Cubus simus and Tribonacci Numbers

Cubus simus and Tribonacci Numbers
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2017-12-10 19:39
This example demonstrates the relationship between Cubus simus and Tribonacci numbers. Key mathematical concepts include sequences and geometric construction. Using the Polygon command, it illustrates the properties of sequences and the transformation of geometric shapes. Suitable for high school and above math enthusiasts and educators.

GeoGebra Commands & Parameters

  1. Polygon(G_1, E_1, E, G) → v1, g_3, e_2, e_3, g_4
  2. Polygon(K, S, W, O) → v2, k_3, s_3, w, o
  3. Polygon(C, A, A_1, C_1) → v3, c_2, a_2, a_3, c_3
  4. Polygon(I, Q, U, M) → v4, i_3, q_3, u, m_3
  5. Polygon(T_1, L_1, K_1, S_1) → v5, t_2, l_3, k_4, s_4
  6. Polygon(R_1, J_1, I_1, Q_1) → v6, r_3, j_3, i_4, q_4
  7. Polygon(R, J, N, V) → v7, r_4, j_4, n_3, v
  8. Polygon(L, P, Z, T) → v8, l_4, p_3, z_1, t_3
  9. Polygon(M_1, N_1, V_1, U_1) → v9, m_4, n_4, v_1, u_1
  10. Polygon(O_1, P_1, Z_1, W_1) → v10, o_1, p_4, z_2, w_1
  11. Polygon(F, H, H_1, F_1) → v11, f_3, h_3, h_4, f_4
  12. Polygon(D, D_1, B_1, B) → v12, d_2, d_3, b_2, b_3
  13. Polygon(I_1, Q, I, A, A_1, Q_1) → Vieleck1, i_1, q, i, a, a_1, q_1
  14. Polygon(S_1, C_1, C, K, S, K_1) → Vieleck2, s_1, c_1, c, k, s_2, k_1
  15. Polygon(O_1, W, O, G, G_1, W_1) → Vieleck3, o_2, w_2, o_3, g, g_1, w_3
  16. Polygon(U_1, E_1, E, M, U, M_1) → Vieleck4, u_2, e_1, e, m, u_3, m_1
  17. Polygon(N, F, F_1, V_1, N_1, V) → Vieleck5, n, f, f_1, v_2, n_1, v_3
  18. Polygon(B, J, R, J_1, R_1, B_1) → Vieleck6, b, j, r, j_1, r_1, b_1
  19. Polygon(L, D, D_1, T_1, L_1, T) → Vieleck7, l, d, d_1, t_1, l_1, t_4
  20. Polygon(H, P, Z, P_1, Z_1, H_1) → Vieleck8, h, p, z_3, p_1, z_4, h_1
  21. Polygon(A, I, M, E, G, O, K, C) → Vieleck9, a_4, i_2, m_2, e_4, g_2, o_4, k_2, c_4
  22. Polygon(V_1, F_1, H_1, Z_1, W_1, G_1, E_1, U_1) → Vieleck10, v_4, f_2, h_2, z_5, w_4, g_5, e_5, u_4
  23. Polygon(R, V, N_1, M_1, U, Q, I_1, J_1) → Vieleck11, r_2, v_5, n_2, m_5, u_5, q_2, i_5, j_2
  24. Polygon(D_1, B_1, R_1, Q_1, A_1, C_1, S_1, T_1) → Vieleck12, d_4, b_4, r_5, q_5, a_5, c_5, s_5, t_5
  25. Polygon(Z, T, L_1, K_1, S, W, O_1, P_1) → Vieleck13, z_6, t_6, l_2, k_5, s_6, w_5, o_5, p_2
  26. Polygon(F, N, J, B, D, L, P, H) → Vieleck14, f_5, n_5, j_5, b_5, d_5, l_5, p_5, h_5
  27. Polygon(E_1, W_1, G) → d1, g_6, e_6, w_6
  28. Polygon(W_1, W, G) → d2, g_7, w_7, w_8
  29. Polygon(W_1, P_1, W) → d3, w_9, w_{10}, p_6
  30. Polygon(G, W, K) → d4, k_6, g_8, w_{11}
  31. Polygon(M, E_1, G) → d5, g_9, m_6, e_7
  32. Polygon(W_1, H_1, V_1, E_1) → v13, w_{12}, h_6, v_6, e_8
  33. Polygon(H_1, P_1, W_1) → d6, w_{13}, h_7, p_7
  34. Polygon(M_1, V_1, E_1) → d7, e_9, m_7, v_7
  35. Polygon(M_1, E_1, M) → d8, m_8, m_9, e_{10}
  36. Polygon(M, E_1, G) → d9, g_{10}, m_{10}, e_{11}
  37. Polygon(M_1, V, V_1) → d10, v_8, m_{11}, v_9
  38. Polygon(M, Q, M_1) → d11, m_{12}, m_{13}, q_6
  39. Polygon(Q, M_1, V, J_1) → v14, q_7, m_{14}, v_{10}, j_6
  40. Polygon(Q, M, A) → d12, a_7, q_8, m_{15}
  41. Polygon(J_1, Q, Q_1) → d13, q_9, j_7, q_{10}
  42. Polygon(Q_1, Q, A) → d14, a_8, q_{11}, q_{12}
  43. Polygon(A, M, G, K) → v15, a_9, m_{16}, g_{11}, k_7
  44. Polygon(C_1, Q_1, A) → d15, a_{10}, c_6, q_{13}
  45. Polygon(B_1, J_1, Q_1) → d16, q_{14}, b_7, j_8
  46. Polygon(B_1, Q_1, C_1, T_1) → v16, b_8, q_{15}, c_7, t_7
  47. Polygon(C_1, A, K) → d17, k_8, c_8, a_{11}
  48. Polygon(C_1, K_1, T_1) → d18, t_8, c_9, k_9
  49. Polygon(C_1, K, K_1) → d19, k_{10}, c_{10}, k_{11}
  50. Polygon(W, K_1, K) → d20, k_{12}, w_{14}, k_{13}
  51. Polygon(K_1, T, T_1) → d21, t_9, k_{14}, t_{10}
  52. Polygon(P_1, T, K_1, W) → v17, p_8, t_{11}, k_{15}, w_{15}
  53. Polygon(P_1, W, W_1) → d22, w_{16}, p_9, w_{17}
  54. Polygon(V, F, V_1) → d23, v_{11}, v_{12}, f_6
  55. Polygon(F, H_1, V_1) → d24, v_{13}, f_7, h_8
  56. Polygon(F, P, H_1) → d25, h_9, f_8, p_{10}
  57. Polygon(P, P_1, H_1) → d26, h_{10}, p_{11}, p_{12}
  58. Polygon(P, T, P_1) → d27, p_{13}, p_{14}, t_{12}
  59. Polygon(P, D, T) → d28, t_{13}, p_{15}, d_6
  60. Polygon(D, T_1, T) → d29, t_{14}, d_7, t_{15}
  61. Polygon(D, B_1, T_1) → d30, t_{16}, d_8, b_9
  62. Polygon(D, J, B_1) → d31, b_{10}, d_9, j_9
  63. Polygon(B_1, J, J_1) → d32, j_{10}, b_{11}, j_{11}
  64. Polygon(J_1, J, V) → d33, v_{14}, j_{12}, j_{13}
  65. Polygon(J, F, V) → d34, v_{15}, j_{14}, f_9
  66. Polygon(D, P, F, J) → v18, d_{10}, p_{16}, f_{10}, j_{15}

AI Drawing Prompt Reference

Draw a series of polygons to illustrate their geometric relationships and transformations. Start by creating polygons connected by four line segments, then sequentially draw more polygons using different points to show the evolution of the sequence. The polygons are interconnected through shared vertices and edges, forming a complex geometric structure that demonstrates the transformation between sequences and geometric constructions.
The prompt above was compiled from the original drawing commands and is for reference only.