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轴对称图形 by Katerina Atmatzidou

轴对称图形 by Katerina Atmatzidou
几何画板及绘图内容加载中，请稍等……
2016-06-15 00:22
解析几何变换几何作图
该范例演示轴对称图形的动态变化。核心数学概念包括轴对称性、几何变换。通过使用GeoGebra命令如Segment、OrthogonalLine、Line等，可以构造轴对称图形。适合初中及以上学生学习几何变换和对称性。

GeoGebra 命令及参数

  1. Segment(A1, B) → a
  2. OrthogonalLine(A1, a) → b
  3. OrthogonalLine(B, a) → c
  4. Line(A1, B) → d
  5. Circle(B, A1) → e
  6. Intersect(e, d, 2) → C
  7. Circle(C, B) → f
  8. Intersect(f, d, 2) → D
  9. OrthogonalLine(C, d) → g
  10. OrthogonalLine(D, d) → h
  11. Intersect(e, c, 1) → E
  12. Intersect(f, g, 1) → F
  13. Circle(E, B) → k
  14. Intersect(k, c) → G, H
  15. Circle(H, E) → p
  16. Intersect(p, c, 2) → I
  17. OrthogonalLine(I, c) → i
  18. OrthogonalLine(H, c) → j
  19. Intersect(b, i) → J
  20. Intersect(g, i) → K
  21. Intersect(h, i) → L
  22. Intersect(g, j) → M
  23. Midpoint(H, M) → N
  24. Midpoint(E, F) → O
  25. Line(N, O) → l
  26. Point(l) → P
  27. Midpoint(N, O) → Q
  28. Circle(Q, P) → q
  29. Point(q) → R
  30. Point(q) → S
  31. CircumcircleArc(R, P, S) → r
  32. Rotate(i, 45*°, J) → m
  33. Intersect(l, m) → T
  34. Line(I, m) → s
  35. Intersect(l, s) → U
  36. Line(H, s) → n
  37. Line(B, n) → t
  38. Intersect(l, n) → V
  39. Intersect(l, t) → W
  40. Vector(J, T) → u
  41. Translate(J, Vector[o * u]) → Y
  42. Vector(T, L) → v
  43. Translate(T, Vector[(o - 1) * v]) → Z
  44. Vector(I, U) → w
  45. Vector(U, K) → z
  46. Point(r) → A
  47. Line(Q, A) → a_1
  48. If(o ≤ 1, Y, Z) → B_1
  49. If(c_1 < b_1, J, B_1) → C_1
  50. Translate(I, Vector[o * w]) → D_1
  51. Translate(H, Vector[o * w]) → E_1
  52. Translate(E, Vector[o * w]) → F_1
  53. Translate(G, Vector[o * w]) → G_1
  54. Translate(U, Vector[(o - 1) * z]) → H_1
  55. Translate(V, Vector[(o - 1) * z]) → I_1
  56. Translate(Q, Vector[(o - 1) * z]) → J_1
  57. Translate(W, Vector[(o - 1) * z]) → K_1
  58. If(o ≤ 1, D_1, H_1) → L_1
  59. If(o ≤ 1, E_1, I_1) → M_1
  60. If(o ≤ 1, F_1, J_1) → N_1
  61. If(o ≤ 1, G_1, K_1) → O_1
  62. Translate(Q, Vector[(o - 1) * u]) → P_1
  63. Translate(Q, Vector[(o - 1) * v]) → Q_1
  64. If(o ≤ 1, P_1, Q_1) → R_1
  65. If(c_1 < b_1, I, L_1) → S_1
  66. If(c_1 < b_1, H, M_1) → T_1
  67. If(c_1 < b_1, E, N_1) → U_1
  68. If(c_1 < b_1, G, O_1) → V_1
  69. If(c_1 < b_1, A1, R_1) → W_1
  70. Polygon(L, D, C, F, O, N, M, K) → Y_1, l_1, d_1, c_2, f_1, o_1, n_1, m_1, k_1
  71. Polygon(C_1, S_1, T_1, N, O, U_1, V_1, W_1) → Z_1, c_3, s_1, t_1, n_2, o_2, u_1, v_1, w_1
  72. Polygon(J, A1, G, E, O, N, H, I) → P_2, j_1, a_2, g_1, e_1, o_3, n_3, h_1, i_1