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使用复数演示X+Y+Z

使用复数演示X+Y+Z
几何画板及绘图内容加载中，请稍等……
2017-04-22 07:41
向量复数几何作图
①本范例通过复数演示三角形X+Y+Z的几何意义；②涉及核心数学概念包括复数、向量、角度和几何作图；③构造过程中运用了Intersect（交点）、Vector（向量）、Point（点）、Angle（角度）、Sequence（数列）、If（条件判断）等GeoGebra命令；④适合高中及以上数学学习者，用于理解复数与几何图形的关联及作图技巧。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Point(xAxis) → C
  4. Vector(C, D) → v
  5. Point(xAxis) → E
  6. Vector(E, F) → w
  7. Angle(E, A, B) → α
  8. Angle(E, C, D) → β
  9. Point(xAxis) → z_1
  10. Angle(z_1, E, F) → γ
  11. Sequence(Segment[(0, q), (3, q)], q, 0, 3) → list1
  12. Sequence(Segment[(q, 0), (q, 3)], q, 0, 3) → list2
  13. If(1 ≤ a < 2, Vector[(0, 0), Dilate[(0, 0), 2 - a, (1, 1)]], Vector[(1, 1)]) → b
  14. If(3 ≤ a < 4, Vector[(1, 1), Dilate[(1, 1), 4 - a, (0, 2)]], Vector[(1, 1), (0, 2)]) → c
  15. If(4 ≤ a < 5, Vector[(0, 2), Dilate[(0, 2), 5 - a, (-1, 3)]], Vector[(0, 2), (-1, 3)]) → d
  16. If(6 ≤ a < 7, Vector[(0, 0), Dilate[(0, 0), 7 - a, (-1, 3)]], Vector[(0, 0), (-1, 3)]) → e
  17. If(9 ≤ a < 10, Vector[(-4, 2), Dilate[(-4, 2), 10 - a, (-7, 1)]], Vector[(-4, 2), (-7, 1)]) → g
  18. If(8 ≤ a < 9, Vector[(-1, 3), Dilate[(-1, 3), 9 - a, (-4, 2)]], Vector[(-1, 3), (-4, 2)]) → f
  19. If(10 ≤ a < 11, Vector[(-7, 1), Dilate[(-7, 1), 11 - a, (-10, 0)]], Vector[(-7, 1), (-10, 0)]) → h
  20. If(12 ≤ a < 13, Vector[Dilate[(0, 0), 13 - a, (-10, 0)]], Vector[(-10, 0)]) → i
  21. Angle((1, 0), (0, 0), (1, 1)) → δ
  22. Angle((1, 1), (0, 0), (-1, 3)) → ε
  23. Angle((-1, 3), (0, 0), (-10, 0)) → ζ