向量的球面表示

GeoGebra 命令及参数

1. Line(D6, D7) → i_1
2. Line(A, i_1) → j_1
3. Segment(D6, D7) → d_1
4. Segment(D7, D4) → d_2
5. Segment(D4, D5) → d_3
6. Segment(D5, D6) → d_4
7. Segment(D2, D3) → d_5
8. Segment(D3, D0) → d_6
9. Segment(D0, D1) → d_7
10. Segment(D1, D2) → d_8
11. Segment(D6, D2) → d_9
12. Segment(D5, D1) → d_{12}
13. Segment(D4, D0) → d_{11}
14. Segment(D7, D3) → d_{10}
15. Polygon(A - e / 5 * u - e / 5 * v, A + e / 5 * u - e / 5 * v, A + e / 5 * u + e / 5 * v, A - e / 5 * u + e / 5 * v) → Vieleck1, f, g, h, i
16. Segment(P_x, P_{xy}) → s2_x
17. Segment(P_y, P_{xy}) → s2_y
18. Segment(P, P_{xy}) → s_p
19. Segment(P_{yz}, P) → s3_x
20. Segment(P_{xz}, P) → s3_y
21. Segment(P_{xz}, P_y) → s2_z
22. Segment(P_{yz}, P_x) → s3_z
23. Segment(P_{yz}, P_z) → c
24. Segment(P_{xz}, P_z) → d
25. PolyLine(D0, P_y, P_{xy}, P) → szy
26. Point(szy) → Q_2
27. Vector(D0, Q_2) → vqy
28. Vector(A, P) → vp
29. Vector(A, P_{xy}) → e_1
30. Segment(A, P_y) → s_x
31. Segment(A, P_x) → s_y
32. Segment(A, P_z) → s_z
33. Polygon(A - e / 5 * u - e / 5 * w, A + e / 5 * u - e / 5 * w, A + e / 5 * u + e / 5 * w, A - e / 5 * u + e / 5 * w) → Vieleck2, j, k, l, m
34. Polygon(A - e / 5 * w - e / 5 * v, A + e / 5 * w - e / 5 * v, A + e / 5 * w + e / 5 * v, A - e / 5 * w + e / 5 * v) → Vieleck3, n, p, q, s
35. Midpoint(A, P) → Pos_1
36. Vector(A, M) → v_M
37. Vector(M, Q) → v_{MQ}
38. Vector(A, Q) → v_Q
39. Midpoint(M, Q) → Pos_2
40. Midpoint(A, Q) → Pos_3
41. Midpoint(A, M) → Pos_4
42. Sequence(Segment[A - e / 5 * u - e / 5 * v + i / 5 * v, A + e / 5 * u - e / 5 * v + i / 5 * v], i, 0, 2 * e) → Liste1
43. Sequence(Segment[A - e / 5 * v - e / 5 * u + i / 5 * u, A + e / 5 * v - e / 5 * u + i / 5 * u], i, 0, 2 * e) → Liste2
44. Sequence(Segment[A - e / 5 * w - e / 5 * v + i / 5 * v, A + e / 5 * w - e / 5 * v + i / 5 * v], i, 0, 2 * e) → Liste3
45. Sequence(Segment[A - e / 5 * v - e / 5 * w + i / 5 * w, A + e / 5 * v - e / 5 * w + i / 5 * w], i, 0, 2 * e) → Liste4
46. Sequence(Segment[A + e / 5 * u - e / 5 * w + i / 5 * w, A - e / 5 * u - e / 5 * w + i / 5 * w], i, 0, 2 * e) → Liste5
47. Sequence(Segment[A - e / 5 * w - e / 5 * u + i / 5 * u, A + e / 5 * w - e / 5 * u + i / 5 * u], i, 0, 2 * e) → Liste6
48. Segment(B_1, B_6) → bb_1
49. Segment(B_8, B_9) → bb_2
50. Segment(B_{10}, B_{11}) → bb_3
51. Segment(B_4, B_7) → bb_4
52. Polygon(B, B_2, B_{13}, B_{12}) → Vieleck4, b_1, b_2, b_{13}, b_{12}
53. Vector(A - e / 5 * v, Pos_y) → v_2
54. Vector(A - e / 5 * u, Pos_x) → u_2
55. Vector(A - e / 5 * w, Pos_z) → w_2