另一个流行的三角恒等式：面积几何图解

GeoGebra 命令及参数

1. Point(Segment[(0, 0), (π / 2, 0)]) → A
2. Intersect(f, eq1, (0.8228536275037948, 0.6801320145437539)) → B
3. Intersect(h, eq1, (0.8228536275037948, 1.0778637671534934)) → C
4. Intersect(xAxis, eq2) → E
5. Polygon(A, E, D, C) → q1, a, e, d, c
6. Intersect(p, eq1, (0.8228536275037948, -1.2669103446421748)) → F
7. Intersect(eq1, g) → G
8. Polygon(H, G, F, I) → q2, h_1, g_1, f_1, i
9. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
10. Segment(A, A') → k
11. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
12. Vector(C, C') → u
13. Translate(A, u) → A'_{1}
14. Translate(A', u) → A''
15. Segment(A'_{1}, A'') → k'
16. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], B) → A'_{2}
17. Segment(A, A'_{2}) → l
18. Rotate(B, If[5 < j ≤ 6, ((-(j - 5)) * π / 2), ((-π)) / 2], A) → B'
19. Segment(A, B') → m
20. Dilate(D, If[6 < j ≤ 7, 7 - j, 0], C) → D'
21. Vector(D, D') → v
22. Translate(A'_{1}, v) → J
23. Translate(A'', v) → A'''
24. Segment(J, A''') → k''
25. Dilate(A, If[7 < j ≤ 8, 8 - j, 0], C) → A'_{3}
26. Vector(A, A'_{3}) → w
27. Translate(A, w) → A'_{4}
28. Translate(B', w) → B''
29. Segment(A'_{4}, B'') → m'
30. Polygon(A, E, D, C) → q3, a_1, e_1, d_1, c_1
31. Intersect(h, yAxis, (0, 0)) → K
32. Line(A, C) → n
33. Ray(K, A) → r
34. Ray(M, G) → s
35. Dilate(G, If[9 < j ≤ 10, 10 - j, 0], F) → G'
36. Segment(G, G') → t
37. Dilate(K, If[11 < j ≤ 12, 12 - j, 0], L) → K'
38. Segment(K, K') → i_1
39. Dilate(K, If[13 < j ≤ 14, 14 - j, 0], F) → K'_{1}
40. Vector(K, K'_{1}) → u_1
41. Translate(K, u_1) → K'_{2}
42. Translate(K', u_1) → K''
43. Segment(K'_{2}, K'') → j_1
44. Rotate(K'_{2}, If[14 < j ≤ 15, ((-(j - 14)) * π / 2), ((-π)) / 2], F) → N
45. Rotate(K'', If[14 < j ≤ 15, ((-(j - 14)) * π / 2), ((-π)) / 2], F) → K'''
46. Segment(N, K''') → k_1
47. Dilate(I, If[15 < j ≤ 16, 16 - j, 0], H) → I'
48. Vector(I, I') → v_1
49. Translate(N, v_1) → N'
50. Translate(K''', v_1) → O
51. Segment(N', O) → l_1
52. Dilate(F, If[16 < j ≤ 17, 17 - j, 0], I) → F'
53. Vector(F, F') → w_1
54. Translate(G, w_1) → G'_{1}
55. Translate(G', w_1) → G''
56. Segment(G'_{1}, G'') → t'
57. Circle(D, 1) → p_1
58. Intersect(p_1, n, 1) → P
59. Dilate(C, If[19 < j ≤ 20, 20 - j, 0], P) → C'_{1}
60. Vector(C, C'_{1}) → b_1
61. Translate(C, b_1) → C'_{2}
62. Translate(A, b_1) → A'_{5}
63. Polygon(D, C'_{1}, A'_{5}, E) → q4, d_2, c'_{1}, a'_{5}, e_2
64. Line(A'_{5}, E) → m_1
65. OrthogonalLine(D, m_1) → n_1
66. Intersect(m_1, n_1) → Q
67. Line(P, D) → q_1
68. Dilate(E, If[21 < j ≤ 22, 22 - j, 0], Q) → E'
69. Vector(E, E') → r_1
70. Translate(A'_{5}, r_1) → R
71. Polygon(E', D, P, R) → q5, e', d_3, p_2, r_2
72. Line(P, k_1) → s_1
73. Point(s_1) → S
74. Line(P, n_1) → t_1
75. Point(t_1) → T
76. Angle(A, P, T) → α
77. Dilate(P, If[23 < j ≤ 24, 24 - j, 0], F) → P'
78. Vector(P, P') → u_2
79. Translate(E', u_2) → E''
80. Translate(D, u_2) → D'_{1}
81. Translate(P, u_2) → P'_{1}
82. Translate(R, u_2) → R'
83. Polygon(E'', D'_{1}, P'_{1}, R') → q5', e'', d'_{1}, p'_{1}, r'
84. Rotate(E'', If[23 < j ≤ 24, ((-(j - 23)) * α), (-α)], P'_{1}) → E'''
85. Rotate(D'_{1}, If[23 < j ≤ 24, ((-(j - 23)) * α), (-α)], P'_{1}) → U
86. Rotate(P'_{1}, If[23 < j ≤ 24, ((-(j - 23)) * α), (-α)], P'_{1}) → V
87. Rotate(R', If[23 < j ≤ 24, ((-(j - 23)) * α), (-α)], P'_{1}) → R''
88. Polygon(E''', U, V, R'') → q5'', e''', u_3, v_2, r''
89. Segment(K, A) → f_2
90. Segment(M, W) → g_2