_2
  63. Intersect(r_1, b_1) → I_2
  64. Intersect(t_1, b_1) → J_2
  65. Intersect(t_1, d_1) → K_2
  66. Intersect(b_1, d_1) → L_2
  67. Intersect(s_1, e_1) → M_2
  68. Intersect(a_1, e_1) → N_2
  69. Intersect(a_1, g_2) → O_2
  70. Intersect(c_1, g_2) → P_2
  71. Intersect(h_1, c_1) → Q_2
  72. Intersect(h_1, e_1) → R_2
  73. Intersect(j_1, e_1) → S_2
  74. Intersect(j_1, g_2) → T_2
  75. Intersect(l_1, g_2) → U_2
  76. Intersect(h_1, l_1) → V_2
  77. Intersect(h_1, n_1) → W_2
  78. Intersect(j_1, n_1) → Z_2
  79. Intersect(j_1, q_1) → A_3
  80. Intersect(l_1, q_1) → B_3
  81. Intersect(l_1, s_1) → C_3
  82. Intersect(n_1, s_1) → D_3
  83. Intersect(n_1, a_1) → E_3
  84. Intersect(q_1, a_1) → F_3
  85. Intersect(q_1, c_1) → G_3
  86. Intersect(s_1, c_1) → H_3
  87. PolyLine(Q_1, R_1, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, S_1, Q_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2) → h_2
  88. PolyLine(O_2, P_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, M_2, N_2, Q_2, O_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2) → i_2
  89. PolyLine(Q_1, U, C_2, B_1, E_2, C_1, G_2, D_1, I_2, E_1, K_2, F_1, S_1, Q_1, V, U_1, W, W_1, Z, A_2, A_1) → j_2
  90. PolyLine(O_2, G_1, A_3, L_1, C_3, M_1, E_3, N_1, G_3, O_1, M_2, P_1, Q_2, O_2, H_1, S_2, I_1, U_2, J_1, W_2, K_1) → k_2

AI Drawing Prompt Reference

Draw two decagons rotated by 36 degrees, find the midpoints of each side, connect adjacent midpoints to form a new polygon, and draw auxiliary lines at intersection points to showcase symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.