十个动点诱导球面上的两个对跖几何中心

GeoGebra 命令及参数

1. Polygon({B01, B02, B04, B03}) → q2
2. PointIn(q2) → B1
3. PointIn(q2) → B2
4. PointIn(q2) → B3
5. PointIn(q2) → B4
6. PointIn(q2) → B5
7. PointIn(q2) → B6
8. PointIn(q2) → B7
9. PointIn(q2) → B8
10. PointIn(q2) → B9
11. PointIn(q2) → B10
12. First({P1, P2, P3, P4, P5, P6, P7, P8, P9, P10}, n) → lP
13. Polygon({((-π), ((-π)) / 2), ((-π), π / 2), (π, π / 2), (π, ((-π)) / 2)}) → q
14. PointIn(q) → A_2
15. Sphere(O, R) → b
16. Circle(O, R, xOyPlane) → c
17. Angle(sumunitA_q, vA) → αA
18. Zip(Segment[A, p], p, lP) → seg
19. Sum(seg) → sum_seg
20. PolyLine({((-π), ((-π)) / 2), ((-π), π / 2), (π, π / 2), (π, ((-π)) / 2), ((-π), ((-π)) / 2)}) → q1
21. Flatten(Sequence[Sequence[((-π) + ((2 * π / na) * i), ((-π)) / 2 + (π / na * j)), j, 1, na - 1], i, 1, na - 1]) → ltest_2
22. Zip((R; x(a); y(a)), a, ltest_2) → ltest_3
23. Zip((arg(a), alt(a)), a, lP) → lP_2
24. Textfield(n) → InputBox11
25. KeepIf(x > 0, Sequence[If[abs(Element[αsad, i] - π) < 0.001 ∨ abs(Element[αsad, i]) < 0.001, i, 0], i, 1, Length[αsad]]) → Nαsad
26. Textfield(R) → InputBox1
27. Textfield(na) → InputBox2
28. Function(f01, (-π), π, ((-π)) / 2, π / 2) → f0
29. Sequence(Vector[(1.3 * Point[O, Vector[Element[sumunit_sad, i]]]), (1.5 * Point[O, Vector[Element[sumunit_sad, i]]])], i, 1, Length[sumunit_sad]) → sumunit_sad1
30. Zip((Length[a]; arg(a); alt(a)), a, lP) → lPsphere
31. CurveCartesian((-π) + ((2 * π) * a), ((-π)) / 2, f0((-π) + ((2 * π) * a), ((-π)) / 2), a, 0, 1) → par1
32. CurveCartesian((-π) + ((2 * π) * a), π / 2, f0((-π) + ((2 * π) * a), π / 2), a, 0, 1) → par2
33. CurveCartesian(π, ((-π)) / 2 + (π * a), f0(π, ((-π)) / 2 + (π * a)), a, 0, 1) → par4
34. Zip(Text["d_{" + (a) + "}", (A + Element[lP, a]) / 2], a, 1…n) → lPtxt
35. CurveCartesian((-π), ((-π)) / 2 + (π * a), f0((-π), ((-π)) / 2 + (π * a)), a, 0, 1) → par3
36. Zip((x(a), y(a)), a, lP) → lP_{Gr1}
37. First({aP1, aP2, aP3, aP4, aP5, aP6, aP7, aP8, aP9, aP10}, n) → Output
38. Vector((1.3 * A), (1.5 * A)) → lvA_a
39. Zip(Segment[F_o, p], p, lP) → segF_o
40. Sum(segF_o) → sum_segFo
41. Sum(seg^(2)) → sum_q
42. Vector((1.3 * A), (1.1 / 1.7 * Point[O, Vector[(-sumunitA_q)]])) → l1A_q
43. Vector((1.3 * Zq), (1.5 * Zq)) → lvZq
44. Vector((1.3 * Zq'), (1.5 * Zq')) → lvZq'
45. Vector((1.3 * Zq), (1.1 / 1.7 * Point[O, Vector[(-sumunitZ_q)]])) → l1Z_q
46. Vector((1.3 * Zq'), (1.1 / 1.7 * Point[O, Vector[(-sumunitZ_q')]])) → l1Z_q'
47. Segment(Zq, Zq') → antipodalAchse
48. Segment(Zq, Cm_0) → segZq
49. Segment(Zq', Cm_0) → segZq'
50. Zip(Segment[Cm_0, p], p, lP) → segC_m
51. Sum(Zip[a^(2), a, segC_m]) → sum_segCmoq
52. Zip(Text["P_{" + (a) + "}", b + (0.1, 0.1)], a, 1…n, b, lP_2) → l1
53. Zip(Segment[(x(a), y(a), -1), (x(a), y(a), f0(x(a), y(a)))], a, {((-π), ((-π)) / 2), ((-π), π / 2), (π, π / 2), (π, ((-π)) / 2)}) → lseg
54. Translate(q, Vector[(0, 0, -1)]) → q'
55. RotateText(txt, 90°) → txt1