根矩形1

根矩形1
几何画板及绘图内容加载中,请稍等……
2019-04-22 15:11
①本范例演示了根矩形与函数图像、切线、交点的几何关系;②涉及核心数学概念包括函数、切线、根、矩形、复数、解析几何;③构造要点:使用Point, Segment, Polygon, Line, Circle, Intersect, OrthogonalLine, CircleArc等命令绘制图形;④适合高中及以上数学学习者和教师用于函数图像分析、切线绘制及复数几何表示的教学与探索。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → D
  4. Point(yAxis) → E
  5. Segment(O, P) → n
  6. Point(xAxis) → C
  7. Point(xAxis) → G
  8. Polygon(C, G, 4) → poly1, f, g, h, i, H, I
  9. Segment(C, H) → j
  10. Line(C, G) → k
  11. Circle(C, H) → c
  12. Intersect(c, k, 2) → J
  13. OrthogonalLine(J, k) → l
  14. Line(H, k) → m
  15. Intersect(l, m) → A_1
  16. Polygon(G, H, A_1, J) → q1, g_1, h_1, a_1, j_1
  17. Circle(C, A_1) → d
  18. Intersect(d, k, 2) → B_1
  19. Line(B_1, l) → p
  20. Intersect(m, p) → C_1
  21. Polygon(J, B_1, C_1, A_1) → q2, j_2, b_1, c_1, q
  22. Circle(C, C_1) → e
  23. Intersect(e, k, 2) → D_1
  24. Line(D_1, p) → r
  25. Intersect(m, r) → E_1
  26. Polygon(B_1, D_1, E_1, C_1) → q3, s, d_1, e_1, t
  27. Circle(C, E_1) → f_1
  28. Intersect(f_1, k, 2) → F_1
  29. Line(F_1, r) → a
  30. Intersect(m, a) → G_1
  31. Polygon(D_1, F_1, G_1, E_1) → q4, b, i_1, k_1, l_1
  32. Circle(C, G_1) → p_1
  33. Intersect(p_1, k, 2) → H_1
  34. Line(H_1, a) → m_1
  35. Intersect(m, m_1) → I_1
  36. Polygon(F_1, H_1, I_1, G_1) → q5, n_1, q_1, r_1, s_1
  37. Circle(C, I_1) → t_1
  38. Intersect(t_1, k, 2) → J_1
  39. Line(J_1, m_1) → f_2
  40. Intersect(m, f_2) → K_1
  41. Polygon(H_1, J_1, K_1, I_1) → q6, g_2, h_2, i_2, k_2
  42. Circle(C, K_1) → c_2
  43. Intersect(c_2, k, 2) → L_1
  44. Line(L_1, f_2) → l_2
  45. Intersect(m, l_2) → M_1
  46. Polygon(J_1, L_1, M_1, K_1) → q7, m_2, n_2, p_2, q_2
  47. Circle(C, M_1) → d_2
  48. Intersect(d_2, k, 2) → N_1
  49. Line(N_1, l_2) → r_2
  50. Intersect(m, r_2) → O_1
  51. Polygon(L_1, N_1, O_1, M_1) → q8, s_2, t_2, o_1, a_2
  52. CircleArc(C, J, H) → e_2
  53. CircleArc(C, B_1, A_1) → c_3
  54. CircleArc(C, D_1, C_1) → d_3
  55. CircleArc(C, F_1, E_1) → e_3
  56. CircleArc(C, J_1, I_1) → f_3
  57. CircleArc(C, H_1, G_1) → g_3
  58. CircleArc(C, L_1, K_1) → h_3
  59. CircleArc(C, N_1, M_1) → k_3
  60. Point(xAxis) → P_1
  61. Polygon(P_1, C, 4) → poly2, b_2, i_3, j_3, l_3, Q_1, R_1
  62. Polygon(G, C, 4) → poly3, m_3, n_3, p_3, q_3, S_1, T_1
  63. Polygon(C, P_1, 4) → poly4, r_3, s_3, t_3, a_3, U_1, V_1
  64. Segment(U_1, C) → b_3
  65. Line(U_1, T_1) → f_4
  66. Line(A_1, J) → g_4
  67. Line(C_1, B_1) → h_4
  68. Intersect(f_4, g_4) → W_1
  69. Circle(U_1, H) → c_4
  70. Intersect(c_4, f_4, 2) → Z_1
  71. Point(g_4) → A_2
  72. OrthogonalLine(Z_1, f_4) → i_4
  73. Intersect(i_4, e_1) → B_2
  74. Segment(Z_1, B_2) → j_4
  75. Circle(U_1, B_2) → d_4
  76. Intersect(d_4, f_4, 2) → C_2
  77. OrthogonalLine(C_2, f_4) → k_4
  78. Intersect(k_4, i_2) → D_2
  79. Segment(D_2, C_2) → l_4
  80. Circle(U_1, D_2) → e_4
  81. Intersect(e_4, f_4, 2) → E_2
  82. OrthogonalLine(E_2, f_4) → m_4
  83. Segment(E_2, N_1) → n_4
  84. Circle(S_1, E_1) → p_4
  85. Intersect(p_4, f_4, 2) → F_2
  86. Intersect(p_4, f_4, 2) → G_2
  87. Segment(G_2, L_1) → q_4

AI 绘图提示语参考

画一个函数图像,并在其上绘制多个矩形,每个矩形与函数图像相切,且其边平行于坐标轴。每个矩形的顶点都在函数图像上,且矩形的对角线与函数图像的切线垂直。用圆表示每个矩形的内切圆,并用线段连接矩形的顶点。展示函数图像、切线、矩形、圆和交点的几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。