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三圆柱螺旋线

三圆柱螺旋线
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2018-12-08 01:34
向量立体几何
该范例演示了三圆柱螺旋线的构造。涉及的核心数学概念包括圆柱、向量和三维几何。通过使用GeoGebra命令如Intersect、Circle、Surface、Rotate等，可以构造出三圆柱螺旋线。适合高中数学教学和学习三维几何的学生。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → A
  2. Circle(A, 1, zAxis) → c
  3. Cylinder(c, 1) → a, a_2, a_3
  4. Surface((u * cos(t)), (u * sin(t)), t / ((2 * π)), t, 0, (2 * π), u, 0, 1) → b
  5. Rotate(b, (2 * π / 3)) → d
  6. Rotate(b, (4 * π / 3)) → e
  7. CurveCartesian(t, 0, 1, t, 0, 1) → f
  8. Surface(f, (2 * π / 3), zAxis) → g
  9. CurveCartesian(cos(t), sin(t), t / ((2 * π)), t, 0, (2 * π)) → h
  10. Surface(h, (2 * π / 3), zAxis) → i
  11. Rotate(i, (2 * π / 3)) → i'
  12. Rotate(i, (4 * π / 3)) → i'_1
  13. Translate(Rotate[g, n, zAxis], Vector[(0, 0, n / ((2 * π)))]) → j
  14. Translate(Rotate[i, n, zAxis], Vector[(0, 0, n / ((2 * π)))]) → k
  15. Translate(Rotate[d, n, zAxis], Vector[(0, 0, n / ((2 * π)))]) → l
  16. Translate(Rotate[Rotate[d, (4 * π / 3), zAxis], n, zAxis], Vector[(0, 0, n / ((2 * π)))]) → m
  17. CurveCartesian(t, 0, 0, t, 0, 1) → o
  18. CurveCartesian((t * cos((-2 * π / 3))), (t * sin((-2 * π / 3))), 0, t, 0, 1) → p
  19. Surface(p, (2 * π / 3), zAxis) → q
  20. Translate(Rotate[q, (-n), zAxis], Vector[(0, 0, ((-n)) / ((2 * π)))]) → r
  21. Translate(Rotate[i'_1, (-n), zAxis], Vector[(0, 0, ((-n)) / ((2 * π)))]) → s
  22. Translate(Rotate[Rotate[d, (4 * π / 3), zAxis], (-n), zAxis], Vector[(0, 0, ((-n)) / ((2 * π)))]) → t
  23. Translate(Rotate[Rotate[d, (2 * π / 3), zAxis], (-n), zAxis], Vector[(0, 0, ((-n)) / ((2 * π)))]) → u
  24. Translate(r, Vector[(0, 0, 1)]) → r'
  25. Translate(j, Vector[(0, 0, -1)]) → j'
  26. Surface(CurveCartesian[(t * cos((2 * π / 3))), (t * sin((2 * π / 3))), 1, t, 0, 1], (2 * π / 3), zAxis) → v
  27. Translate(v, Vector[(0, 0, -1)]) → v'