球面三角形的中线与重心

GeoGebra 命令及参数

1. Sphere((0, 0, 0), 1) → a
2. PointIn(a) → A
3. PointIn(a) → B
4. PointIn(a) → C
5. Plane(A, O, B) → b
6. Plane(A, O, C) → c
7. Plane(C, O, B) → d
8. IntersectPath(b, a) → e
9. IntersectPath(d, a) → f
10. IntersectPath(c, a) → g
11. Midpoint(A, B) → D
12. Midpoint(B, C) → E
13. Midpoint(C, A) → F
14. OrthogonalLine(O, g) → i
15. OrthogonalLine(O, e) → j
16. OrthogonalLine(O, f) → h
17. Plane(E, h) → k
18. Plane(D, j) → l
19. Plane(F, i) → m
20. IntersectPath(l, a) → p
21. IntersectPath(m, a) → q
22. IntersectPath(k, a) → r
23. Intersect(f, r, 2) → G
24. Intersect(g, q, 2) → H
25. Intersect(p, e, 1) → I
26. Plane(A, O, G) → n
27. OrthogonalLine(O, n) → s
28. Plane(G, s) → o
29. OrthogonalLine(O, o) → t
30. Intersect(t, a, 2) → J
31. CurveCartesian((x(G) * cos(t)) + (x(J) * sin(t)), (y(G) * cos(t)) + (y(J) * sin(t)), (z(G) * cos(t)) + (z(J) * sin(t)), t, 0, Angle[G, O, A]) → u
32. Plane(O, I, C) → v
33. OrthogonalLine(O, v) → a_1
34. Plane(I, a_1) → w
35. OrthogonalLine(O, w) → b_1
36. Intersect(b_1, a, 2) → K
37. CurveCartesian((x(I) * cos(t)) + (x(K) * sin(t)), (y(I) * cos(t)) + (y(K) * sin(t)), (z(I) * cos(t)) + (z(K) * sin(t)), t, 0, Angle[I, O, C]) → c_1
38. Plane(B, O, H) → d_1
39. OrthogonalLine(O, d_1) → e_1
40. Plane(H, e_1) → f_1
41. OrthogonalLine(O, f_1) → g_1
42. Intersect(g_1, a, 2) → L
43. CurveCartesian((x(H) * cos(t)) + (x(L) * sin(t)), (y(H) * cos(t)) + (y(L) * sin(t)), (z(H) * cos(t)) + (z(L) * sin(t)), t, 0, Angle[B, O, H]) → h_1