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Sierpinski Triangle by Sangeeta Gulati

Sierpinski Triangle by Sangeeta Gulati
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2015-11-20 21:58
TriangleGeometric Construction
This example demonstrates the construction of the Sierpinski Triangle, a fractal geometry figure. The process involves creating an initial triangle and recursively generating smaller triangles using the Polygon, Midpoint, and Sierpinski commands. Suitable for high school mathematics education and learning fractal geometry concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(a) → D
  3. Midpoint(b) → E
  4. Midpoint(c) → F
  5. Polygon(F, E, D) → poly2, d, f, e
  6. Sierpinski(B, D, F) → G, H, I, g, h, i, poly3
  7. Sierpinski(D, C, E) → J, K, L, j, k, l, poly4
  8. Sierpinski(F, E, A) → M, N, O, m, n, p, poly5
  9. Sierpinski(B, I, H) → P, Q, R, q, r, s, poly6
  10. Sierpinski(I, D, G) → S, T, U, t, a_1, b_1, poly7
  11. Sierpinski(H, G, F) → V, W, Z, c_1, d_1, e_1, poly8
  12. Sierpinski(F, O, N) → A_1, B_1, C_1, f_1, g_1, h_1, poly9
  13. Sierpinski(N, M, A) → D_1, E_1, F_1, i_1, j_1, k_1, poly10
  14. Sierpinski(O, E, M) → G_1, H_1, I_1, l_1, m_1, n_1, poly11
  15. Sierpinski(K, J, E) → J_1, K_1, L_1, p_1, q_1, r_1, poly12
  16. Sierpinski(D, L, K) → M_1, N_1, O_1, s_1, t_1, a_2, poly13
  17. Sierpinski(L, C, J) → P_1, Q_1, R_1, b_2, c_2, d_2, poly14
  18. Sierpinski(E_1, D_1, A) → S_1, T_1, U_1, e_2, f_2, g_2, poly15
  19. Sierpinski(N, F_1, E_1) → V_1, W_1, Z_1, h_2, i_2, j_2, poly16
  20. Sierpinski(F_1, M, D_1) → A_2, B_2, C_2, k_2, l_2, m_2, poly17
  21. Sierpinski(B_1, A_1, N) → D_2, E_2, F_2, n_2, p_2, q_2, poly18
  22. Sierpinski(H_1, G_1, M) → G_2, H_2, I_2, r_2, s_2, t_2, poly19
  23. Sierpinski(F, C_1, B_1) → J_2, K_2, L_2, a_3, b_3, c_3, poly20
  24. Sierpinski(C_1, O, A_1) → M_2, N_2, O_2, d_3, e_3, f_3, poly21
  25. Sierpinski(O, I_1, H_1) → P_2, Q_2, R_2, g_3, h_3, i_3, poly22
  26. Sierpinski(I_1, E, G_1) → S_2, T_2, U_2, j_3, k_3, l_3, poly23
  27. Sierpinski(W, V, F) → V_2, W_2, Z_2, m_3, n_3, p_3, poly24
  28. Sierpinski(H, Z, W) → A_3, B_3, C_3, q_3, r_3, s_3, poly25
  29. Sierpinski(Z, G, V) → D_3, E_3, F_3, t_3, a_4, b_4, poly26
  30. Sierpinski(Q, P, H) → G_3, H_3, I_3, c_4, d_4, e_4, poly27
  31. Sierpinski(G, T, S) → J_3, K_3, L_3, f_4, g_4, h_4, poly28
  32. Sierpinski(Q, B, R) → M_3, N_3, O_3, i_4, j_4, k_4, poly29
  33. Sierpinski(P, R, I) → P_3, Q_3, R_3, l_4, m_4, n_4, poly30
  34. Sierpinski(T, I, U) → S_3, T_3, U_3, p_4, q_4, r_4, poly31
  35. Sierpinski(S, U, D) → V_3, W_3, Z_3, s_4, t_4, a_5, poly32
  36. Sierpinski(E, K_1, J_1) → A_4, B_4, C_4, b_5, c_5, d_5, poly33
  37. Sierpinski(K_1, K, L_1) → D_4, E_4, F_4, e_5, f_5, g_5, poly34
  38. Sierpinski(J_1, L_1, J) → G_4, H_4, I_4, h_5, i_5, j_5, poly35
  39. Sierpinski(J, Q_1, P_1) → J_4, K_4, L_4, k_5, l_5, m_5, poly36
  40. Sierpinski(P_1, R_1, C) → M_4, N_4, O_4, n_5, p_5, q_5, poly37
  41. Sierpinski(Q_1, L, R_1) → P_4, Q_4, R_4, r_5, s_5, t_5, poly38
  42. Sierpinski(K, N_1, M_1) → S_4, T_4, U_4, a_6, b_6, c_6, poly39
  43. Sierpinski(N_1, D, O_1) → V_4, W_4, Z_4, d_6, e_6, f_6, poly40
  44. Sierpinski(M_1, O_1, L) → A_5, B_5, C_5, g_6, h_6, i_6, poly41