兰博基尼转向角

兰博基尼转向角
几何画板及绘图内容加载中,请稍等……
2023-06-01 22:41
本范例通过几何作图展示了多边形外角定理。通过旋转、平移、缩放等命令,构造了一个多边形,并通过调整顶点位置来演示多边形外角和的性质。使用了Polygon, Rotate, Dilate, Vector, Translate等命令。适合初中及以上学生学习多边形几何。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → C
  2. Polygon(C, D, 6) → poly1, f, H, g, h, i, j, k, E, F, G
  3. Rotate(pic1, pi / 3, D) → pic1'
  4. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], E) → D'
  5. Vector(D, D') → u
  6. Translate(pic1', u) → pic1''
  7. Ray(D, E) → l
  8. Rotate(pic1'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → pic1'''
  9. Dilate(E, If[2 < a ≤ 3, 3 - a, 0], F) → E'
  10. Vector(E, E') → v
  11. Translate(pic1''', v) → pic2
  12. Rotate(I, pi / 3, D) → I'
  13. Translate(I', u) → I''
  14. Rotate(I'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → I'''
  15. CircleSector(E, I'', I''') → c
  16. Rotate(pic2, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → pic2'
  17. Translate(I''', v) → J
  18. Rotate(J, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → J'
  19. CircleSector(F, J, J') → d
  20. Dilate(E', If[4 < a ≤ 5, 5 - a, 0], G) → E''
  21. Vector(E', E'') → w
  22. Translate(pic2', w) → pic2''
  23. Translate(J', w) → J''
  24. Ray(E, E') → m
  25. Rotate(pic2'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → pic2'''
  26. Rotate(J'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → J'''
  27. CircleSector(G, J'', J''') → e
  28. Ray(E', G) → n
  29. Dilate(G, If[6 < a ≤ 7, 7 - a, 0], H) → G'
  30. Vector(G, G') → b
  31. Translate(pic2''', b) → pic3
  32. Translate(J''', b) → K
  33. Rotate(pic3, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → pic3'
  34. Rotate(K, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → K'
  35. CircleSector(H, K, K') → p
  36. Ray(E'', H) → q
  37. Dilate(H, If[8 < a ≤ 9, 9 - a, 0], C) → H'
  38. Vector(H, H') → r
  39. Translate(pic3', r) → pic3''
  40. Translate(K', r) → K''
  41. Rotate(pic3'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → pic3'''
  42. Rotate(K'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → K'''
  43. CircleSector(C, K'', K''') → s
  44. Ray(H, C) → t
  45. Dilate(C, If[10 < a ≤ 11, 11 - a, 0], D) → C'
  46. Vector(C, C') → u_1
  47. Translate(pic3''', u_1) → pic4
  48. Translate(K''', u_1) → L
  49. Rotate(pic4, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → pic4'
  50. Rotate(L, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → L'
  51. Ray(C, D) → f_1
  52. CircleSector(C', L, L') → c_1
  53. Segment(C, D) → g_1
  54. Segment(D, E) → h_1
  55. Segment(E, F) → i_1
  56. Segment(F, G) → j_1
  57. Segment(G, H) → k_1
  58. Segment(H, C) → l_1
  59. Dilate(C, If[13 < a ≤ 14, 14 - a, 0], M) → C'_{1}
  60. Dilate(H, If[13 < a ≤ 14, 14 - a, 0], M) → H'_{1}
  61. Dilate(G, If[13 < a ≤ 14, 14 - a, 0], M) → G'_{1}
  62. Dilate(F, If[13 < a ≤ 14, 14 - a, 0], M) → F'
  63. Dilate(E, If[13 < a ≤ 14, 14 - a, 0], M) → E'_{1}
  64. Dilate(D, If[13 < a ≤ 14, 14 - a, 0], M) → D'_{1}
  65. Vector(H, H'_{1}) → v_1
  66. Vector(C, C'_{1}) → w_1
  67. Vector(D, D'_{1}) → a_1
  68. Vector(E, E'_{1}) → b_1
  69. Vector(F, F') → d_1
  70. Vector(G, G'_{1}) → e_1
  71. Translate(p, v_1) → p'
  72. Translate(s, w_1) → s'
  73. Translate(c, b_1) → c'
  74. Translate(d, d_1) → d'
  75. Translate(e, e_1) → e'
  76. Translate(c_1, a_1) → p_1
  77. CircleArc(E, I'', I''') → q_1
  78. CircleArc(F, J, J') → r_1
  79. CircleArc(G, J'', J''') → s_1
  80. CircleArc(H, K, K') → t_1
  81. CircleArc(C, K'', K''') → c_2
  82. CircleArc(D, I, I') → d_2

AI 绘图提示语参考

在直角坐标系中取两条坐标轴的交点作为中心,先构造以多边形某个顶点为起点的正多边形(边数取为6),并得到该多边形的各顶点。以其中一个顶点为旋转中心,按固定角度分段旋转、平移复制出外侧构型,使相邻位置形成连续的折转关系;再以若干对应顶点分别作扇形,用每个扇形的两条边所夹的角来刻画外角。最后从外侧各关键点向多边形方向作射线,整体呈现外角逐段展开、并对应于角和定理的几何图景。
以上提示语为根据原始绘图命令整理而来,仅供参考。