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Steffen全等图形动态演示

Steffen全等图形动态演示
几何画板及绘图内容加载中，请稍等……
2019-03-12 05:41
最值优化参数方程几何作图
①本范例动态演示Steffen全等图形的构造与性质；②涉及核心数学概念：全等、平移、参数曲线、减法、最值优化、置信区间、统计特征；③作图要点：运用了Segment, Circle, Point, Angle, Rotate, Ray, Intersect, Line, Dilate, Vector, Polygon, Translate, If, Mirror等GeoGebra命令与对象；④适合高中及以上数学学习者和教师用于理解几何变换与优化问题。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Circle(D, (k * a)) → d
  5. Point(d) → E
  6. Segment(D, E) → e
  7. Circle(E, (k * b)) → f
  8. Angle(A, B, C) → α
  9. Rotate(D, α, E) → D'
  10. Angle(D, E, D') → β
  11. Ray(E, D') → g
  12. Intersect(f, g, 1) → F
  13. Angle(C, A, B) → γ
  14. Rotate(E, (-γ), D) → E'
  15. Angle(E', D, E) → δ
  16. Ray(D, E') → h
  17. Segment(D, E') → i
  18. Segment(E', E) → j
  19. Line(E, D') → l
  20. Line(E, D') → n
  21. Circle(D, (k * c)) → p
  22. Ray(D, E') → m
  23. Intersect(p, m, 1) → G
  24. Segment(E, G) → q
  25. Segment(D, G) → r
  26. Dilate(D, If[0 < s ≤ 1, 1 - s], A) → D'_1
  27. Vector(D, D'_1) → u
  28. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  29. Polygon(D, E, G) → poly2, g_1, d_1, e_1
  30. Translate(D, u) → D'_2
  31. Translate(E, u) → E'_1
  32. Translate(G, u) → G'
  33. Polygon(D'_2, E'_1, G') → poly2', g', d'_2, e'_1
  34. Vector(D, A) → v
  35. Translate(D, v) → D'_3
  36. Translate(E, v) → E'_2
  37. Translate(G, v) → G'_1
  38. Polygon(D'_3, E'_2, G'_1) → poly2'_1, g'_1, d'_3, e'_2
  39. Segment(D'_1, G') → t
  40. Segment(E'_1, D'_1) → h_1
  41. Segment(A, G'_1) → i_1
  42. Segment(G'_1, E'_2) → j_1
  43. Segment(E'_2, A) → k_1
  44. Angle(C, A, E'_2) → ε
  45. If(ε > γ, ε - γ, γ - ε) → ζ
  46. Rotate(D'_3, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → H
  47. Rotate(E'_2, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → I
  48. Rotate(G'_1, If[1 < s ≤ 2, ((-(s - 1)) * ζ), (-ζ)], A) → J
  49. Polygon(H, I, J) → poly3, j_2, h_2, i_2
  50. Segment(A, J) → l_1
  51. Segment(A, I) → m_1
  52. Segment(I, J) → n_1
  53. Dilate(J, If[2 < s ≤ 3, 3 - s, 0], C) → J'
  54. Dilate(I, If[2 < s ≤ 3, 3 - s, 0], B) → I'
  55. Segment(I', J') → p_1
  56. Angle(A, I, J) → θ
  57. Angle(D'_2, E'_1, G') → ι
  58. Angle(J, A, I) → λ
  59. Angle(G', D'_1, E'_1) → μ
  60. Polygon(A, J', I') → poly4, i', a_2, j'
  61. Segment(G'_1, E'_2) → q_1
  62. Segment(G', E'_1) → f_1
  63. Rotate(D'_3, ((s - 1) * ζ), A) → K
  64. Rotate(D'_3, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → L
  65. Rotate(E'_2, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → M
  66. Rotate(G'_1, If[1 < s ≤ 2, ((s - 1) * ζ), ζ], A) → N
  67. Polygon(L, M, N) → poly5, n_2, l_2, m_2
  68. Dilate(M, If[2 < s ≤ 3, 3 - s, 0], B) → M'
  69. Dilate(N, If[2 < s ≤ 3, 3 - s, 0], C) → N'
  70. Segment(M', N') → r_1
  71. Polygon(A, M', N') → poly6, n', a_3, m'
  72. Angle(A, M', N') → ο
  73. Angle(A, M, N) → ρ
  74. Segment(A, M) → t_1
  75. Segment(M, N) → b_2
  76. Segment(A, N) → c_2
  77. Angle(B, A, C) → σ
  78. Angle(G, E, D) → τ
  79. Angle(N, M, A) → υ
  80. Angle(N', M', A) → ϕ
  81. Line(E, G) → s_1
  82. Mirror(D, q) → D'_4
  83. Mirror(E, q) → E'_3
  84. Mirror(G, q) → G'_2
  85. Polygon(D'_4, E'_3, G'_2) → poly2'_2, g'_2, d'_4, e'_3
  86. Segment(E, D'_4) → f_2
  87. Segment(D'_4, G) → g_2