从半球区域到莫比乌斯带的双曲平面

GeoGebra 命令及参数

1. CircumcircleArc((0, 0, -1), (0, 1, 0), (0, 0, 1)) → d
2. Circle(P, π, xOyPlane) → c
3. Line(P, yAxis) → f
4. Sphere(P, π / 2) → g
5. Intersect(f, g) → G, H
6. Sphere(G, Width / 2) → j
7. Line(H, zAxis) → i
8. Line(G, zAxis) → h
9. Intersect(h, j) → I, J
10. Line(I, f) → n
11. Intersect(n, i) → K
12. Line(J, f) → k
13. Intersect(i, k) → L
14. Polygon(I, K, L, J) → Rectangle, i_1, k_4, l_1, j_1
15. Intersect(xOyPlane, Rectangle) → S, U
16. Line(S, U) → l
17. Intersect(zAxis, xAxis) → F
18. Semicircle(O, N, xOyPlane) → EquatorLineSphere
19. Sphere(F, P) → e
20. Segment(G, H) → q
21. Line(N, q) → f_1
22. Plane(f_1, zAxis) → p_1
23. IntersectPath(p_1, e) → r
24. Point(d) → M
25. Plane(M, xAxis) → q_1
26. IntersectPath(q_1, e) → FullLine
27. Intersect(FullLine, r, 2) → Q
28. CircumcircleArc(Q, P, M) → LineSphere_1
29. Point(LineSphere_1) → S_S
30. Plane(S_S, zAxis) → r_1
31. Intersect(r_1, EquatorLineSphere) → R, T
32. CurveCartesian(cos(t), sin(t), 0, t, 0, (2 * π)) → EquatorLineMobius
33. Point(EquatorLineMobius) → B
34. Point(EquatorLineMobius) → C
35. Point(EquatorLineMobius) → D
36. Point(EquatorLineMobius) → E
37. Surface((cos(u) * cos(v)), (cos(u) * sin(v)), sin(u), u, 0, (2 * π), v, 0, π) → Sphere
38. CurveCartesian(((1 + (Distance * cos(t / 2))) * cos(t)), ((1 + (Distance * cos(t / 2))) * sin(t)), (Distance * sin(t / 2)), t, 0, (4 * π)) → Equidistant
39. Point(EquatorLineSphere) → A
40. Angle(N, F, A, xOyPlane) → α
41. Circle(P, α, xOyPlane) → p
42. Circle(P, (2 * π) - α, xOyPlane) → p2
43. Surface(1 + (v * cos(u)), u, (v * sin(u)), u, ((-π)) / 2, π / 2, v, ((-Width)) / 2, Width / 2) → Twisted
44. Surface(sin(u), (cos(u) * cos(v)), (cos(u) * sin(v)), u, 0, π, v, 0, π) → HalfSphere
45. Rotate(N, (2 * α), F, xOyPlane) → A_m
46. Angle(N, F, A_m, xOyPlane) → δ
47. Angle(R, F, S_S) → γ
48. Angle(Q, F, S_S, q_1) → β
49. Angle(q_1, xOyPlane) → ε
50. CurveCartesian(sin(u), (cos(u) * cos(ε)), (cos(u) * sin(ε)), u, 0, π) → LineSphere
51. Surface(1 - (v * sin((Twisting * u))), u - π / 2, (v * cos((Twisting * u))), u, 0, π, v, ((-Width)) / 2, Width / 2) → Twist
52. Surface(((-cos(u)) * sin(v)), (cos(u) * cos(v)), sin(u), u, (-atan(Width / 2)) - π, atan(Width / 2) - π, v, 0, π) → SphericalStrip
53. Surface(((1 - Flattening) * ((-cos(u)) * sin(v))) + Flattening, (((1 - Flattening) * cos(u)) * cos(v)) + (Flattening * (v - π / 2)), ((1 - Flattening) * sin(u)) + (Flattening * tan((-u) + π)), u, (-atand(Width / 2)) - π, atand(Width / 2) - π, v, 0, π) → Flatten
54. Surface(1 + (v * cos(u)), ((1 + Prolonging) * u), (v * sin(u)), u, ((-π)) / 2, π / 2, v, ((-Width)) / 2, Width / 2) → ProlongTwisted
55. Surface(1 + (v * cos(u / 2)), u, (v * sin(u / 2)), u, (-π), π, v, ((-Width)) / 2, Width / 2) → Prolonged
56. Surface(((1 + (v * cos(u / 2))) * cos(u)), ((1 + (v * cos(u / 2))) * sin(u)), (v * sin(u / 2)), v, ((-Width)) / 2, Width / 2, u, 0, (2 * π)) → MobiusStrip
57. Surface(((1 + (v * cos(u / 2))) * cos((Glueing * u))), ((1 - Glueing) * u) + ((Glueing * (1 + (v * cos(u / 2)))) * sin((Glueing * u))), (v * sin(u / 2)), u, (-π), π, v, ((-Width)) / 2, Width / 2) → Glue
58. CurveCartesian(1, u - π / 2, (-tan(asin((cos(u) * sin(ε))))), u, 0, π) → LineRectangle
59. CurveCartesian(1 - (tan(asin((cos(u - π / 2) * sin(ε)))) * cos(u)), u, ((-tan(asin((cos(u - π / 2) * sin(ε))))) * sin(u)), u, ((-π)) / 2, π / 2) → LineTwisted
60. CurveCartesian(1 - (tan(asin((cos(u / 2 - π / 2) * sin(ε)))) * cos(u / 2)), u, ((-tan(asin((cos(u / 2 - π / 2) * sin(ε))))) * sin(u / 2)), u, (-π), π) → LineProlonged
61. CurveCartesian(((1 - (tan(asin((cos(u / 2 - π / 2) * sin(ε)))) * cos(u / 2))) * cos(u)), ((1 - (tan(asin((cos(u / 2 - π / 2) * sin(ε)))) * cos(u / 2))) * sin(u)), ((-tan(asin((cos(u / 2 - π / 2) * sin(ε))))) * sin(u / 2)), u, (-π), π) → LineMobius
62. IntersectPath(xOyPlane, Rectangle) → EquatorLineRectangle
63. Intersect(xOyPlane, p2) → V,
64. Intersect(l, c) → W, Z
65. Segment(W, Z) → EquatorLineProlonged
66. Circle(F, 1, xOyPlane) → Equator
67. Mirror(S_S, F) → S'
68. Mirror(A, F) → A'