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螺旋艺术：球体与几何变换

螺旋艺术：球体与几何变换
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2019-05-26 00:52
函数解析几何立体几何几何作图
所属专题 EQUILATERAL TRIANGLE SPIRAL
①本范例演示了通过球体、质心、抛物线等元素构建的螺旋艺术图形；②涉及核心数学概念包括球体几何、质心计算、抛物线方程、多项式函数等；③作图要点运用了Polygon（多边形）、Midpoint（中点）、Intersect（交点）、Mirror（镜像）、Segment（线段）等GeoGebra命令；④适合高中及以上数学爱好者学习空间几何与函数图像的动态变化。

GeoGebra 命令及参数

  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 绘图提示语参考

绘制一个螺旋艺术作品，包含一系列围绕点A旋转的多边形。首先绘制一个三角形，然后在每个顶点处依次绘制新的三角形，直到形成一个螺旋效果。最后，将所有多边形镜像到y轴上。
以上提示语为根据原始绘图命令整理而来，仅供参考。