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旋转与对称变换

旋转与对称变换
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2016-11-06 12:51
角变换几何作图
所属专题 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
该范例演示了旋转和平面对称变换的几何图形。核心数学概念包括旋转、对称、几何作图。使用了Line, OrthogonalLine, Point, Ray, Midpoint, Segment, Circle, Intersect, CircleSector, Polygon, Rotate, Dilate, Angle等GeoGebra命令。适合初中及以上学生学习几何变换。

GeoGebra 命令及参数

  1. Line(C, B_1) → a
  2. OrthogonalLine(C, a) → d
  3. OrthogonalLine(B_1, a) → e
  4. Point(d) → C_1
  5. Ray(C, C_1) → c
  6. Point(d) → E
  7. Ray(C, E) → b
  8. Ray(C, B_1) → g
  9. Point(g) → F
  10. Ray(C, F) → h
  11. Point(h) → B
  12. Ray(C, E) → i
  13. Point(i) → A
  14. Midpoint(A, B) → M
  15. Segment(C, A) → j
  16. Segment(C, B) → k
  17. Circle(C, Min[(0.15 * j), (0.15 * k)]) → p
  18. Intersect(p, a, 2) → I
  19. Intersect(p, i, 1) → J
  20. Intersect(p, a, 1) → K
  21. CircleSector(C, J, K) → q
  22. Polygon(C, B, A) → poly1, h_1, a_1, g_1
  23. Rotate(q, If[0 < f ≤ 1, ((-f) * π / 2), -1.5707963267948966], C) → q'
  24. Dilate(B, If[1 < f ≤ 2, 2 - f, 0], M) → G'
  25. Rotate(B, If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G'_1
  26. Rotate(G', If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G''
  27. Angle(A, M, C) → α
  28. Rotate(G'_1, If[3 < f ≤ 4, ((f - 3) * α), α], M) → L
  29. Rotate(G'', If[3 < f ≤ 4, ((f - 3) * α), α], M) → G'''
  30. Rotate(B, 45°, C) → G'_2
  31. Angle(B, C, G'_2) → β
  32. Ray(C, G'_2) → m
  33. Segment(B, A) → n
  34. Intersect(m, n) → D
  35. OrthogonalLine(C, n) → r
  36. Intersect(r, n) → P
  37. Segment(C, P) → s
  38. Segment(C, M) → t
  39. Segment(C, D) → f_1
  40. Circle(P, (0.06 * n)) → c_1
  41. Intersect(c_1, s, 1) → O
  42. Intersect(c_1, n, 2) → P_1
  43. CircleSector(P, P_1, O) → d_1
  44. Dilate(C, If[1 < f ≤ 2, 2 - f, 0], D) → A'
  45. Segment(C, A') → l
  46. Circle(C, Radius[p]) → e_1
  47. Intersect(e_1, f_1) → Q,
  48. Intersect(e_1, j) → R,
  49. CircleSector(C, Q, R) → k_1
  50. Rotate(k_1, If[3 < f ≤ 4, ((-(f - 3)) * π / 4), ((-π)) / 4], C) → p_1
  51. Dilate(C, If[4.5 < f ≤ 5.5, 5.5 - f, 0], P) → A'_1
  52. Segment(C, A'_1) → i_1
  53. Rotate(d_1, If[6.25 < f ≤ 7.25, ((f - 6.25) * π / 2), π / 2], P) → q_1
  54. Dilate(B, If[8 < f ≤ 9, 9 - f, 0], M) → G'_3
  55. Rotate(B, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → G'_4
  56. Rotate(G'_3, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → S
  57. Dilate(A, If[8 < f ≤ 9, 9 - f, 0], M) → H'
  58. Segment(A, H') → j_1
  59. Angle(A, M, C) → γ
  60. Rotate(A, If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H'_1
  61. Rotate(H', If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H''
  62. Segment(H'_1, H'') → l_1
  63. Rotate(H'_1, If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → T
  64. Rotate(H'', If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → H'''
  65. Segment(T, H''') → m_1
  66. Intersect(e_1, s, 1) → U
  67. Intersect(e_1, f_1, 1) → V
  68. CircleSector(C, V, U) → r_1
  69. Angle(V, C, U) → δ
  70. Rotate(r_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * δ), (-δ)], C) → s_1
  71. Segment(A, P) → n_1
  72. Intersect(e_1, l, 1) → W
  73. Intersect(e_1, l_1, 1) → Z
  74. CircleSector(C, W, Z) → t_1
  75. Rotate(t_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * ((2 * π) - δ)), (-((2 * π) - δ))], C) → c_2