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万花筒变换：旋转与反射

万花筒变换：旋转与反射
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2016-10-31 03:54
多边形变换几何作图
①本范例演示通过旋转与反射操作构建万花筒图案；②涉及核心数学概念包括旋转、反射、多边形构造；③作图要点：运用了Circle（圆）、Line（线）、OrthogonalLine（垂线）、Intersect（交点）、Point（点）、Segment（线段）、Mirror（镜像）、Polygon（多边形）、Rotate（旋转）等GeoGebra命令；④适合初中及以上学生学习几何变换与对称性知识，也可用于数学兴趣小组活动。

GeoGebra 命令及参数

  1. Circle(A, b) → p
  2. Circle(A, B) → c
  3. Circle(A, C) → d
  4. Circle(A, D) → e
  5. Circle(A, E) → f
  6. Line(F, A) → g
  7. OrthogonalLine(A, g) → h
  8. Intersect(f, g) → G, H
  9. Point(e) → I_1
  10. Segment(G, I_1) → i
  11. Point(g) → J
  12. Segment(J, I_1) → j
  13. Mirror(G, g) → G'
  14. Mirror(I_1, g) → I'
  15. Segment(G', I') → i'
  16. Mirror(J, g) → J'
  17. Mirror(I_1, g) → I'_1
  18. Segment(J', I'_1) → j'
  19. Polygon(G, I_1, J, I') → PreImageKite, g_1, i_1, j_1, i'_1
  20. Mirror(G, h) → G'_1
  21. Mirror(I_1, h) → I'_2
  22. Mirror(J, h) → J'_1
  23. Mirror(I', h) → I''
  24. Polygon(G'_1, I'_2, J'_1, I'') → ReflectedKite, g'_1, i'_2, j'_1, i''
  25. Rotate(G, (-(90°)), A) → G'_2
  26. Rotate(I_1, (-(90°)), A) → I'_3
  27. Rotate(J, (-(90°)), A) → J'_2
  28. Rotate(I', (-(90°)), A) → I''_1
  29. Polygon(G'_2, I'_3, J'_2, I''_1) → RotatedKite90, g'_2, i'_3, j'_2, i''_1
  30. Rotate(G, (-(270°)), A) → G'_3
  31. Rotate(I_1, (-(270°)), A) → I'_4
  32. Rotate(J, (-(270°)), A) → J'_3
  33. Rotate(I', (-(270°)), A) → I''_2
  34. Polygon(G'_3, I'_4, J'_3, I''_2) → RotatedKite270, g'_3, i'_4, j'_3, i''_2
  35. Rotate(G, (-(60°)), A) → G'_4
  36. Rotate(I_1, (-(60°)), A) → I
  37. Rotate(J, (-(60°)), A) → J'_4
  38. Rotate(I', (-(60°)), A) → I''_3
  39. Polygon(G'_4, I, J'_4, I''_3) → RotatedKite60, g'_4, i_2, j'_4, i''_3
  40. Rotate(G, (-(120°)), A) → G'_5
  41. Rotate(I_1, (-(120°)), A) → K
  42. Rotate(J, (-(120°)), A) → J'_5
  43. Rotate(I', (-(120°)), A) → I''_4
  44. Polygon(G'_5, K, J'_5, I''_4) → RotatedKite120, g'_5, k, j'_5, i''_4
  45. Rotate(G, (-(2400°)), A) → G'_6
  46. Rotate(I_1, (-(2400°)), A) → L
  47. Rotate(J, (-(2400°)), A) → J'_6
  48. Rotate(I', (-(2400°)), A) → I''_5
  49. Polygon(G'_6, L, J'_6, I''_5) → RotatedKite240, g'_6, l, j'_6, i''_5
  50. Intersect(h, j_1) → M
  51. Rotate(M, 90°, A) → M'
  52. Point(p) → N
  53. Polygon(A, M', N, M) → Quad2, a, m', n, m
  54. Mirror(A, A) → A'
  55. Mirror(M', A) → M''
  56. Mirror(N, A) → N'
  57. Mirror(M, A) → M'_1
  58. Polygon(A', M'', N', M'_1) → Quad2Reflected, a', m'', n', m'_1
  59. Rotate(A, 90°, A) → A'_1
  60. Rotate(M', 90°, A) → M''_1
  61. Rotate(N, 90°, A) → N'_1
  62. Rotate(M, 90°, A) → M'_2
  63. Polygon(A'_1, M''_1, N'_1, M'_2) → Quad2Rotated90, a'_1, m''_1, n'_1, m'_2
  64. Rotate(A, 270°, A) → A'_2
  65. Rotate(M', 270°, A) → M''_2
  66. Rotate(N, 270°, A) → N'_2
  67. Rotate(M, 270°, A) → M'_3
  68. Polygon(A'_2, M''_2, N'_2, M'_3) → Quad2Rotated270, a'_2, m''_2, n'_2, m'_3
  69. Rotate(G, (-(300°)), A) → G'_7
  70. Rotate(I_1, (-(300°)), A) → O
  71. Rotate(J, (-(300°)), A) → J'_7
  72. Rotate(I', (-(300°)), A) → I''_6
  73. Polygon(G'_7, O, J'_7, I''_6) → RotatedKite300, g'_7, o, j'_7, i''_6
  74. Rotate(G, (-(30°)), A) → G'_8
  75. Rotate(I_1, (-(30°)), A) → P
  76. Rotate(J, (-(30°)), A) → J'_8
  77. Rotate(I', (-(30°)), A) → I''_7
  78. Polygon(G'_8, P, J'_8, I''_7) → RotatedKite30, g'_8, p_1, j'_8, i''_7
  79. Rotate(G, (-(150°)), A) → G'_9
  80. Rotate(I_1, (-(150°)), A) → Q
  81. Rotate(J, (-(150°)), A) → J'_9
  82. Rotate(I', (-(150°)), A) → I''_8
  83. Polygon(G'_9, Q, J'_9, I''_8) → RotatedKite150, g'_9, q, j'_9, i''_8
  84. Rotate(G, (-(210°)), A) → G'_{10}
  85. Rotate(I_1, (-(210°)), A) → R
  86. Rotate(J, (-(210°)), A) → J'_{10}
  87. Rotate(I', (-(210°)), A) → I''_9
  88. Polygon(G'_{10}, R, J'_{10}, I''_9) → RotatedKite210, g'_{10}, r, j'_{10}, i''_9
  89. Rotate(G, (-(330°)), A) → G'_{11}
  90. Rotate(I_1, (-(330°)), A) → S
  91. Rotate(J, (-(330°)), A) → J'_{11}
  92. Rotate(I', (-(330°)), A) → I''_{10}
  93. Polygon(G'_{11}, S, J'_{11}, I''_{10}) → RotatedKite330, g'_{11}, s, j'_{11}, i''_{10}
  94. Rotate(A, (-(30°)), A) → A'_3
  95. Rotate(M', (-(30°)), A) → M''_3
  96. Rotate(N, (-(30°)), A) → N'_3
  97. Rotate(M, (-(30°)), A) → M'_4
  98. Polygon(A'_3, M''_3, N'_3, M'_4) → QuadRotated30, a'_3, m''_3, n'_3, m'_4
  99. Rotate(A, (-(120°)), A) → A'_4
  100. Rotate(M', (-(120°)), A) → M''_4
  101. Rotate(N, (-(120°)), A) → N'_4
  102. Rotate(M, (-(120°)), A) → M'_5
  103. Polygon(A'_4, M''_4, N'_4, M'_5) → QuadRotated120, a'_4, m''_4, n'_4, m'_5