菱形堆叠

菱形堆叠
几何画板及绘图内容加载中,请稍等……
2017-03-16 03:52
这个范例展示了菱形堆叠的几何挑战。核心数学概念包括菱形、正方形和几何变换。通过使用GeoGebra命令如点、中点、交点、线段、镜像、角度、多边形等,可以构造菱形堆叠。适合初中及以上学生或教师教学使用。

GeoGebra 命令及参数

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Point(Ray[B, B + (1, 0)]) → C
  3. Point(Ray[C, C + (1, 0)]) → D
  4. Point(Ray[D, D + (1, 0)]) → E
  5. Point(Ray[E, E + (1, 0)]) → F
  6. Midpoint(A, B) → G
  7. Intersect(Circle[A, d], Ray[G, G + (0, 1)]) → H,
  8. Point(Ray[H, H + (0, 1)]) → I
  9. Segment(A, I) → f
  10. Segment(B, I) → g
  11. Intersect(Circle[B, f], Ray[Midpoint[B, C], Midpoint[B, C] + (0, 1)]) → J,
  12. Intersect(Circle[C, f], Ray[Midpoint[D, C], Midpoint[D, C] + (0, 1)]) → K,
  13. Intersect(Circle[D, f], Ray[Midpoint[D, E], Midpoint[D, E] + (0, 1)]) → L, T
  14. Intersect(Circle[E, f], Ray[Midpoint[F, E], Midpoint[F, E] + (0, 1)]) → M,
  15. Segment(B, J) → h
  16. Segment(J, C) → i
  17. Segment(C, K) → j
  18. Segment(K, D) → k
  19. Segment(D, L) → l
  20. Segment(L, E) → m
  21. Segment(E, M) → n
  22. Segment(M, F) → p
  23. Mirror(B, Midpoint[I, J]) → B'
  24. Mirror(C, Midpoint[K, J]) → C'
  25. Mirror(D, Midpoint[K, L]) → D'
  26. Mirror(E, Midpoint[M, L]) → E'
  27. Segment(I, B') → q
  28. Segment(J, B') → r
  29. Segment(J, C') → s
  30. Segment(C', K) → t
  31. Segment(K, D') → a
  32. Segment(D', L) → b
  33. Segment(L, E') → c
  34. Segment(E', M) → e
  35. Mirror(J, Midpoint[B', C']) → J'
  36. Mirror(K, Midpoint[D', C']) → K'
  37. Mirror(L, Midpoint[D', E']) → L'
  38. Segment(B', J') → f_1
  39. Segment(J', C') → g_1
  40. Segment(C', K') → h_1
  41. Segment(K', D') → i_1
  42. Segment(D', L') → j_1
  43. Segment(L', E') → k_1
  44. Mirror(C', Midpoint[J', K']) → C''
  45. Mirror(D', Midpoint[L', K']) → D''
  46. Mirror(K', Midpoint[C'', D'']) → K''
  47. Segment(J', C'') → l_1
  48. Segment(C'', K') → m_1
  49. Segment(K', D'') → n_1
  50. Segment(D'', L') → p_1
  51. Segment(C'', K'') → q_1
  52. Segment(K'', D'') → r_1
  53. Angle(C'', K'', D'') → α
  54. Polygon(O, N, 4) → poly1, s_1, t_1, a_1, b_1, P, Q
  55. Circle(O, N) → d_1
  56. Circle(P, N) → e_1
  57. Intersect(d_1, c_1, 1) → R
  58. Intersect(e_1, c_1, 2) → S
  59. Segment(R, O) → f_2
  60. Segment(S, P) → g_2
  61. Angle(R, O, N) → β
  62. Angle(N, P, S) → γ
  63. Intersect(Circle[A, d'], Ray[G, G + (0, 1)]) → I',
  64. Segment(R, N) → h_2
  65. Angle(O, Q, P) → δ
  66. Segment(A, B) → i_2
  67. Segment(E, F) → j_2

AI 绘图提示语参考

绘制一个由多个菱形组成的堆叠图形。首先在直线上依次放置点A、B、C、D、E、F,然后构造每个菱形的顶点,通过镜像和交点找到每个菱形的其他顶点。最后连接这些顶点形成菱形,并通过镜像操作生成更多菱形,形成堆叠效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。