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旋转对称再探

旋转对称再探
几何画板及绘图内容加载中，请稍等……
2015-10-02 05:52
多边形变换几何作图
这个范例演示了旋转对称的几何图形。核心数学概念包括旋转对称性和几何变换。通过使用GeoGebra命令如Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, Mirror等，可以构造出具有旋转对称性的多边形。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(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. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  8. Segment(C, B) → e
  9. Segment(D, A) → f
  10. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  11. Segment(I, G) → j
  12. Segment(H, F) → k
  13. Segment(K, L) → l
  14. Circle(K, L) → p
  15. Point(p) → M
  16. Segment(K, M) → m
  17. Line(M, l) → n
  18. Line(L, m) → q
  19. Intersect(n, q) → N
  20. Segment(M, L) → r
  21. Segment(N, K) → s
  22. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  23. Rotate(C, (-α), E) → C'
  24. Rotate(D, (-α), E) → D'
  25. Rotate(B, (-α), E) → B'
  26. Rotate(A, (-α), E) → A'
  27. Polygon(C', D', B', A') → poly1', c', d', b', a'
  28. Rotate(M, (-α), O) → M'
  29. Rotate(N, (-α), O) → N'
  30. Rotate(L, (-α), O) → L'
  31. Rotate(K, (-α), O) → K'
  32. Polygon(M', N', L', K') → poly3', m', n', l', k'
  33. Segment(P, Q) → t
  34. Segment(P, R) → e_1
  35. Line(Q, e_1) → g_1
  36. Line(R, t) → h_1
  37. Intersect(g_1, h_1) → S
  38. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
  39. Segment(R, Q) → i_1
  40. Segment(S, P) → j_1
  41. Rotate(P, (-α), T) → P'
  42. Rotate(R, (-α), T) → R'
  43. Rotate(S, (-α), T) → S'
  44. Rotate(Q, (-α), T) → Q'
  45. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  46. Segment(U, V) → t_1
  47. Segment(U, W) → a_2
  48. Line(W, t_1) → b_2
  49. Point(b_2) → Z
  50. Segment(Z, V) → c_2
  51. Polygon(U, V, Z, W) → poly5, u, v, z, w
  52. Segment(W, V) → d_2
  53. Segment(Z, U) → e_2
  54. Rotate(U, (-α), A_1) → U'
  55. Rotate(V, (-α), A_1) → V'
  56. Rotate(Z, (-α), A_1) → Z'
  57. Rotate(W, (-α), A_1) → W'
  58. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  59. Line(B_1, C_1) → f_2
  60. Mirror(D_1, f_2) → E_1
  61. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
  62. Segment(D_1, E_1) → g_2
  63. Rotate(D_1, (-α), F_1) → G_1
  64. Rotate(B_1, (-α), F_1) → H_1
  65. Rotate(E_1, (-α), F_1) → I_1
  66. Rotate(C_1, (-α), F_1) → J_1
  67. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  68. Rotate(poly2, (-α), J) → poly2'