欧拉公式多面体动态证明

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Polygon(A, B, 4) → mnohoúhelník1, a, b, c, d, C, D
4. Segment(A, C) → e
5. Segment(B, D) → f
6. Intersect(f, e) → E
7. Vector(A, E) → u
8. Translate(B, u) → B'
9. Translate(C, u) → C'
10. Translate(D, u) → D'
11. Segment(D, D') → g
12. Segment(D', C') → h
13. Segment(C', B') → i
14. Segment(B', B) → j
15. Segment(C, C') → k
16. Segment(D', E) → l
17. Segment(B', E) → m
18. Segment(E, A) → n
19. Polygon(D, C, C', D') → mnohoúhelník2, d_1, c_1, c', d'
20. Polygon(B, B', C', C) → mnohoúhelník3, b_1, b', c'_1, c_2
21. Intersect(c, d_1) → F
22. Intersect(l, c) → G
23. Intersect(m, b) → H
24. Segment(E, H) → s
25. Segment(E, G) → p
26. Segment(A, E) → q
27. Circle(C, A) → r
28. Rotate(A, 90*°, C) → A'
29. Rotate(A', 90*°, C) → A''
30. Rotate(A'', 90*°, C) → A'''
31. Vector(D, A''') → v
32. Vector(C, A'') → w
33. Vector(B, A') → t
34. Translate(D, Vector[((o - 0.1) * v)]) → D'_1
35. Translate(C, Vector[((o - 0.1) * w)]) → C'_1
36. Translate(B, Vector[((o - 0.1) * t)]) → B'_1
37. Segment(D'_1, D') → a_1
38. Segment(C', C'_1) → e_1
39. Segment(D'_1, A) → f_1
40. Segment(D'_1, C'_1) → g_1
41. Segment(B', B'_1) → h_1
42. Segment(A, B'_1) → i_1
43. Segment(C'_1, B'_1) → j_1
44. Segment(A''', A) → k_1
45. Segment(A''', A'') → l_1
46. Segment(A, A') → m_1
47. Segment(A'', A') → n_1
48. Segment(A''', D') → p_1
49. Segment(C', A'') → q_1
50. Segment(A', B') → r_1
51. Polygon(D'_1, C'_1, C', D') → mnohoúhelník4, d'_1, c'_2, c'_3, d'_2
52. Polygon(C'_1, B'_1, B', C') → mnohoúhelník5, c'_4, b'_1, b'_2, c'_5
53. Intersect(g_1, l) → I
54. Segment(E, I) → s_1
55. Segment(D', E) → t_1
56. Segment(E, B') → a_2
57. Intersect(m, j_1) → J
58. Segment(E, J) → b_2
59. Segment(A''', E) → d_2
60. Segment(E, C') → e_2
61. Segment(D', A'') → f_2
62. Segment(C', A') → g_2
63. Segment(B', A) → h_2
64. Translate(A'', Vector[((3.2 - o) * w)]) → A'''_1
65. Translate(A'', Vector[(-w)]) → A'''_2
66. Translate(A', Vector[((3.2 - o) * t)]) → A''_1
67. Translate(A', Vector[(-t)]) → A''_2
68. Translate(A''', Vector[((3.2 - o) * v)]) → K
69. Translate(A''', Vector[(-v)]) → L
70. Segment(K, A) → i_2
71. Segment(A, A''_1) → j_2
72. Segment(K, A'''_1) → k_2
73. Segment(A'''_1, A''_1) → l_2
74. Segment(K, D') → m_2
75. Segment(C', A'''_1) → n_2
76. Segment(B', A''_1) → p_2
77. Segment(L, A) → q_2
78. Segment(A, A''_2) → r_2
79. Segment(A'''_2, A''_2) → s_2
80. Segment(L, A'''_2) → t_2
81. Segment(L, D') → a_3
82. Segment(A'''_2, C') → b_3
83. Segment(A''_2, B') → c_3
84. Intersect(k_2, t_1) → M
85. Segment(M, E) → d_3
86. Segment(D', M) → e_3
87. Segment(D', E) → f_3
88. Intersect(a_2, l_2) → N
89. Segment(E, N) → h_3
90. Segment(E, B') → i_3
91. Segment(E, B') → g_3
92. Polygon(D', K, A'''_1, C') → mnohoúhelník6, d'_3, k_3, a'''_1, c'_6
93. Polygon(A'''_1, A''_1, B', C') → mnohoúhelník7, a'''_2, a''_1, b'_3, c'_7
94. Polygon(L, A'''_2, C', D') → mnohoúhelník8, l_3, a'''_3, c'_8, d'_4
95. Polygon(A'''_2, A''_2, B', C') → mnohoúhelník9, a'''_4, a''_2, b'_4, c'_9
96. Polygon(A, A''_2, A'''_2, L) → mnohoúhelník10, a_4, a''_3, a'''_5, l_4