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Spiral Sofia S

Spiral Sofia S
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2019-05-26 01:11
Coordinate GeometryGeometric Construction
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates the construction and properties of the Spiral Sofia S, involving hyperbolas, logarithmic functions, conic sections, and similar triangles. Key GeoGebra commands and objects used include Polygon, OrthogonalLine, and Intersect. Suitable for high school and above learners to understand complex geometric constructions and applications of related mathematical concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. OrthogonalLine(C, f) → i
  3. Intersect(i, f) → D
  4. Polygon(C, D, 3) → poly2, j, k, l, E
  5. OrthogonalLine(C, k) → m
  6. Intersect(m, k) → F
  7. Polygon(C, F, 3) → poly3, n, p, q, G
  8. OrthogonalLine(C, p) → r
  9. Intersect(r, p) → H
  10. Polygon(C, H, 3) → poly4, s, t, a, I
  11. OrthogonalLine(C, t) → b
  12. Intersect(b, t) → J
  13. Polygon(C, J, 3) → poly5, c, d, e, K
  14. OrthogonalLine(C, d) → f_1
  15. Intersect(f_1, d) → L
  16. Polygon(C, L, 3) → poly6, g_1, h_1, i_1, M
  17. OrthogonalLine(C, h_1) → j_1
  18. Intersect(j_1, h_1) → N
  19. Polygon(C, N, 3) → poly7, k_1, l_1, m_1, O
  20. Intersect(l_1, i) → P
  21. Polygon(C, P, 3) → poly8, n_1, p_1, q_1, Q
  22. Intersect(m, m_1) → R
  23. Intersect(m, m_1) → S
  24. Intersect(m, m_1) → T
  25. Intersect(p_1, m) → U
  26. Polygon(C, U, 3) → poly9, r_1, s_1, t_1, V
  27. Intersect(s_1, r) → W
  28. Polygon(C, W, 3) → poly10, a_1, b_1, c_1, Z
  29. Intersect(b_1, b) → A_1
  30. Polygon(C, A_1, 3) → poly11, d_1, e_1, f_2, B_1
  31. Intersect(e_1, f_1) → C_1
  32. Polygon(C, C_1, 3) → poly12, g_2, h_2, i_2, D_1
  33. Intersect(j_1, h) → E_1
  34. Intersect(h_2, j_1) → F_1
  35. Polygon(C, F_1, 3) → poly13, j_2, k_2, l_2, G_1
  36. Intersect(k_2, i) → H_1
  37. Polygon(C, H_1, 3) → poly14, m_2, n_2, p_2, I_1
  38. Intersect(n_2, m) → J_1
  39. Polygon(C, J_1, 3) → poly15, q_2, r_2, s_2, K_1
  40. Intersect(r_2, r) → L_1
  41. Polygon(C, L_1, 3) → poly16, t_2, a_2, b_2, M_1
  42. Intersect(b, q) → N_1
  43. Intersect(a_2, b) → O_1
  44. Polygon(C, O_1, 3) → poly17, c_2, d_2, e_2, P_1
  45. Intersect(j_1, e) → Q_1
  46. Intersect(j_1, e) → R_1
  47. Intersect(f_1, a) → S_1
  48. Intersect(d_2, f_1) → T_1
  49. Polygon(C, T_1, 3) → poly18, f_3, g_3, h_3, U_1
  50. Intersect(i, i_1) → V_1
  51. Intersect(g_3, j_1) → W_1
  52. Polygon(C, W_1, 3) → poly19, i_3, j_3, k_3, Z_1
  53. Intersect(j_3, i) → A_2
  54. Polygon(C, A_2, 3) → poly20, l_3, m_3, n_3, B_2
  55. Intersect(m, m_1) → C_2
  56. Intersect(m_3, m) → D_2
  57. Polygon(C, D_2, 3) → poly21, p_3, q_3, r_3, E_2
  58. Intersect(q_3, r) → F_2
  59. Polygon(C, F_2, 3) → poly22, s_3, t_3, a_3, G_2
  60. Intersect(b, t_1) → H_2
  61. Intersect(t_3, b) → I_2
  62. Polygon(C, I_2, 3) → poly23, b_3, c_3, d_3, J_2
  63. Intersect(f_1, c_1) → K_2
  64. Intersect(c_3, f_1) → L_2
  65. Polygon(C, L_2, 3) → poly24, e_3, f_4, g_4, M_2
  66. Intersect(j_1, h) → N_2
  67. Intersect(j_1, h) → O_2
  68. Intersect(f_4, j_1) → P_2
  69. Polygon(C, P_2, 3) → poly25, h_4, i_4, j_4, Q_2
  70. Intersect(i, j) → R_2
  71. Intersect(i_4, i) → S_2
  72. Polygon(C, S_2, 3) → poly26, k_4, l_4, m_4, T_2
  73. Intersect(m, g) → U_2
  74. Intersect(l_4, m) → V_2
  75. Polygon(C, V_2, 3) → poly27, n_4, p_4, q_4, W_2
  76. Intersect(r, l) → Z_2
  77. Intersect(p_4, r) → A_3
  78. Polygon(C, A_3, 3) → poly28, r_4, s_4, t_4, B_3
  79. Intersect(s_4, b) → C_3
  80. Polygon(C, C_3, 3) → poly29, a_4, b_4, c_4, D_3
  81. Intersect(b_4, f_1) → E_3
  82. Polygon(C, E_3, 3) → poly30, d_4, e_4, f_5, F_3
  83. Intersect(j_1, e) → G_3
  84. Intersect(e_4, j_1) → H_3
  85. Polygon(C, H_3, 3) → poly31, g_5, h_5, i_5, I_3