根矩形4-8

根矩形4-8
几何画板及绘图内容加载中,请稍等……
2019-04-23 04:29
①本范例演示根矩形4-8的几何构造与性质;②涉及核心数学概念包括矩形、根号运算、对称性、线段运算、百分比计算;③作图要点:使用Point, Segment, Polygon, Line, Circle, Intersect, OrthogonalLine, CircleArc, Rotate, Angle等GeoGebra命令进行点线面构造与变换;④适合高中数学教学,用于理解几何变换与代数运算的结合应用。

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. Polygon(C, G, 8) → poly2, b_2, Q_1, R_1, S_1, T_1, U_1, i_3, j_3, l_3, m_3, n_3, p_3, q_3, P_1
  61. Rotate(H, (-(135°)), I) → H'
  62. Angle(H', I, H) → β
  63. Rotate(H, 135°, I) → H'_1
  64. Angle(H, I, H'_1) → γ
  65. Rotate(H, (-(67.5°)), I) → H'_2
  66. Angle(H'_2, I, H) → α
  67. Line(I, H'_2) → r_3
  68. Intersect(r_3, f) → V_1
  69. Rotate(I_1, 67.5°, M_1) → Z_1
  70. Angle(I_1, M_1, Z_1) → ε
  71. Line(M_1, Z_1) → s_3
  72. Intersect(s_3, n_1) → A_2
  73. Segment(V_1, I) → t_3
  74. Segment(A_2, M_1) → a_3
  75. Polygon(I, V_1, 8) → poly3, b_3, C_2, D_2, E_2, F_2, G_2, f_4, g_4, h_4, i_4, j_4, k_4, l_4, B_2
  76. Segment(G_2, E_2) → m_4
  77. Polygon(E_2, G_2, 4) → poly4, n_4, p_4, q_4, r_4, W_1, H_2
  78. Segment(I, F_2) → s_4
  79. Polygon(F_2, I, 4) → poly5, t_4, a_4, b_4, c_4, I_2, J_2
  80. Point(xAxis) → K_2
  81. Point(xAxis) → L_2
  82. Polygon(K_2, L_2, 8) → poly6, d_4, N_2, O_2, P_2, Q_2, R_2, e_4, f_5, g_5, h_5, i_5, j_5, k_5, M_2
  83. Segment(P_2, K_2) → l_5
  84. Segment(R_2, M_2) → m_5
  85. Intersect(l_5, m_5) → S_2
  86. Segment(S_2, R_2) → n_5
  87. Point(xAxis) → T_2
  88. Line(T_2, K_2) → p_5
  89. OrthogonalLine(T_2, p_5) → q_5
  90. Intersect(q_5, n_5) → U_2
  91. Polygon(U_2, S_2, 4) → poly7, r_5, s_5, t_5, a_5, V_2, W_2
  92. Segment(S_2, W_2) → b_5
  93. CircleArc(S_2, W_2, R_2) → c_5
  94. Rotate(U_2, 45°, S_2) → Z_2
  95. CircleArc(S_2, U_2, Z_2) → d_5
  96. Segment(Z_2, S_2) → e_5

AI 绘图提示语参考

画一个由四个矩形组成的图形,每个矩形都通过正方形根、对称性、线段操作和百分比计算构造。首先在x轴上创建四个点,然后连接这些点形成矩形。接着,通过旋转、绘制圆和正交线等操作,在每个矩形内部构造新的几何形状,最终形成复杂的几何图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。