二维向量与反射的几何作图 by Claudio Martínez Gil

二维向量与反射的几何作图 by Claudio Martínez Gil
几何画板及绘图内容加载中,请稍等……
2020-05-26 23:26
①本范例演示了二维向量、反射、函数图像与几何图形的交互关系;②涉及的核心数学概念包括向量运算、函数图像绘制、反射变换、解析几何作图等;③作图要点:利用Line, Vector, OrthogonalVector, LineBisector, OrthogonalLine, Mirror, Intersect, Polygon, CircleArc等GeoGebra命令进行几何构造与变换;④适合高中数学教学,用于理解向量、反射、函数图像及优化问题的几何意义。

GeoGebra 命令及参数

  1. Line(A, B) → s
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A_1, A) → l
  5. OrthogonalLine(K, s) → j
  6. LineBisector(A, B) → m
  7. LineBisector(A_1, A) → n
  8. LineBisector(A_1, A) → h
  9. OrthogonalLine(D, s) → i
  10. OrthogonalLine(A, s) → b
  11. OrthogonalLine(B, u, xOyPlane) → g
  12. Mirror(i, m) → i'
  13. OrthogonalLine(A_1, b) → r
  14. Intersect(g, r) → C
  15. Intersect(b, l) → O
  16. Intersect(m, l) → L
  17. Mirror(A_1, l) → D_2
  18. Mirror(A_1, l) → F_2
  19. Mirror(C, l) → C'_1
  20. OrthogonalLine(F, b) → f
  21. Mirror(f, l) → f'
  22. Mirror(f, l) → f'_1
  23. Intersect(m, f) → M
  24. Polygon(A, B, C, A_1) → c1, a_1, b_1, c_1, f_1
  25. Intersect(b, f') → I
  26. OrthogonalLine(J, b) → q
  27. OrthogonalLine(R, b) → a
  28. OrthogonalLine(T, s) → e
  29. OrthogonalLine(E, s) → k
  30. Intersect(i, f) → N
  31. Intersect(j, q) → D_1
  32. Intersect(i, f') → E_1
  33. Intersect(m, f') → F_1
  34. Intersect(m, q) → G_1
  35. Mirror(N, m) → N'
  36. Mirror(F_1, m) → I_1
  37. Mirror(G_1, m) → J_1
  38. OrthogonalLine(Q, s) → t
  39. OrthogonalLine(V, s) → c
  40. Intersect(a, t) → B_1
  41. Intersect(q, e) → W
  42. Intersect(j, l) → P
  43. Line(P, M) → d
  44. Intersect(d, t) → G
  45. Intersect(c, d) → H
  46. OrthogonalLine(S, b) → p
  47. Intersect(p, k) → U
  48. OrthogonalLine(Z, b) → g_1
  49. Intersect(g_1, k) → C_1
  50. LineBisector(B_1, E_1) → h_1
  51. Intersect(h_1, p) → H_1
  52. CircleArc(H_1, B_1, E_1) → d_1
  53. LineBisector(W, B_1) → i_1
  54. Intersect(p, i_1) → K_1
  55. CircleArc(K_1, B_1, W) → k_1
  56. LineBisector(C_1, W) → j_1
  57. Intersect(j_1, j) → L_1
  58. CircleArc(L_1, C_1, W) → p_1
  59. LineBisector(G, U) → l_1
  60. LineBisector(E_1, D_1) → m_1
  61. Intersect(a, m_1) → M_1
  62. CircleArc(M_1, D_1, E_1) → q_1
  63. Intersect(l_1, l) → N_1
  64. CircleArc(N_1, U, G) → r_1
  65. LineBisector(O_1, L) → n_1
  66. Intersect(n_1, l) → P_1
  67. CircleArc(P_1, L, O_1) → s_1
  68. Polygon(D_1, S, G, U, C_1, W, B_1, E_1) → polígono1, t_1, s_2, g_2, u_1, f_2, w, h_2, i_2
  69. Polygon(O_1, H, M, L) → c2, o_1, h_3, m_2, l_2
  70. Mirror(O_1, m) → Q_1
  71. Mirror(H, m) → H'
  72. Mirror(M, m) → M'
  73. Mirror(L, m) → L'
  74. Polygon(Q_1, H', M', L') → c2', j_2, h', m', l'
  75. Mirror(d_1, m) → c_2
  76. Mirror(d_1, m) → d_2
  77. Mirror(k_1, m) → k_2
  78. Mirror(p_1, m) → p_2
  79. Mirror(q_1, m) → q_2
  80. Mirror(r_1, m) → r_2
  81. Mirror(s_1, m) → t_2
  82. Mirror(D_1, m) → R_1
  83. Mirror(S, m) → S'
  84. Mirror(G, m) → G'
  85. Mirror(U, m) → U'
  86. Mirror(C_1, m) → S_1
  87. Mirror(W, m) → W'
  88. Mirror(B_1, m) → T_1
  89. Mirror(E_1, m) → U_1
  90. Polygon(R_1, S', G', U', S_1, W', T_1, U_1) → polígono1', n_2, s', g', u', a_2, w', b_2, f_3

AI 绘图提示语参考

画一个二维向量与反射的几何构造图,包含两个向量和它们的反射线,展示向量操作、函数图像和几何形状的交互。先画出一条线段和两个向量,再求出其中一个向量的正交向量,并画出两条垂直线。接着,利用中垂线和反射变换构造多个点和几何形状,如多边形和圆弧,最终呈现一个复杂的几何图形,体现向量、反射、函数图像和解析几何的综合应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。