Parametric Star of David Construction

Parametric Star of David Construction
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2019-12-05 13:07
This example demonstrates the geometric construction of the Star of David using parametric equations and transformations. It involves core concepts like equilateral triangles, dilation, and parametric curves. Key GeoGebra commands used include Polygon, Intersect, and Point. Suitable for high school and advanced mathematics learners exploring parametric curves and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D) → t1, d, a, c
  2. Polygon(E, F, G) → t2, g, e, f
  3. Intersect(d, f) → H
  4. Intersect(c, g) → I
  5. Point(e) → J
  6. Polygon(H, I, J) → t3, j, h, i
  7. Intersect(c, f) → K
  8. Intersect(d, e) → L
  9. Intersect(a, g) → M
  10. Polygon(K, L, M) → t4, m, k, l
  11. Polygon(E, A, G, C, F, D) → poly1, e_1, a_1, g_1, c_1, f_1, d_1
  12. Polygon(A, N, G, S, E, O, D, P, F, Q, C, R) → poly2, a_2, r, g_2, s, n, e_2, o, d_2, p, f_2, q, c_2
  13. Point(m) → T
  14. Intersect(h, l) → U
  15. Intersect(i, k) → V
  16. Polygon(T, U, V) → t5, v, t, u
  17. Intersect(j, l) → W
  18. Intersect(i, m) → Z
  19. Intersect(h, k) → A_1
  20. Polygon(W, Z, A_1) → t6, b, w, z_1
  21. Intersect(v, b) → B_1
  22. Intersect(t, z_1) → C_1
  23. Intersect(u, w) → D_1
  24. Polygon(B_1, C_1, D_1) → t7, h_1, b_1, i_1
  25. Intersect(u, b) → E_1
  26. Intersect(v, z_1) → F_1
  27. Intersect(t, w) → G_1
  28. Polygon(E_1, F_1, G_1) → t8, j_1, k_1, l_1
  29. Intersect(i_1, j_1) → H_1
  30. Intersect(h_1, k_1) → I_1
  31. Intersect(b_1, l_1) → J_1
  32. Polygon(H_1, I_1, J_1) → t9, m_1, n_1, p_1
  33. Intersect(h_1, j_1) → K_1
  34. Intersect(i_1, l_1) → L_1
  35. Intersect(b_1, k_1) → M_1
  36. Polygon(K_1, L_1, M_1) → t10, q_1, r_1, s_1
  37. Intersect(m_1, q_1) → N_1
  38. Intersect(n_1, s_1) → O_1
  39. Intersect(p_1, r_1) → P_1
  40. Polygon(N_1, O_1, P_1) → t11, t_1, h_2, o_1
  41. Intersect(p_1, q_1) → Q_1
  42. Intersect(m_1, s_1) → R_1
  43. Intersect(n_1, r_1) → S_1
  44. Polygon(Q_1, R_1, S_1) → t12, i_2, j_2, k_2
  45. Intersect(o_1, i_2) → T_1
  46. Intersect(t_1, j_2) → U_1
  47. Intersect(h_2, k_2) → V_1
  48. Polygon(T_1, U_1, V_1) → t13, v_1, l_2, u_1
  49. Intersect(t_1, i_2) → W_1
  50. Intersect(h_2, j_2) → Z_1
  51. Intersect(o_1, k_2) → A_2
  52. Polygon(W_1, Z_1, A_2) → t14, m_2, w_1, n_2
  53. Intersect(v_1, n_2) → B_2
  54. Intersect(l_2, m_2) → C_2
  55. Intersect(u_1, w_1) → D_2
  56. Polygon(B_2, C_2, D_2) → t15, p_2, b_2, q_2
  57. Intersect(l_2, w_1) → E_2
  58. Intersect(v_1, m_2) → F_2
  59. Intersect(u_1, n_2) → G_2
  60. Polygon(E_2, F_2, G_2) → t16, r_2, s_2, t_2
  61. Intersect(p_2, s_2) → H_2
  62. Intersect(b_2, r_2) → I_2
  63. Intersect(q_2, t_2) → J_2
  64. Polygon(H_2, I_2, J_2) → t17, f_3, g_3, h_3
  65. Intersect(q_2, s_2) → K_2
  66. Intersect(p_2, r_2) → L_2
  67. Intersect(b_2, t_2) → M_2
  68. Polygon(K_2, L_2, M_2) → t18, i_3, j_3, k_3
  69. Intersect(h_3, i_3) → N_2
  70. Intersect(f_3, j_3) → O_2
  71. Intersect(g_3, k_3) → P_2
  72. Polygon(N_2, O_2, P_2) → t19, l_3, m_3, o_2
  73. Intersect(g_3, j_3) → Q_2
  74. Intersect(f_3, i_3) → R_2
  75. Intersect(h_3, k_3) → S_2
  76. Polygon(Q_2, R_2, S_2) → t20, n_3, p_3, q_3
  77. Intersect(l_3, p_3) → T_2
  78. Intersect(m_3, n_3) → U_2
  79. Intersect(o_2, q_3) → V_2
  80. Polygon(T_2, U_2, V_2) → t21, v_2, r_3, u_2
  81. Intersect(o_2, p_3) → W_2
  82. Intersect(l_3, n_3) → Z_2
  83. Intersect(m_3, q_3) → A_3
  84. Polygon(W_2, Z_2, A_3) → t22, a_3, w_2, z_2
  85. Intersect(u_2, a_3) → B_3
  86. Intersect(v_2, w_2) → C_3
  87. Intersect(r_3, z_2) → D_3
  88. Polygon(B_3, C_3, D_3) → t23, d_3, b_3, c_3
  89. Intersect(u_2, z_2) → E_3
  90. Intersect(v_2, a_3) → F_3
  91. Intersect(r_3, w_2) → G_3
  92. Polygon(E_3, F_3, G_3) → t24, s_3, e_3, t_3

AI Drawing Prompt Reference

Draw a geometric construction of the Star of David, featuring two interwoven hexagons created through equilateral triangles, dilation, and parametric curves. Start by constructing two hexagons, then find their intersection points to form new triangles, progressively building the star pattern. The final image should highlight symmetry and geometric beauty, showcasing the application of parametric equations and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.