球面丝线图：三维球体上的正弦曲线与旋转对称图案

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Circle((0, 0, 0), 4, Vector[(0, 1, 0)]) → d
3. Point(xAxis) → B
4. Rotate(B, 72°, A) → B'
5. Angle(B, A, B') → α
6. Rotate(Circle[(0, 0, 0), 4, Vector[(0, 1, 0)]], α) → e
7. Circle(A, B) → c
8. Rotate(B', 72°, A) → B''
9. Angle(B', A, B'') → β
10. Rotate(B'', 72°, A) → B'''
11. Angle(B'', A, B''') → γ
12. Rotate(B''', 72°, A) → C
13. Angle(B''', A, C) → δ
14. Intersect(zAxis, d, 1) → D
15. Rotate(Circle[(0, 0, 0), 4, Vector[(0, 1, 0)]], (2 * α)) → f
16. Rotate(Circle[(0, 0, 0), 4, Vector[(0, 1, 0)]], (3 * α)) → g
17. Rotate(Circle[(0, 0, 0), 4, Vector[(0, 1, 0)]], (4 * α)) → h
18. Intersect(d, e, 2) → E
19. Point(d, n / 360) → F
20. Point(e, (n - 180) / 360) → G
21. Sequence(Segment[Point[e, t / 360], Point[f, (270 - t) / 360]], t, 0, (2 * 180), a) → Liste2
22. Sequence(Segment[Point[f, t / 360], Point[g, (270 - t) / 360]], t, 0, (2 * 180), a) → Liste3
23. Sequence(Segment[Point[g, t / 360], Point[h, (270 - t) / 360]], t, 0, (2 * 180), a) → Liste4
24. Sequence(Segment[Point[h, t / 360], Point[d, (270 - t) / 360]], t, 0, (2 * 180), a) → Liste5
25. Mirror(Liste2, xOyPlane) → Liste2'
26. Mirror(Liste3, xOyPlane) → Liste3'
27. Sequence(Segment[Point[d, t / 360], Point[e, (270 - t) / 360]], t, 0, 360, a) → Liste1
28. Mirror(Liste1, xOyPlane) → Liste1'
29. Mirror(Liste5, xOyPlane) → Liste5'
30. Mirror(Liste4, xOyPlane) → Liste4'
31. Sequence(Point[d, t / 360], t, 0, 180, a) → l1
32. Sequence(Segment[Point[d, t / 360], Point[e, (270 - t) / 360]], t, 0, 360, a) → l2