Dandelin 球体演示

GeoGebra 命令及参数

1. Cone(B_2, A_2, r) → a, c, b
2. Segment((0, 0, 0), (0, 0, 10)) → f
3. Point(f) → A
4. Segment(A, (0, 0, 10)) → g
5. Line(A_2, C) → i
6. Distance(A, i) → d
7. Sphere(A, d) → e
8. PointIn(e) → H
9. Line(A, H) → j
10. Vector(A, H) → u
11. OrthogonalLine(H, u, xOyPlane) → k
12. Rotate(k, π / 2, j) → k'
13. Sphere(H, 2) → l
14. Intersect(k', l) → I, J
15. Intersect(k, l) → K, L
16. Plane(J, L, K) → m
17. IntersectPath(m, a) → p
18. Focus(p) → O, P
19. OrthogonalLine(P, m) → q
20. Line((0, 0, 0), (0, 0, 1)) → s
21. Intersect(s, q) → B
22. Sphere(B, P) → o
23. Point(p) → M
24. Vertex(p) → N, R, S, T
25. IntersectPath(t, o) → c_1
26. IntersectPath(v, e) → d_1
27. Line(A_2, M) → f_1
28. Intersect(f_1, e) → U, V
29. Intersect(f_1, o) → W, Z
30. Dilate(A_2, If[0 < w ≤ 1, 1 - w, 0], U) → A'
31. Segment(A_2, A') → g_1
32. Dilate(U, If[1 < w ≤ 2, 2 - w, 0], M) → U'
33. Segment(U, U') → h_1
34. Dilate(M, If[2 < w ≤ 3, 3 - w, 0], W) → M'
35. Segment(M, M') → i_1
36. Angle(H, M, U) → α
37. Rotate(U, If[4 < w ≤ 5, ((w - 4) * α), α], M, Plane[M, U, H]) → U'_1
38. Rotate(U', If[4 < w ≤ 5, ((w - 4) * α), α], M, Plane[M, U, H]) → U''
39. Segment(U'_1, U'') → j_1
40. Angle(P, M, W) → β
41. Rotate(M, If[5 < w ≤ 6, ((-(w - 5)) * β), (-β)], M, Plane[P, W, M]) → M'_1
42. Rotate(M', If[5 < w ≤ 6, ((-(w - 5)) * β), (-β)], M, Plane[P, W, M]) → M''
43. Segment(M'_1, M'') → k_1
44. Line(N, R) → l_1
45. Sphere(N, j_1) → a_1
46. Intersect(l_1, a_1) → A_1, B_1
47. Dilate(H, If[7 < w ≤ 8, 8 - w, 0], N) → H'
48. Vector(H, H') → u_1
49. Translate(U'_1, u_1) → C_1
50. Translate(U'', u_1) → U'''
51. Segment(C_1, U''') → m_1
52. Angle(M, H, R) → γ
53. Rotate(C_1, If[7 < w ≤ 8, ((-(w - 7)) * γ), (-γ)], H', Plane[H', R, M]) → D_1
54. Rotate(U''', If[7 < w ≤ 8, ((-(w - 7)) * γ), (-γ)], H', Plane[H', R, M]) → E_1
55. Segment(D_1, E_1) → n_1
56. Dilate(P, If[8 < w ≤ 9, 9 - w, 0], R) → P'
57. Vector(P, P') → v_1
58. Translate(M'_1, v_1) → F_1
59. Translate(M'', v_1) → M'''
60. Segment(F_1, M''') → p_1
61. Angle(N, P, M) → δ
62. Rotate(F_1, If[8 < w ≤ 9, ((w - 8) * δ), δ], P', Plane[N, R, M]) → G_1
63. Rotate(M''', If[8 < w ≤ 9, ((w - 8) * δ), δ], P', Plane[N, R, M]) → H_1
64. Segment(G_1, H_1) → q_1