Surface Area of a Sphere by Mark Dabbs

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Line(A, A') → b
3. Sphere(O, A) → a
4. Line(B, B') → c
5. Line(C, C') → d
6. Circle(A, C, A') → e
7. Circle(B, C, B') → f
8. Rotate(C, (-α), b) → D
9. Circle(A, B, A') → g
10. CircumcircleSector(A, D, A') → Slice
11. Point(Slice) → E
12. Point(Slice) → F
13. Segment(E, F) → i
14. Midpoint(E, F) → G
15. Segment(G, O) → j
16. Segment(D, O) → k
17. Line(F, k) → l
18. Line(G, k) → m
19. Line(E, k) → n
20. Line(E, b) → p
21. Intersect(p, l) → H
22. Intersect(m, p) → I
23. Intersect(b, n) → J
24. Intersect(b, m) → K
25. Intersect(b, l) → L
26. Segment(E, H) → q
27. Segment(F, L) → r
28. Segment(G, K) → s
29. Segment(E, J) → t
30. Segment(E, F) → SegTrace
31. Circle(b, F) → c_1
32. Circle(b, E) → d_1
33. Intersect
34. Intersect(c_1, e) → M, N, ,
35. Intersect
36. Intersect(d_1, e) → P, Q, ,
37. Intersect
38. Intersect(c_1, g) → R, S, ,
39. Intersect
40. Intersect(d_1, g) → T, U, ,
41. Rotate(C, (-α), b) → C'_1
42. Rotate(c_1, (-(α / 2)), b) → e_1
43. Rotate(M, (-hα), b) → M'
44. Rotate(P, (-hα), b) → P'
45. CircumcircleArc(M, M', F) → f_1
46. CircumcircleArc(P, P', E) → g_1
47. Point(SegTrace) → V
48. Point(t) → W
49. Ray(F, E) → a_1
50. Intersect(a_1, b) → Z
51. Distance(J, P) → topRad
52. Point(b) → A_1
53. Point(b) → B_1
54. Cone(J, Z, topRad) → b_1, h_1, EndCone
55. Circle(b, F) → k_1
56. Distance(Z, L) → h_D
57. Distance(F, Z) → distanceFZ
58. Intersect(xAxis, yAxis) → C_1
59. Distance(E, F) → l_D
60. Rotate(D_1, θ, C_1) → F_1
61. Rotate(E_1, θ, C_1) → G_1
62. CircleArc(C_1, D_1, F_1) → h
63. CircleSector(C_1, E_1, G_1) → p_1
64. Segment(D_1, C_1) → i_1
65. Segment(F_1, C_1) → j_1
66. Sequence(Segment[Rotate[D_1, k°, C_1], Rotate[E_1, k°, C_1]], k, 1, Maxk) → list1