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非对称螺旋桨

非对称螺旋桨
几何画板及绘图内容加载中，请稍等……
2017-08-10 20:30
测试改名0多边形几何作图
①本范例演示非对称螺旋桨的几何构造与动态变化；②涉及相似三角形、三角形、散点图、随机实验、垂心、正态分布、整数等核心数学概念；③构造过程中运用了多边形、旋转、射线、直线、交点、线段、角度、中点、点在对象内等 GeoGebra 命令与对象；④适合高中数学教学，用于展示几何变换与数据分析的结合应用。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Rotate(C', β, B) → C''
  3. Ray(B, C'') → m
  4. Line(C, B') → k_2
  5. Rotate(A, (-β), B') → A'_1
  6. Ray(B', A'_1) → i
  7. Rotate(B', α, A) → B''
  8. Ray(A, B'') → j
  9. Intersect(i, j) → C_1
  10. Rotate(B, (-Angle[A, C_1, B']), C') → B'_1
  11. Ray(C', B'_1) → n
  12. Intersect(m, n) → A_1
  13. Line(A_1, C') → n_2
  14. Segment(A, B') → f
  15. Segment(C', B) → g
  16. Segment(C, A') → h
  17. Segment(A, C_1) → k
  18. Segment(B', C_1) → l
  19. Segment(C', A_1) → p
  20. Segment(A_1, B) → q
  21. Rotate(A', Angle[A, C_1, B'], C) → A''
  22. Ray(C, A'') → r
  23. Rotate(C, (-α), A') → C'_1
  24. Ray(A', C'_1) → s
  25. Intersect(r, s) → B_1
  26. Segment(C, B_1) → t
  27. Segment(A', B_1) → d
  28. Segment(A_1, C_1) → e
  29. Segment(B_1, C_1) → f_1
  30. Segment(A_1, B_1) → g_1
  31. Angle(B, A_1, C') → γ
  32. Angle(B', A, C_1) → δ
  33. Angle(B_1, A', C) → ε
  34. Angle(C_1, B', A) → ζ
  35. Angle(C, B_1, A') → η
  36. Angle(C', B, A_1) → θ
  37. Angle(B_1, A_1, C_1) → ι
  38. Rotate(A, Angle[A, C_1, B'], C') → A'_2
  39. Ray(C', A'_2) → h_1
  40. Rotate(C', (-α), A) → C''_1
  41. Ray(A, C''_1) → i_1
  42. Intersect(h_1, i_1) → B_2
  43. Segment(C', B_2) → j_1
  44. Segment(B_2, A) → k_1
  45. Segment(A, C') → l_1
  46. Rotate(B', (-Angle[A, C_1, B']), C) → B''_1
  47. Ray(C, B''_1) → m_1
  48. Rotate(C, β, B') → C'_2
  49. Ray(B', C'_2) → n_1
  50. Intersect(m_1, n_1) → A_2
  51. Segment(B', A_2) → p_1
  52. Segment(C, A_2) → q_1
  53. Segment(C, B') → r_1
  54. Rotate(B, α, A') → B'_2
  55. Ray(A', B'_2) → s_1
  56. Rotate(A', (-β), B) → A''_1
  57. Ray(B, A''_1) → t_1
  58. Intersect(s_1, t_1) → C_2
  59. Segment(B, C_2) → a_1
  60. Segment(C_2, A') → b_1
  61. Segment(A', B) → c_1
  62. Angle(B_1, A_1, C_1) → κ
  63. Angle(C_1, B_1, A_1) → μ
  64. Angle(C', B_2, A) → ν
  65. Angle(C, B', A_2) → ξ
  66. Angle(C_2, B, A') → ο
  67. Angle(B_2, A, C') → ρ
  68. Angle(B', A_2, C) → σ
  69. Angle(B, A', C_2) → τ
  70. Segment(B_2, C_2) → d_1
  71. Segment(C_2, A_2) → e_1
  72. Segment(A_2, B_2) → f_2
  73. Midpoint(A_1, B_1) → E_1
  74. Midpoint(B_1, C_1) → F_1
  75. Segment(A_1, F_1) → g_2
  76. Segment(C_1, E_1) → h_2
  77. Intersect(g_2, h_2) → G
  78. Midpoint(B_2, A_2) → H
  79. Midpoint(A_2, C_2) → I
  80. Segment(B_2, I) → i_2
  81. Segment(C_2, H) → j_2
  82. Intersect(i_2, j_2) → J
  83. PointIn(poly1) → K
  84. Line(A, C') → l_2
  85. Line(C, B_1) → m_2
  86. Intersect(l_2, m_2) → E
  87. Intersect(k_2, n_2) → F
  88. Angle(C', F, C) → υ
  89. Angle(C', E, C) → ϕ
  90. Angle(A_1, C', A) → χ
  91. Angle(B', C, B_1) → ψ
  92. Midpoint(B, B') → P
  93. Segment(B', B) → p_2
  94. Segment(C', C) → q_2
  95. Segment(A', A) → r_2