旧灯笼：三维立体与几何构造的数学演示

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Midpoint(C, A) → E
3. Midpoint(f) → F
4. Midpoint(A, F) → G
5. Midpoint(F, B) → H
6. Midpoint(h) → I
7. Midpoint(I, C) → J
8. Midpoint(I, D) → K
9. Midpoint(g) → L
10. Midpoint(i) → M
11. Midpoint(C, L) → N
12. Midpoint(L, B) → O
13. Midpoint(A, M) → P
14. Midpoint(M, D) → Q
15. Segment(K, G) → j
16. Segment(J, H) → k
17. Segment(Q, N) → l
18. Segment(P, O) → m
19. Intersect(l, j) → R
20. Intersect(m, j) → S
21. Intersect(j, l) → T
22. Intersect(j, poly1) → U, V
23. Midpoint(k) → W
24. Midpoint(l) → Z
25. Centroid(poly1) → A_1
26. Centroid(poly1) → B_1
27. Midpoint(m) → C_1
28. CircumcircleArc(G, C_1, H) → c
29. Midpoint(j) → D_1
30. CircumcircleArc(Q, D_1, P) → d
31. CircumcircleArc(N, W, O) → e
32. CircumcircleArc(K, Z, J) → p
33. Circle(E, W) → q
34. CircleArc(A, G, P) → r
35. Intersect(m, poly1) → E_1, F_1
36. Intersect(m, k) → G_1
37. Intersect(l, k) → H_1
38. Segment(S, H_1) → s
39. Intersect(q, s) → K_1, L_1
40. Midpoint(E, W) → M_1
41. CircumcircleArc(H_1, M_1, G_1) → t
42. Midpoint(D_1, E) → I_1
43. Midpoint(Z, E) → J_1
44. Midpoint(E, C_1) → N_1
45. CircumcircleArc(R, J_1, H_1) → c_1
46. CircumcircleArc(R, I_1, S) → d_1
47. CircumcircleArc(S, N_1, G_1) → e_1
48. Midpoint(W, L) → O_1
49. CircumcircleArc(H_1, O_1, G_1) → f_1
50. Midpoint(M, D_1) → P_1
51. CircumcircleArc(R, P_1, S) → g_1
52. CircleArc(B, O, H) → h_1
53. CircleArc(C, J, N) → k_1
54. CircleArc(D, Q, K) → p_1
55. Midpoint(C_1, F) → Q_1
56. Midpoint(Z, I) → R_1
57. CircumcircleArc(R, R_1, H_1) → q_1
58. CircumcircleArc(S, Q_1, G_1) → r_1
59. Intersect(p, q_1) → S_1, T_1, ,
60. Intersect(d, g_1) → U_1, V_1, ,
61. Intersect(c, r_1) → W_1, Z_1, ,
62. Intersect(e, f_1) → A_2, B_2, ,
63. CircumcircleArc(B_2, L, A_2) → s_1
64. CircumcircleArc(Z_1, F, W_1) → t_1
65. CircumcircleArc(U_1, M, V_1) → c_2
66. CircumcircleArc(T_1, I, S_1) → d_2
67. Segment(A, C) → n
68. Segment(D, B) → a
69. Line(A, B) → b
70. Rotate(l1, 90°, b) → l1'
71. Line(E, zAxis) → i_1
72. Rotate(l1', 90°, i_1) → l1''
73. Rotate(l1', (2 * 90°), i_1) → l1''_{1}
74. Rotate(l1', (3 * 90°), i_1) → l1''_{2}
75. Midpoint(D_2, A) → H_2
76. Midpoint(E_2, B) → I_2
77. Polygon(A, B, 4) → poly2, j_1, l_1, m_1, n_1, J_2, K_2
78. Join(Sequence[Sequence[(x(C_2) + ((ray * cos(i + π / 4)) * cos(j)), y(C_2) + ((ray * sin(i + π / 4)) * cos(j)), z(C_2) + (ray * sin(j))), i, 0, 6.28319, (2 * π / n1)], j, 0, 1.5708, π / m1]) → l2
79. Sequence(Polygon[Element[l2, i], Element[l2, i + 1], Element[l2, i + n1 + 2], Element[l2, i + n1 + 1]], i, 1, Length[l2]) → l3
80. Polygon(D_2, E_2, 4, xOyPlane) → poly3, a_1, b_1, f_2, g_2, L_2, M_2
81. Line(D_2, A) → h_2
82. Cube(poly1, true) → o, N_2, arête1, arête4, arête6, arête5, arête2, arête7, arête3, arête8, O_2, P_2, Q_2, face2, face1, face3, face4, face5
83. Circle(H_2, Distance[A, B], i_1) → e_2
84. Ray(R_2, H_2) → i_2
85. Intersect(i_2, e_2) → S_2,
86. CircleArc(H_2, I_2, S_2) → k_2
87. Point(k_2) → T_2
88. Angle(I_2, H_2, T_2) → α
89. Rotate(l1', α, h_2) → l1''_{3}
90. Polygon(A, B, O_2, N_2) → q1, j_2, l_2, m_2, n_2
91. Rotate(q1, α, h_2) → q1'
92. Midpoint(arête7) → U_2
93. Midpoint(arête6) → V_2
94. Circle(E, 0.65, i_1) → p_2
95. Cylinder(p_2, 0.65) → u, q_2, v
96. Circle(E, 0.6, i_1) → r_2
97. Cylinder(r_2, 2) → w, w_{2}, w_{3}
98. Segment(E + (0, 0, 2), E + (0, 0, 2.25)) → s_2
99. CircumcircleArc(U_2, W_2, V_2) → t_2