Shortest Path on a Sphere

GeoGebra Commands & Parameters

1. PointIn(b) → A
2. PointIn(b) → B
3. CircleArc(C, B, A) → c
4. PointIn(b) → D
5. Circle(A, D, B) → d
6. Plane(A, D, B) → e
7. Center(d) → E
8. OrthogonalLine(E, e) → f
9. CircleArc(E, A, B) → g
10. Line(B, C) → h
11. Intersect(h, b) → F, G
12. Circle(B, A, G) → k
13. Plane(A, B, C) → i
14. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], C) → B'
15. Vector(B, B') → u
16. Sphere(B, c) → l
17. Plane((0, 0, 0), (1, 0, 0), (3, 2, 0)) → m
18. Intersect(h, l) → H, I
19. Translate(B, u) → B'_1
20. Rotate(i, π / 2, Line[H, I]) → i'
21. OrthogonalLine(B, i') → n
22. Intersect(n, l) → J, K
23. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], J) → B'_2
24. Vector(B, B'_2) → v
25. Translate(k, v) → k'
26. Translate(C, v) → C'
27. Translate(A, v) → A'
28. Angle(A, C, B) → α
29. Rotate(A', If[0 < j ≤ 1, (j * α), α], C', i) → A''
30. Segment(B, B'_2) → p
31. CircleArc(C', A'', B'_2) → q
32. Sphere(B, g) → o
33. Rotate(A, π / 2, B, e) → C'_1
34. Line(B, C'_1) → r
35. Intersect(r, o) → L, M
36. Dilate(B, If[2 < j ≤ 3, 3 - j, 0], M) → B'_3
37. Vector(B, B'_3) → w
38. Translate(d, w) → d'
39. Translate(E, w) → E'
40. Translate(A, w) → A'_1
41. Angle(A'_1, E', B'_3) → β
42. Rotate(A'_1, If[2 < j ≤ 3, ((j - 2) * β), β], E', e) → N
43. Segment(B, B'_3) → s
44. CircleArc(E', N, B'_3) → t
45. Plane(B, J, M) → a_1
46. Angle(M, B, J) → γ
47. Rotate(J, If[4 < j ≤ 5, ((j - 4) * γ), γ], B, a_1) → J'
48. Segment(B, J') → f_1
49. Angle(A, D, B) → δ
50. Sphere(B, f_1) → b_1
51. Intersect(s, b_1) → P, O
52. Segment(O, M) → g_1
53. IntersectPath(m, b) → c_1
54. Plane(B, E, A) → d_1
55. Line(A, B) → h_1
56. OrthogonalLine(B, d_1) → i_1
57. Point(i_1) → Q
58. Plane(A, B, Q) → e_1
59. Mirror(B, e_1) → B'_4
60. Mirror(B'_3, e_1) → R
61. Mirror(B, e_1) → B'_5
62. Segment(P, M) → j_1