虚数轨道

虚数轨道
几何画板及绘图内容加载中,请稍等……
2016-01-02 10:24
所属专题 Complex Math
①这个范例演示了虚数在复平面上的运动轨迹;②涉及的核心数学概念包括复数、向量、变换和轨迹;③作图要点使用了GeoGebra命令Polygon(多边形)、Segment(线段)、Vector(向量)、Translate(平移)、Intersect(交点);④适合高中数学学习,用于理解复数的几何意义和动态变化。

GeoGebra 命令及参数

  1. Polygon(z_1, z_2, z_τ) → poly1, z_3, z_4, z_5
  2. Segment(z_6, z_2) → a
  3. Segment(z_6, z_τ) → b
  4. Segment(z_6, z_1) → c
  5. Segment(z_2, z_7) → d
  6. Segment(z_7, z_6) → e
  7. Segment(z_1, z_7) → i
  8. Polygon(z_1, z_6, z_τ) → poly2, z_8, z_9, z_{10}
  9. Polygon(z_τ, z_2, z_6) → poly3, z_{11}, z_{12}, z_{13}
  10. Polygon(z_6, z_7, z_2) → poly4, z_{14}, z_{15}, z_{16}
  11. Polygon(z_7, z_1, z_6) → poly5, z_{17}, z_{18}, z_{19}
  12. Vector(A, B) → u
  13. Translate(z_1, u) → z_{9}
  14. Translate(z_2, u) → z_{20}
  15. Translate(z_τ, u) → z_{21}
  16. Polygon(z_{9}, z_{20}, z_{21}) → poly1', z_{22}, z_{23}, z_{24}
  17. Vector(C, D) → v
  18. Translate(z_1, v) → z_{25}
  19. Translate(z_6, v) → z_{26}
  20. Translate(z_τ, v) → z_{27}
  21. Polygon(z_{25}, z_{26}, z_{27}) → poly2', z_{28}, z_{29}, z_{30}
  22. Vector(E, F) → w
  23. Translate(z_6, w) → z_{31}
  24. Translate(z_7, w) → z_{32}
  25. Translate(z_2, w) → z_{33}
  26. Polygon(z_{31}, z_{32}, z_{33}) → poly4', z_{34}, z_{35}, z_{36}
  27. Vector(G, H) → j
  28. Translate(z_7, j) → z_{37}
  29. Translate(z_1, j) → z_{38}
  30. Translate(z_6, j) → z_{39}
  31. Polygon(z_{37}, z_{38}, z_{39}) → poly5', z_{40}, z_{41}, z_{42}
  32. Intersect(z_{28}, z_{29}) → I
  33. Intersect(z_{41}, z_{42}) → J
  34. Segment(I, J) → l
  35. Intersect(z_{28}, z_{30}) → K
  36. Intersect(z_{40}, z_{41}) → L
  37. Segment(K, L) → m
  38. Intersect(z_{29}, z_{30}) → M
  39. Intersect(z_{40}, z_{42}) → N
  40. Segment(M, N) → n
  41. Intersect(z_{22}, z_{24}) → O
  42. Intersect(z_{34}, z_{36}) → P
  43. Segment(O, P) → q
  44. Intersect(z_{23}, z_{24}) → Q
  45. Segment(Q, P) → r
  46. Intersect(xAxis, yAxis) → R
  47. Intersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → S
  48. Intersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → T
  49. Segment(R, z_τ) → s
  50. Segment(z_{46}, z_{44}) → a_1
  51. Segment(z_{45}, z_{43}) → b_1