三角恒等式的面积证明（二）：动态图解

GeoGebra 命令及参数

1. Point(Segment[(0, 0), (1, 0)]) → A
2. Polygon(C, A, 4) → poly1, h, i, j, k, E, F
3. Polygon(D, A, 4) → poly2, l, m, n, p, G, H
4. Line(C, F) → q
5. Intersect(q, n) → I
6. Line(D, H) → r
7. OrthogonalLine(F, r) → s
8. Intersect(r, s) → J
9. Distance(E, G) → b
10. Line(C, F) → t
11. Circle(C, 1) → c
12. Intersect(c, t, 2) → K
13. Intersect(c, r) → L, M
14. Polygon(E, G, I, F) → q1, e, g_1, i_1, f_1
15. Polygon(C, I, H, D) → q2, c_1, i_2, h_1, d
16. Segment(C, F) → j_1
17. Segment(F, E) → k_1
18. Segment(E, G) → l_1
19. Segment(G, H) → m_1
20. Segment(C, D) → n_1
21. Segment(A, E) → p_1
22. Segment(A, C) → q_1
23. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], L) → D'
24. Vector(D, D') → u
25. Translate(H, u) → H'
26. Polygon(D', C, I, H') → q3, d', c_2, i_3, h'
27. Line(I, H') → b_1
28. Line(C, L) → d_1
29. OrthogonalLine(L, d_1) → e_1
30. Intersect(b_1, e_1) → N
31. Dilate(H', If[2 < a ≤ 3, 3 - a, 0], N) → H''
32. Vector(H', H'') → v
33. Translate(I, v) → I'
34. Polygon(L, C, I', H'') → q4, l_2, c_3, i', h''
35. Dilate(N, If[4 < a ≤ 5, 5 - a, 0], O) → N'
36. Vector(N, N') → w
37. Translate(L, w) → L'
38. Translate(C, w) → C'
39. Translate(I', w) → I''
40. Translate(H'', w) → H'''
41. Polygon(L', C', I'', H''') → q4', l', c', i'', h'''
42. Point(r_1) → P
43. Angle(I, N, P) → α
44. Rotate(L', If[4 < a ≤ 5, ((a - 4) * α), α], H''') → L''
45. Rotate(C', If[4 < a ≤ 5, ((a - 4) * α), α], H''') → C''
46. Rotate(I'', If[4 < a ≤ 5, ((a - 4) * α), α], H''') → I'''
47. Rotate(H''', If[4 < a ≤ 5, ((a - 4) * α), α], H''') → Q
48. Polygon(L'', C'', I''', Q) → q4'', l'', c'', i''', q_2
49. Line(C, F) → t_1
50. Circle(G, 1) → s_1
51. Line(F, E) → a_1
52. Intersect(s_1, a_1) → R, S
53. Dilate(E, If[6 < a ≤ 7, 7 - a, 0], S) → F'
54. Vector(E, F') → u_1
55. Translate(E, u_1) → E'
56. Translate(F, u_1) → F'_1
57. Polygon(I, F'_1, F', G) → q5, i_4, f'_1, f', g_2
58. Distance(G, F') → o
59. Line(I, F'_1) → f_2
60. OrthogonalLine(S, f_2) → h_2
61. Intersect(f_2, h_2) → T
62. Dilate(F'_1, If[9 < a ≤ 10, 10 - a, 0], T) → U
63. Vector(F'_1, U) → v_1
64. Translate(A, v_1) → A'
65. Translate(I, v_1) → I'_1
66. Polygon(I'_1, U, S, G) → q6, i'_1, u_2, s_2, g_3
67. Dilate(T, If[11 < a ≤ 12, 12 - a, 0], L'') → T'
68. Vector(T, T') → w_1
69. Translate(I'_1, w_1) → V
70. Translate(U, w_1) → U'
71. Translate(S, w_1) → S'
72. Translate(G, w_1) → G'
73. Polygon(V, U', S', G') → q6', v_2, u', s', g'
74. Point(f_2) → W
75. Point(p_2) → Z
76. Angle(Z, T, W) → β
77. Rotate(V, If[11 < a ≤ 12, ((-(a - 11)) * β), (-β)], U') → V'
78. Rotate(U', If[11 < a ≤ 12, ((-(a - 11)) * β), (-β)], U') → U''
79. Rotate(S', If[11 < a ≤ 12, ((-(a - 11)) * β), (-β)], U') → S''
80. Rotate(G', If[11 < a ≤ 12, ((-(a - 11)) * β), (-β)], U') → G''
81. Polygon(V', U'', S'', G'') → q6'', v', u'', s'', g''
82. Line(I, F'_1) → j_2
83. Line(G, F') → k_2
84. Segment(A, G) → m_2
85. Segment(G, H) → n_2
86. Segment(C, D) → r_2
87. Segment(D, H) → t_2
88. Segment((0, 0), A) → a_2