球面三角形：特殊直角三角形

GeoGebra 命令及参数

1. Sphere((0, 0, 0), 1) → a
2. PointIn(a) → A
3. PointIn(a) → B_1
4. Plane(O, A, B_1) → b
5. IntersectPath(b, a) → c
6. Point(c) → B
7. OrthogonalLine(O, b) → d
8. Plane(A, d) → e
9. IntersectPath(e, a) → f
10. OrthogonalLine(O, e) → g
11. Intersect(g, a, 2) → D
12. Intersect(d, a, 2) → E
13. CurveCartesian((x(A) * cos(t)) + (x(D) * sin(t)), (y(A) * cos(t)) + (y(D) * sin(t)), (z(A) * cos(t)) + (z(D) * sin(t)), t, 0, Angle[A, O, B]) → h
14. Line(O, B) → i
15. Rotate(A, -60*°, i) → A'
16. Plane(A', i) → j
17. IntersectPath(j, a) → k
18. Intersect
19. Intersect(f, k, 2) → C
20. OrthogonalLine(O, j) → l
21. Plane(C, l) → m
22. OrthogonalLine(O, m) → n
23. CurveCartesian((x(A) * cos(t)) + (x(E) * sin(t)), (y(A) * cos(t)) + (y(E) * sin(t)), (z(A) * cos(t)) + (z(E) * sin(t)), t, 0, Angle[C, O, A]) → p
24. Line(O, A) → q
25. OrthogonalPlane(A, q) → r
26. IntersectPath(b, r) → s
27. IntersectPath(e, r) → t
28. Point(t) → G
29. Point(s) → H
30. Angle(H, A, G) → α
31. OrthogonalLine(O, m) → a_1
32. Intersect(a_1, a, 1) → F
33. CurveCartesian((x(C) * cos(t)) + (x(F) * sin(t)), (y(C) * cos(t)) + (y(F) * sin(t)), (z(C) * cos(t)) + (z(F) * sin(t)), t, 0, Angle[C, O, B]) → o
34. OrthogonalPlane(B, i) → u
35. IntersectPath(b, u) → b_1
36. IntersectPath(j, u) → c_1
37. Point(c_1) → I
38. Point(b_1) → J
39. Angle(I, B, J) → β