MathPlotAI Logo MathPlotAI

Imam's Drum Pattern

Imam's Drum Pattern
Loading the math board and drawing, please wait…
2019-12-31 22:23
PolygonTransformationGeometric Construction
This example demonstrates the construction of Islamic geometric patterns. Key mathematical concepts include geometric construction, polygons, and transformations. It uses commands such as Polygon, Centroid, Midpoint, Segment, Intersect, Sequence, Translate, Point, PolyLine, and Mirror in GeoGebra. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Polygon(G, H, I, E, F) → veelhoek1, g, h, i, e, f
  2. Centroid(veelhoek1) → K_1
  3. Polygon(G, J, K, L, M) → veelhoek2, g_1, j, k, l, m
  4. Centroid(veelhoek2) → L_1
  5. Polygon(L_1, K_1, 10) → veelhoek3, n, d, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, p, q, r, s, t, a, b, c
  6. Polygon(K_1, L_1, 10) → veelhoek4, f_1, q_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, h_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1
  7. Polygon(V_1, U_1, 10) → veelhoek5, r_1, g_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, s_1, t_1, a_1, b_1, c_1, d_1, e_1, f_2
  8. Polygon(F_2, S_1, 10) → veelhoek6, h_2, r_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2
  9. Polygon(U_1, L_1, T_1, S_1, F_2, E_2) → veelhoek7, u_1, s_2, t_2, a_2, b_2, e_2
  10. Polygon(P, Q, L, N, O) → veelhoek8, p_3, q_3, l_3, n_3, o
  11. Polygon(F_1, E_1, D_1, C_1, S) → veelhoek9, c_2, d_2, f_3, g_3, s_3
  12. Polygon(Z, U, C_1, B_1, A_1) → veelhoek10, z_1, u, h_3, i_3, j_3
  13. Polygon(E_1, J_1, I_1, H_1, G_1) → veelhoek11, k_3, m_3, r_3, t_3, a_3
  14. Polygon(V, N, W, K, R, S, T, U) → veelhoek12, v, n_4, w, k_4, r_4, s_4, t_4, u_2
  15. Midpoint(H_2, G_2) → U_2
  16. Segment(N, U_2) → b_3
  17. Midpoint(L_2, V_1) → V_2
  18. Segment(U, V_2) → c_3
  19. Midpoint(K_2, L_2) → W_2
  20. Segment(W_2, N) → d_3
  21. Segment(P, A_1) → e_3
  22. Intersect(c_3, e_3) → Z_2
  23. Centroid(veelhoek5) → A_3
  24. Polygon(N, V, Z_2, O) → vierhoek1, n_5, v_1, z_2, o_1
  25. Sequence(Polygon[Rotate[N, (nn * 36°), A_3], Rotate[V, (nn * 36°), A_3], Rotate[Z_2, (nn * 36°), A_3], Rotate[O, (nn * 36°), A_3]], nn, 1, 10) → l1
  26. Centroid(veelhoek6) → B_3
  27. Translate(l1, Vector[A_3, B_3]) → l1'
  28. Centroid(veelhoek4) → C_3
  29. Translate(l1, Vector[A_3, C_3]) → l1'_1
  30. Centroid(veelhoek3) → D_3
  31. Translate(l1, Vector[A_3, D_3]) → l1'_2
  32. Point(l1'_1) → E_3
  33. Point(l1'_2) → F_3
  34. Point(l1) → G_3
  35. PolyLine(E_3, F_3, W, G_3, E_3) → f_4
  36. Mirror(E_3, yAxis) → H_3
  37. Mirror(E_3, yAxis) → K_3
  38. Point(l1') → I_3
  39. Point(l1'_2) → J_3
  40. PolyLine(I_3, U, T, J_3, I_3) → g_4
  41. Translate(U_1, Vector[A_3, B_3]) → L_3
  42. Translate(L_1, Vector[A_3, B_3]) → M_3
  43. Translate(T_1, Vector[A_3, B_3]) → N_3
  44. Translate(S_1, Vector[A_3, B_3]) → O_3
  45. Translate(F_2, Vector[A_3, B_3]) → P_3
  46. Translate(E_2, Vector[A_3, B_3]) → Q_3
  47. Polygon(L_3, M_3, N_3, O_3, P_3, Q_3) → veelhoek7', h_4, i_4, j_4, o_3, l_4, m_4
  48. Translate(U_1, Vector[A_3, C_3]) → R_3
  49. Translate(L_1, Vector[A_3, C_3]) → S_3
  50. Translate(T_1, Vector[A_3, C_3]) → T_3
  51. Translate(S_1, Vector[A_3, C_3]) → U_3
  52. Translate(F_2, Vector[A_3, C_3]) → V_3
  53. Translate(E_2, Vector[A_3, C_3]) → W_3
  54. Polygon(R_3, S_3, T_3, U_3, V_3, W_3) → veelhoek7'_1, p_4, q_4, a_4, u_3, v_3, w_3
  55. Translate(E_3, Vector[A_3, B_3]) → Z_3
  56. Translate(F_3, Vector[A_3, B_3]) → A_4
  57. Translate(W, Vector[A_3, B_3]) → W'
  58. Translate(G_3, Vector[A_3, B_3]) → B_4
  59. Translate(E_3, Vector[A_3, B_3]) → C_4
  60. PolyLine(Z_3, A_4, W', B_4, C_4) → b_4
  61. Translate(I_3, Vector[A_3, B_3]) → D_4
  62. Translate(U, Vector[A_3, B_3]) → U'
  63. Translate(T, Vector[A_3, B_3]) → T'
  64. Translate(J_3, Vector[A_3, B_3]) → E_4
  65. Translate(I_3, Vector[A_3, B_3]) → F_4
  66. Translate(E_3, Vector[A_3, C_3]) → G_4
  67. Translate(F_3, Vector[A_3, C_3]) → H_4
  68. Translate(W, Vector[A_3, C_3]) → W'_1
  69. Translate(G_3, Vector[A_3, C_3]) → I_4
  70. Translate(E_3, Vector[A_3, C_3]) → J_4
  71. Translate(I_3, Vector[A_3, C_3]) → K_4
  72. Translate(U, Vector[A_3, C_3]) → U'_1
  73. Translate(T, Vector[A_3, C_3]) → T'_1
  74. Translate(J_3, Vector[A_3, C_3]) → L_4
  75. Translate(I_3, Vector[A_3, C_3]) → M_4
  76. PolyLine(K_4, U'_1, T'_1, L_4, M_4) → e_4

AI Drawing Prompt Reference

Draw an Islamic drum pattern. Start with two intersecting pentagons, find their centroids, and construct two regular decagons centered at these points. Use one decagon's side to build another decagon, creating a star-like rotational symmetry. Add surrounding pentagons and decagons for outer decoration. Connect midpoints of certain sides to form segments, find their intersection, and construct a quadrilateral. Rotate this quadrilateral around its centroid ten times to form a circular array. Translate this array to the centroids of the other decagons, yielding four symmetric groups. Finally, connect points on the arrays with polylines and mirror across the vertical axis to complete the symmetric geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.