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四边形的旋转对称性 by youngcar

四边形的旋转对称性 by youngcar
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2016-06-01 10:20
多边形变换几何作图
①本范例演示了四边形（特别是梯形）的旋转对称性现象；②涉及的核心数学概念包括对称性、旋转、几何作图；③作图要点——从下方『构造摘要』提炼用到了Segment（线段）、OrthogonalLine（垂线）、Point（点）、Intersect（交点）、Circle（圆）、Line（直线）、Rotate（旋转）、Polygon（多边形）、Mirror（镜像）等GeoGebra命令/对象；④适合初中及以上学生学习几何变换和对称性知识，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Segment(C, B) → e
  8. Segment(D, A) → f
  9. Intersect(e, f) → E
  10. Segment(K, L) → l
  11. Circle(K, L) → p
  12. Point(p) → M
  13. Segment(K, M) → m
  14. Line(M, l) → n
  15. Line(L, m) → q
  16. Intersect(n, q) → N
  17. Segment(M, L) → r
  18. Segment(N, K) → s
  19. Intersect(r, s) → O
  20. Rotate(C, (-α), E) → C'
  21. Rotate(D, (-α), E) → D'
  22. Rotate(B, (-α), E) → B'
  23. Rotate(A, (-α), E) → A'
  24. Rotate(M, (-α), O) → M'
  25. Rotate(N, (-α), O) → N'
  26. Rotate(L, (-α), O) → L'
  27. Rotate(K, (-α), O) → K'
  28. Segment(P, Q) → t
  29. Segment(P, R) → e_1
  30. Line(Q, e_1) → g_1
  31. Line(R, t) → h_1
  32. Intersect(g_1, h_1) → S
  33. Segment(R, Q) → i_1
  34. Segment(S, P) → j_1
  35. Intersect(i_1, j_1) → T
  36. Rotate(P, (-α), T) → P'
  37. Rotate(R, (-α), T) → R'
  38. Rotate(S, (-α), T) → S'
  39. Rotate(Q, (-α), T) → Q'
  40. Segment(U, V) → t_1
  41. Segment(U, W) → a_2
  42. Line(W, t_1) → b_2
  43. Point(b_2) → Z
  44. Segment(Z, V) → c_2
  45. Polygon(U, V, Z, W) → poly5, u, v, z, w
  46. Segment(W, V) → d_2
  47. Segment(Z, U) → e_2
  48. Intersect(d_2, e_2) → A_1
  49. Rotate(U, (-α), A_1) → U'
  50. Rotate(V, (-α), A_1) → V'
  51. Rotate(Z, (-α), A_1) → Z'
  52. Rotate(W, (-α), A_1) → W'
  53. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  54. Line(B_1, C_1) → f_2
  55. Mirror(D_1, f_2) → E_1
  56. Segment(D_1, E_1) → g_2
  57. Intersect(f_2, g_2) → F_1
  58. Rotate(D_1, (-α), F_1) → G_1
  59. Rotate(B_1, (-α), F_1) → H_1
  60. Rotate(E_1, (-α), F_1) → I_1
  61. Rotate(C_1, (-α), F_1) → J_1
  62. Intersect(z', w') → H
  63. Intersect(a_2, z) → I