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Spiral Art: Sphere and Geometric Transformations

Spiral Art: Sphere and Geometric Transformations
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2019-05-26 00:52
FunctionCoordinate GeometrySolid GeometryGeometric Construction
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates the creation of spiral art involving spheres, centroids, parabolas, and polynomial functions. Key math concepts include spherical geometry, centroid calculation, parabola equations, and polynomial functions. Construction highlights the use of GeoGebra commands like Polygon, Midpoint, Intersect, Mirror, and Segment. Ideal for high school and above students exploring spatial geometry and dynamic function graph 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(D', xAxis) → D''
  63. Mirror(D'', yAxis) → D'''
  64. Polygon(S_1, A', 3) → poly18, t_2, a_2, b_2, V_1
  65. Intersect(b_2, poly1') → W_1
  66. Polygon(W_1, A', 3) → poly19, c_2, d_2, e_2, Z_1
  67. Intersect(a_2, e_2) → A_2
  68. Polygon(A_2, A', 3) → poly20, f_3, g_3, h_3, B_2
  69. Intersect(d_2, h_3) → C_2
  70. Polygon(C_2, A', 3) → poly21, i_3, j_3, k_3, D_2
  71. Intersect(xAxis, yAxis) → T_1
  72. Mirror(poly1', T_1) → poly1''
  73. Mirror(poly3', T_1) → poly3''
  74. Mirror(poly4', T_1) → poly4''
  75. Mirror(poly5', T_1) → poly5''
  76. Mirror(poly6', T_1) → poly6''
  77. Mirror(poly7', T_1) → poly7''
  78. Mirror(poly8', T_1) → poly8''
  79. Mirror(poly9', T_1) → poly9''
  80. Mirror(poly10', T_1) → poly10''
  81. Mirror(poly11', T_1) → poly11''
  82. Mirror(poly12', T_1) → poly12''
  83. Mirror(poly13', T_1) → poly13''
  84. Mirror(poly18, T_1) → poly18'
  85. Mirror(poly19, T_1) → poly19'
  86. Mirror(poly20, T_1) → poly20'
  87. Mirror(poly21, T_1) → poly21'
  88. Mirror(N', T_1) → N''
  89. Mirror(poly1', yAxis) → poly1''_1
  90. Mirror(poly3', yAxis) → poly3''_1
  91. Mirror(poly4', yAxis) → poly4''_1
  92. Mirror(poly5', yAxis) → poly5''_1
  93. Mirror(poly6', yAxis) → poly6''_1
  94. Mirror(poly7', yAxis) → poly7''_1
  95. Mirror(poly8', yAxis) → poly8''_1
  96. Mirror(poly9', yAxis) → poly9''_1
  97. Mirror(poly10', yAxis) → poly10''_1
  98. Mirror(poly11', yAxis) → poly11''_1
  99. Mirror(poly12', yAxis) → poly12''_1
  100. Mirror(poly13', yAxis) → poly13''_1
  101. Mirror(poly18, yAxis) → poly18'_1
  102. Mirror(poly19, yAxis) → poly19'_1
  103. Mirror(poly20, yAxis) → poly20'_1
  104. Mirror(poly21, yAxis) → poly21'_1
  105. Mirror(N', yAxis) → N''_1
  106. Mirror(T_1, yAxis) → U_1
  107. Mirror(poly1', xAxis) → poly1''_2
  108. Mirror(poly3', xAxis) → poly3''_2
  109. Mirror(poly4', xAxis) → poly4''_2
  110. Mirror(poly5', xAxis) → poly5''_2
  111. Mirror(poly6', xAxis) → poly6''_2
  112. Mirror(poly7', xAxis) → poly7''_2
  113. Mirror(poly8', xAxis) → poly8''_2
  114. Mirror(poly9', xAxis) → poly9''_2
  115. Mirror(poly10', xAxis) → poly10''_2
  116. Mirror(poly11', xAxis) → poly11''_2
  117. Mirror(poly12', xAxis) → poly12''_2
  118. Mirror(poly13', xAxis) → poly13''_2
  119. Mirror(poly18, xAxis) → poly18'_2
  120. Mirror(poly19, xAxis) → poly19'_2
  121. Mirror(poly20, xAxis) → poly20'_2
  122. Mirror(poly21, xAxis) → poly21'_2
  123. Mirror(N', xAxis) → N''_2

AI Drawing Prompt Reference

Create a spiral art piece with a series of triangles rotating around point A. Start by drawing a triangle, then draw new triangles at each vertex, forming a spiral effect. Finally, mirror all triangles across the y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.