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对称与平移的剪裁与折叠探索

对称与平移的剪裁与折叠探索
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2020-02-05 16:11
数列变换几何作图
本范例通过剪裁和折叠图形来研究对称性和平移。它涉及对称、平移等核心数学概念。通过使用GeoGebra中的Circle、Line、Intersect、Mirror、Vector、Translate等命令，可以构造出一系列几何图形。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Circle(Départ, b) → e
  2. Line(Départ, xAxis) → d
  3. Line(Départ, yAxis) → b_1
  4. Intersect(e, b_1) → B, C
  5. Line(B, d) → g
  6. Circle(Départ, a) → c
  7. Intersect(c, d) → D, E
  8. Mirror(Départ, E) → A'
  9. Line(E, b_1) → f
  10. Intersect(g, f) → F
  11. Vector(E, F) → u_2
  12. CircleArc(F, Départ, A') → h
  13. Point(h) → Move
  14. Translate(Move, u_2) → G'
  15. Midpoint(G', Move) → I
  16. Polygon(G', F, E, Move) → poly1, g', f_1, e_1, g_1
  17. Intersect(g_1, d) → H
  18. Mirror(E, H) → E'
  19. Translate(E', u_2) → E''
  20. Polygon(E'', E', Move, G') → poly2, e'', e', g_2, g'_1
  21. Angle(Départ, E, Move) → α
  22. Vector(Départ, E) → u
  23. Line(G', Move) → i_2
  24. Intersect(i_2, d) → I_2
  25. Vector(E, I_2) → v
  26. Vector(E, E') → w
  27. Sequence(Polygon[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]], Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre, 1) → liste2
  28. Sequence(Polygon[Translate[G', Vector[(s * w)]], Translate[F, Vector[(s * w)]], Translate[E, Vector[(s * w)]], Translate[Move, Vector[(s * w)]]], s, 0, Nombre) → liste7
  29. Segment(G', Move) → aa_1
  30. PointIn(poly1) → J
  31. PointIn(poly1) → K
  32. PointIn(poly1) → L
  33. PointIn(poly1) → M
  34. PointIn(poly1) → N
  35. PointIn(poly1) → O
  36. PointIn(poly1) → P
  37. PointIn(poly1) → Q
  38. PointIn(poly1) → R
  39. PointIn(poly1) → S
  40. Polygon(J, K, M, O, P, S, R, Q, N, L) → poly3, j, l, k, m, o, p, s, r, q, n_1
  41. Mirror(J, aa_1) → J'
  42. Mirror(K, aa_1) → K'
  43. Mirror(M, aa_1) → M'
  44. Mirror(O, aa_1) → O'
  45. Mirror(P, aa_1) → P'
  46. Mirror(S, aa_1) → S'
  47. Mirror(R, aa_1) → R'
  48. Mirror(Q, aa_1) → Q'
  49. Mirror(N, aa_1) → N'
  50. Mirror(L, aa_1) → L'
  51. Polygon(J', K', M', O', P', S', R', Q', N', L') → poly3', j', l', k', m', o', p', s', r', q', n'
  52. Sequence(Polygon[Translate[J, Vector[(s * w)]], Translate[K, Vector[(s * w)]], Translate[M, Vector[(s * w)]], Translate[O, Vector[(s * w)]], Translate[P, Vector[(s * w)]], Translate[S, Vector[(s * w)]], Translate[R, Vector[(s * w)]], Translate[Q, Vector[(s * w)]], Translate[N, Vector[(s * w)]], Translate[L, Vector[(s * w)]]], s, 0, Nombre) → liste1
  53. Sequence(Polygon[Translate[J', Vector[(s * w)]], Translate[K', Vector[(s * w)]], Translate[M', Vector[(s * w)]], Translate[O', Vector[(s * w)]], Translate[P', Vector[(s * w)]], Translate[S', Vector[(s * w)]], Translate[R', Vector[(s * w)]], Translate[Q', Vector[(s * w)]], Translate[N', Vector[(s * w)]], Translate[L', Vector[(s * w)]]], s, 0, Nombre) → liste3
  54. Sequence(Segment[Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre) → liste4
  55. Segment(F, E) → aa
  56. Sequence(Segment[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]]], s, 0, Nombre) → liste5
  57. Mirror(G', f_1) → G''
  58. Mirror(F, f_1) → F'
  59. Mirror(E, f_1) → E'_1
  60. Mirror(G', f_1) → G''_1
  61. Mirror(F, f_1) → F'_1
  62. Mirror(E, f_1) → E'_2
  63. Line(F, E) → i
  64. Mirror(G', i) → G''_2
  65. Mirror(F, i) → F'_2
  66. Mirror(E, i) → E'_3
  67. Mirror(Move, i) → G'_1
  68. Polygon(G''_2, F'_2, E'_3, G'_1) → poly1', g''_2, f'_2, e'_3, g'_2
  69. Mirror(J, i) → J'_1
  70. Mirror(K, i) → K'_1
  71. Mirror(M, i) → M'_1
  72. Mirror(O, i) → O'_1
  73. Mirror(P, i) → P'_1
  74. Mirror(S, i) → S'_1
  75. Mirror(R, i) → R'_1
  76. Mirror(Q, i) → Q'_1
  77. Mirror(N, i) → N'_1
  78. Mirror(L, i) → L'_1
  79. Polygon(J'_1, K'_1, M'_1, O'_1, P'_1, S'_1, R'_1, Q'_1, N'_1, L'_1) → poly3'_1, j'_1, l'_1, k'_1, m'_1, o'_1, p'_1, s'_1, r'_1, q'_1, n'_1
  80. Ellipse(C_1, D_1, E_1) → c_1
  81. Circle(F_1, G_1) → d_1
  82. Circle(H_1, I_1) → h_1