螺旋楼梯：几何变换与作图探索

GeoGebra 命令及参数

1. Intersect(zAxis, p_1) → B
2. Rotate(A, 30°, zAxis) → A'
3. CircleSector(B, A, A') → p
4. Line(A, zAxis) → i
5. Line(A', zAxis) → j
6. Rotate(A, 7.5°, zAxis) → A'_{1}
7. Rotate(A'_{1}, 7.5°, zAxis) → H
8. Rotate(H, 7.5°, zAxis) → H'
9. Line(A'_{1}, zAxis) → l
10. Line(H', zAxis) → m
11. Line(H, zAxis) → n
12. CurveCartesian(cos((3 * t)), sin((3 * t)), t, t, (-(((3 * pi)) / 4)), pi) → a_1
13. Point(a_1) → F
14. Point(a_1) → G
15. Point(a_1) → I
16. Point(m) → J
17. Point(a_1) → K
18. Segment(F, A) → a
19. Segment(G, A'_{1}) → b
20. Segment(I, H) → c
21. Segment(J, H') → d
22. Segment(K, A') → e
23. Vector(B, C) → u
24. Rotate(Translate[list1, u], 30°) → l1
25. Rotate(Translate[p, u], 30°) → f1
26. Rotate(Translate[f1, u], 30°) → f2
27. Rotate(Translate[f2, u], 30°) → f3
28. Rotate(Translate[f3, u], 30°) → f4
29. Rotate(Translate[f4, u], 30°) → f5
30. Rotate(Translate[f5, u], 30°) → f6
31. Rotate(Translate[f6, u], 30°) → f7
32. Rotate(Translate[f7, u], 30°) → f8
33. Rotate(Translate[f8, u], 30°) → f9
34. Rotate(Translate[f9, u], 30°) → f10
35. Rotate(Translate[f10, u], 30°) → f11
36. Rotate(Translate[f11, u], 30°) → f12
37. Rotate(Translate[f12, u], 30°) → f13
38. Rotate(Translate[f13, u], 30°) → f14
39. Rotate(Translate[f14, u], 30°) → f15
40. Rotate(Translate[f15, u], 30°) → f16
41. Rotate(Translate[f16, u], 30°) → f17
42. Rotate(Translate[f17, u], 30°) → f18
43. Rotate(Translate[f18, u], 30°) → f19
44. Rotate(Translate[f19, u], 30°) → f20
45. Rotate(Translate[f20, u], 30°) → f21
46. Rotate(Translate[f21, u], 30°) → f22
47. Rotate(Translate[f22, u], 30°) → f23
48. Sequence(Rotate[Translate[list1, Vector[(u * s)]], (30° * s)], s, 1, 22, 1) → m1
49. Point(zAxis) → D
50. Point(zAxis) → E
51. Segment(D, E) → g
52. PointIn(h) → L
53. PointIn(h) → M
54. PointIn(h) → N
55. PointIn(h) → O
56. Polygon(L, O, N, M) → q1, l_1, o, n_1, m_1
57. Intersect(zAxis, q) → P
58. Circle(P, 1, zAxis) → k
59. PointIn(q) → Q
60. PointIn(q) → R
61. PointIn(q) → S
62. PointIn(q) → T
63. Segment(Q, R) → r
64. Segment(R, T) → s
65. Segment(T, S) → t
66. Segment(Q, S) → f_1
67. Point(list2) → U
68. Point(s) → V
69. Segment(U, V) → g_1
70. Surface(g_1, 360°, zAxis) → v
71. Midpoint(R, Q) → W
72. Midpoint(f_1) → Z
73. Midpoint(t) → A_1
74. Polygon(V, A_1, T) → t1, t_1, v_1, a_{2}
75. Rotate(t1, -90°, g) → t1'
76. Rotate(t1', -90°, g) → t1''
77. Rotate(t1'', -90°, g) → t1'''
78. CurveCartesian((k2 * cos((k1 * t))), (k2 * sin((k1 * t))), t + 0.1, t, (-(pi / 2.8)), (9 * pi / 8)) → f