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Spiral Art by Andrei N

Spiral Art by Andrei N
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2019-05-26 01:29
FunctionCoordinate GeometryTransformation
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates spiral art created by Andrei N. It involves core mathematical concepts such as parabolas, algebra, and geometric transformations. Using GeoGebra commands like Polygon, Midpoint, Intersect, Mirror, and Segment, complex geometric shapes can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Midpoint(g) → D
  3. Polygon(A, D, 3) → poly2, i, j, k, E
  4. Intersect(h, j) → F
  5. Polygon(A, F, 3) → poly3, l, m, n, G
  6. Intersect(k, m) → H
  7. Polygon(A, H, 3) → poly4, p, q, r, I
  8. Intersect(n, q) → J
  9. Polygon(A, J, 3) → poly5, s, t, a, K
  10. Intersect(r, t) → L
  11. Polygon(A, L, 3) → poly6, b, c, d, M
  12. Intersect(h, i) → N
  13. Intersect(a, c) → O
  14. Polygon(A, O, 3) → poly7, e, f_1, g_1, P
  15. Intersect(d, f_1) → Q
  16. Polygon(A, Q, 3) → poly8, h_1, i_1, j_1, R
  17. Intersect(g_1, i_1) → S
  18. Polygon(A, S, 3) → poly9, k_1, l_1, m_1, T
  19. Intersect(j_1, l_1) → U
  20. Polygon(A, U, 3) → poly10, n_1, p_1, q_1, V
  21. Intersect(m_1, p_1) → W
  22. Polygon(A, W, 3) → poly11, r_1, s_1, t_1, Z
  23. Intersect(q_1, s_1) → A_1
  24. Polygon(A, A_1, 3) → poly12, a_1, b_1, c_1, B_1
  25. Intersect(b_1, f) → C_1
  26. Polygon(A, C_1, 3) → poly13, d_1, e_1, f_2, D_1
  27. Intersect(i, c_1) → E_1
  28. Intersect(i, e_1) → F_1
  29. Polygon(A, D_1, 3) → poly14, g_2, h_2, i_2, G_1
  30. Intersect(k, p) → H_1
  31. Intersect(k, p) → I_1
  32. Intersect(h_2, k) → J_1
  33. Polygon(A, J_1, 3) → poly15, j_2, k_2, l_2, K_1
  34. Intersect(n, s) → L_1
  35. Intersect(k_2, n) → M_1
  36. Polygon(A, M_1, 3) → poly16, m_2, n_2, p_2, N_1
  37. Intersect(r, b) → O_1
  38. Intersect(r, b) → P_1
  39. Intersect(n_2, r) → Q_1
  40. Polygon(A, Q_1, 3) → poly17, q_2, r_2, s_2, R_1
  41. Mirror(poly1, yAxis) → poly1'
  42. Mirror(poly3, yAxis) → poly3'
  43. Mirror(poly4, yAxis) → poly4'
  44. Mirror(poly5, yAxis) → poly5'
  45. Mirror(poly6, yAxis) → poly6'
  46. Mirror(poly7, yAxis) → poly7'
  47. Mirror(poly8, yAxis) → poly8'
  48. Mirror(poly9, yAxis) → poly9'
  49. Mirror(poly10, yAxis) → poly10'
  50. Mirror(poly11, yAxis) → poly11'
  51. Mirror(poly12, yAxis) → poly12'
  52. Mirror(poly13, yAxis) → poly13'
  53. Mirror(poly14, yAxis) → poly14'
  54. Mirror(poly15, yAxis) → poly15'
  55. Mirror(poly16, yAxis) → poly16'
  56. Mirror(poly17, yAxis) → poly17'
  57. Mirror(A, yAxis) → A'
  58. Mirror(D, yAxis) → D'
  59. Segment(A', D') → i'
  60. Mirror(N, yAxis) → N'
  61. Mirror(F_1, yAxis) → S_1
  62. Mirror(poly1', xAxis) → poly1''
  63. Mirror(poly3', xAxis) → poly3''
  64. Mirror(poly4', xAxis) → poly4''
  65. Mirror(poly5', xAxis) → poly5''
  66. Mirror(poly6', xAxis) → poly6''
  67. Mirror(poly7', xAxis) → poly7''
  68. Mirror(poly8', xAxis) → poly8''
  69. Mirror(poly9', xAxis) → poly9''
  70. Mirror(poly10', xAxis) → poly10''
  71. Mirror(poly11', xAxis) → poly11''
  72. Mirror(poly12', xAxis) → poly12''
  73. Mirror(poly13', xAxis) → poly13''
  74. Mirror(poly14', xAxis) → poly14''
  75. Mirror(poly15', xAxis) → poly15''
  76. Mirror(poly16', xAxis) → poly16''
  77. Mirror(poly17', xAxis) → poly17''
  78. Mirror(A', xAxis) → A''
  79. Mirror(D', xAxis) → D''
  80. Segment(A'', D'') → i''
  81. Mirror(N', xAxis) → N''
  82. Mirror(S_1, xAxis) → T_1
  83. Mirror(poly1'', yAxis) → poly1'''
  84. Mirror(poly3'', yAxis) → poly3'''
  85. Mirror(poly4'', yAxis) → poly4'''
  86. Mirror(poly5'', yAxis) → poly5'''
  87. Mirror(poly6'', yAxis) → poly6'''
  88. Mirror(poly7'', yAxis) → poly7'''
  89. Mirror(poly8'', yAxis) → poly8'''
  90. Mirror(poly9'', yAxis) → poly9'''
  91. Mirror(poly10'', yAxis) → poly10'''
  92. Mirror(poly11'', yAxis) → poly11'''
  93. Mirror(poly12'', yAxis) → poly12'''
  94. Mirror(poly13'', yAxis) → poly13'''
  95. Mirror(poly14'', yAxis) → poly14'''
  96. Mirror(poly15'', yAxis) → poly15'''
  97. Mirror(poly16'', yAxis) → poly16'''
  98. Mirror(poly17'', yAxis) → poly17'''
  99. Mirror(A'', yAxis) → A'''
  100. Mirror(D'', yAxis) → D'''
  101. Segment(A''', D''') → i'''
  102. Mirror(N'', yAxis) → N'''
  103. Mirror(T_1, yAxis) → U_1

AI Drawing Prompt Reference

Create a spiral pattern composed of multiple triangles, each generated by intersecting with the previous triangle. Start by drawing a triangle, then sequentially create new triangles by intersecting with the previous one until a spiral shape is formed. Finally, mirror all triangles across the y-axis to create a symmetrical pattern.
The prompt above was compiled from the original drawing commands and is for reference only.