Francesca. Madonna 数学范例

Francesca. Madonna 数学范例
几何画板及绘图内容加载中,请稍等……
2023-03-20 19:46
所属专题 geometriadinamica.es
①本范例演示了利用 GeoGebra 构建复杂的几何图形与函数图像,特别是涉及正交线、点、线段、旋转、镜像等操作;②核心数学概念包括正交中心、积分、函数图像绘制、平面图形构造;③作图要点:运用了 OrthogonalLine, Point, Segment, If, Dilate, Circle, Intersect, Polygon, Line, Midpoint, Rotate, Mirror 等命令与对象;④适合高中及以上数学学习者,用于理解几何变换与函数图像的交互。

GeoGebra 命令及参数

  1. OrthogonalLine(B, xAxis) → a
  2. Point(a) → C
  3. Segment(B, C) → b
  4. Point(b) → L_2
  5. Point(b) → M_1
  6. If(pas > 1, 0, 100000) → t_2
  7. If(pas > 0, 0, 1000000000) → t_1
  8. OrthogonalLine(A, b) → e
  9. OrthogonalLine(A, e) → g
  10. OrthogonalLine(A, b) → d
  11. Point(d) → D
  12. OrthogonalLine(D, e) → i
  13. Dilate(D, 1.47, A) → E
  14. Circle(A, E) → f
  15. Intersect(f, g, 2) → F
  16. OrthogonalLine(F, g) → h
  17. Intersect(h, i) → G
  18. If(pas > 2, 0, 1000000) → t_3
  19. If(pas > 3, 0, 100000) → t_4
  20. If(pas > 4, 0, 100000) → t_5
  21. If(pas > 5, 0, 100000) → t_6
  22. Segment(P_1, P_7) → c
  23. Polygon(A, F, G, D) → P, a_1, f_1, g_1, d_1
  24. OrthogonalLine(B_1, d_1) → j
  25. Intersect(f_1, j) → I
  26. Segment(B_1, I) → k
  27. OrthogonalLine(B_2, k) → l
  28. Line(L_2, l) → r_2
  29. Midpoint(D, A) → L
  30. Intersect(d_1, k) → H
  31. Circle(H, A) → p
  32. Intersect(p, k) → J,
  33. Circle(J, H) → q
  34. Intersect(f_1, k) → K
  35. Intersect(f_1, k) → M
  36. Point(k) → N
  37. Point(q) → O
  38. Intersect(l, k) → Q
  39. Circle(Q, N) → r
  40. OrthogonalLine(B_3, k) → m
  41. Intersect(m, k) → R
  42. Rotate(O, 59.99999999999999°, R) → S
  43. Rotate(O, 29.999999999999996°, R) → T
  44. Rotate(O, 90°, R) → U
  45. Mirror(U, k) → V
  46. Mirror(A, a_1) → A'
  47. Mirror(F, a_1) → F'
  48. Segment(A', F') → n
  49. Mirror(S, k) → W
  50. Mirror(T, k) → Y
  51. Mirror(T, m) → Z
  52. Mirror(S, m) → C_1
  53. Mirror(O, m) → D_1
  54. Mirror(Z, k) → E_1
  55. Polygon(Y, T, U, Z, E_1, V) → Q_1, s, t, u, z, e_1, v
  56. Mirror(C_1, k) → F_1
  57. Polygon(O, S, C_1, D_1, F_1, W) → R_1, o, s_{1}, c_1, d_2, f_2, w
  58. Circle(Y, T) → h_1
  59. Circle(T, Y) → k_1
  60. Point(k_1) → G_1
  61. Polygon(T, G_1, Y) → S_1, y_1, t_7, g_2
  62. OrthogonalLine(B_4, k) → b_1
  63. Point(b_1) → H_1
  64. OrthogonalLine(B_5, k) → i_1
  65. Point(i_1) → I_1
  66. Point(b_1) → J_1
  67. OrthogonalLine(J_1, b_1) → j_1
  68. OrthogonalLine(H_1, b_1) → l_1
  69. Point(l_1) → K_1
  70. Point(j_1) → L_1
  71. Polygon(H_1, J_1, L_1, K_1) → T_1, h_2, j_2, l_2, k_2
  72. OrthogonalLine(B_5, b) → m_1
  73. OrthogonalLine(B_5, b) → n_1
  74. OrthogonalLine(B_5, b) → p_1
  75. OrthogonalLine(B_5, b) → q_1
  76. Line(B_5, d_1) → r_1
  77. Point(m_1) → N_1
  78. OrthogonalLine(I_1, m_1) → s_1
  79. OrthogonalLine(N_1, m_1) → a_2
  80. Point(s_1) → O_1
  81. Point(a_2) → U_1
  82. Polygon(C_1, O_1, U_1, N_1) → V_1, c_2, o_1, u_1, n_2
  83. Line(B_6, b) → b_2
  84. Point(b_2) → W_1
  85. Point(b_2) → Y_1
  86. Point(b_2) → Z_1
  87. OrthogonalLine(W_1, b) → e_2
  88. OrthogonalLine(Z_1, b) → i_2
  89. OrthogonalLine(Y_1, b) → m_2
  90. Point(m_2) → C_2
  91. Point(m_2) → D_2
  92. Point(i_2) → E_2
  93. Point(e_2) → F_2
  94. Point(e_2) → G_2
  95. Polygon(Y_1, G_2, D_2, Z_1, F_2, C_2, W_1, E_2) → Q_2, y_2, g_3, d_3, z_1, f_3, c_3, w_1, e_3
  96. OrthogonalLine(M_1, b) → p_2
  97. Intersect(p_2, c) → H_2
  98. Point(k) → J_2
  99. Circle(Q, J_2) → q_2
  100. Point(k_2) → K_2
  101. Point(r_2) → I_2
  102. Point(q_2) → M_2
  103. Point(q_2) → N_2
  104. Point(q_2) → O_2
  105. Point(q_2) → R_2
  106. Point(q_2) → S_2
  107. Point(q_2) → T_2
  108. Point(k_2) → U_2
  109. Point(q_2) → V_2
  110. Point(q_2) → W_2
  111. Point(q_2) → Y_2
  112. Point(q_2) → Z_2
  113. Segment(I_2, S_2) → s_2
  114. Segment(I_2, R_2) → a_3
  115. Segment(I_2, O_2) → b_3
  116. Segment(I_2, N_2) → h_3
  117. Segment(I_2, V_2) → i_3
  118. Segment(I_2, Y_2) → j_3
  119. Segment(I_2, W_2) → k_3
  120. Segment(I_2, M_2) → l_3
  121. Segment(I_2, Z_2) → m_3
  122. Segment(I_2, T_2) → n_3

AI 绘图提示语参考

绘制一个复杂的几何图形,包含正交线、点、线段、旋转和反射等元素。首先通过点B和x轴构造正交线a,然后在a上取点C,连接BC得到线段b。接着在b上取点L2和M1,通过点A和线段b构造正交线e和d,再通过d取点D,构造一系列正交线和圆,最终形成一个四边形P,连接P的顶点形成多边形,并通过旋转和反射操作生成新的点和线段,最终得到完整的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。