费马点 - 斐波那契点

费马点 - 斐波那契点
几何画板及绘图内容加载中,请稍等……
2013-09-06 16:23
这个范例演示了费马点的定义,即点M使得∠AMB=∠BMC=∠CMA=2π/3。通过构造三角形ABC的费马点,使用了Segment, Rotate, Polygon, Line, Intersect, Angle, Circle等命令。适合高中几何学习,帮助理解费马点的性质和构造方法。

GeoGebra 命令及参数

  1. Segment(A, M) → a
  2. Segment(B, M) → b
  3. Segment(C, M) → c
  4. Rotate(C, -1.0471975511965976, B) → A'
  5. Rotate(C, 1.0471975511965976, A) → B'
  6. Rotate(B, -1.0471975511965976, A) → C'
  7. Polygon(A, B, C') → poly1, c', a_1, b_1
  8. Polygon(A', B, C) → poly2, c_1, a', b_2
  9. Polygon(A, B', C) → poly3, c_2, a_2, b'
  10. Line(A, A') → e
  11. Line(B, B') → f
  12. Line(C, C') → g
  13. Intersect(e, f) → M'
  14. Rotate(M, 1.0471975511965976, A) → M_B
  15. Rotate(M, -1.0471975511965976, A) → M_C
  16. Segment(M, M_B) → h_B
  17. Segment(B', M_B) → h'_B
  18. Rotate(M, -1.0471975511965976, B) → M_A
  19. Segment(M, M_A) → j
  20. Segment(A', M_A) → k
  21. Segment(C', M_C) → l
  22. Segment(M, M_C) → m
  23. Rotate(M, 1.0471975511965976, C) → M'_A
  24. Segment(M, M'_A) → q
  25. Segment(A', M'_A) → r
  26. Rotate(M, -1.0471975511965976, C) → M'_B
  27. Segment(B', M'_B) → s
  28. Segment(M'_B, M) → t
  29. Rotate(M, 1.0471975511965976, B) → M'_C
  30. Segment(C', M'_C) → d_1
  31. Segment(M, M'_C) → e_1
  32. Angle(C, M, A) → α
  33. Angle(A, M, B) → β
  34. Angle(B, M, C) → γ
  35. Segment(A, M_C) → f_1
  36. Segment(B, M'_C) → g_1
  37. Segment(B, M_A) → h_1
  38. Segment(C, M'_A) → i_1
  39. Segment(A, M_B) → j_1
  40. Segment(C, M'_B) → k_1
  41. Circle(A, B, C') → p_1
  42. Circle(A', B, C) → q_1
  43. Circle(A, B', C) → r_1

AI 绘图提示语参考

绘制一个三角形ABC,然后构造Fermat点M,使得∠AMB=∠BMC=∠CMA=120°。首先通过旋转和构造多边形来找到M点,接着画出从M点到三角形各顶点的线段,最后通过旋转和交点找到Fermat点M。
以上提示语为根据原始绘图命令整理而来,仅供参考。