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交点与线性方程的探索

交点与线性方程的探索
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2016-04-03 07:30
函数三角函数解析几何立体几何几何作图
①本范例演示了通过 GeoGebra 构造并分析直线、角平分线、圆、圆柱体等几何对象的交点与相互关系；②涉及的核心数学概念包括线性方程、斜率差、角平分线、解析几何、立体几何；③作图要点提炼自构造摘要，使用了 Line（直线）、AngularBisector（角平分线）、Intersect（交点）、OrthogonalLine（垂线）、Circle（圆）、Segment（线段）、Mirror（镜像）、Dilate（缩放）、Midpoint（中点）、Center（中心）等命令与对象；④适合高中及以上学生学习和教师教学演示，可用于深入理解几何变换与方程求解。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. AngularBisector(C, A, B) → d
  5. AngularBisector(A, B, C) → e
  6. AngularBisector(B, C, A) → f
  7. Intersect(d, e) → D
  8. AngularBisector(C, A, D) → g
  9. AngularBisector(D, C, A) → h
  10. Intersect(g, h) → E
  11. OrthogonalLine(E, c) → i
  12. Intersect(c, i) → F
  13. Circle(E, F) → k
  14. AngularBisector(D, A, B) → j
  15. AngularBisector(D, B, A) → l
  16. Intersect(j, l) → G
  17. OrthogonalLine(G, a) → m
  18. Intersect(a, m) → H
  19. Circle(G, H) → p
  20. AngularBisector(B, C, D) → n
  21. AngularBisector(D, B, C) → q
  22. Intersect(n, q) → I
  23. OrthogonalLine(I, b) → r
  24. Intersect(b, r) → J
  25. Circle(I, J) → s
  26. Intersect(k, d) → K, N
  27. Intersect(p, d) → L, M
  28. Segment(E, G) → t
  29. Mirror(d, t) → d'
  30. Segment(E, I) → a_1
  31. Segment(I, G) → b_1
  32. Mirror(e, b_1) → e'
  33. Mirror(f, a_1) → f'
  34. Intersect(d', e') → O
  35. AngularBisector(O, F, A) → c_1
  36. AngularBisector(A, H, O) → d_1
  37. Intersect(d, c_1) → P
  38. OrthogonalLine(P, a) → e_1
  39. Intersect(a, e_1) → Q
  40. Circle(P, Q) → f_1
  41. AngularBisector(O, J, B) → g_1
  42. Intersect(e, g_1) → R
  43. OrthogonalLine(R, a) → h_1
  44. Intersect(a, h_1) → S
  45. Circle(R, S) → k_1
  46. AngularBisector(O, J, C) → i_1
  47. Intersect(i_1, f) → T
  48. OrthogonalLine(T, b) → j_1
  49. Intersect(b, j_1) → U
  50. Circle(T, U) → p_1
  51. Intersect(p_1, k_1) → V, , ,
  52. OrthogonalLine(V, b) → l_1
  53. Intersect(b, l_1) → W
  54. Circle(V, W) → q_1
  55. Dilate(q_1, 0.5, W) → r_1
  56. Intersect(k_1, q_1) → Z, A_1, ,
  57. Line(A_1, Z) → m_1
  58. Midpoint(V, W) → B_1
  59. Line(B_1, m_1) → n_1
  60. Intersect(r_1, n_1) → C_1, D_1
  61. Mirror(r_1, D_1) → s_1
  62. Mirror(s_1, q_1) → t_1
  63. Intersect(f_1, p_1, 1) → E_1
  64. OrthogonalLine(E_1, c) → a_2
  65. Intersect(c, a_2) → F_1
  66. Midpoint(F_1, E_1) → G_1
  67. Circle(G_1, F_1) → c_2
  68. Circle(E_1, F_1) → d_2
  69. Intersect(f_1, d_2) → H_1, I_1, ,
  70. Line(I_1, H_1) → b_2
  71. Line(G_1, b_2) → e_2
  72. Intersect(c_2, e_2) → J_1, K_1
  73. Mirror(c_2, J_1) → f_2
  74. Mirror(f_2, d_2) → g_2
  75. Intersect(f_1, k_1, 1) → L_1
  76. OrthogonalLine(L_1, a) → h_2
  77. Intersect(a, h_2) → M_1
  78. Midpoint(M_1, L_1) → N_1
  79. Circle(L_1, M_1) → k_2
  80. Circle(N_1, M_1) → p_2
  81. Intersect(k_2, f_1) → O_1, P_1, ,
  82. Line(P_1, O_1) → i_2
  83. Line(N_1, i_2) → j_2
  84. Intersect(p_2, j_2) → Q_1, R_1
  85. Mirror(p_2, Q_1) → q_2
  86. Mirror(q_2, k_2) → r_2
  87. Center(f_1) → S_1
  88. Center(p_1) → T_1
  89. Center(k_1) → U_1
  90. Center(r_2) → V_1
  91. Center(g_2) → W_1
  92. Center(t_1) → Z_1
  93. Segment(Z_1, A) → l_2
  94. Segment(C, V_1) → m_2
  95. Intersect(l_2, m_2) → A_2
  96. Segment(W_1, B) → n_2