无言证明：勾股定理

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Ray(A, B) → a
4. Point(a) → C
5. Mirror(C, A) → C'
6. Semicircle(C, C') → c
7. Intersect(c, yAxis) → D,
8. CircleArc(A, D, C) → d
9. Point(d) → E
10. Segment(C, E) → b
11. Segment(E, C') → e
12. Segment(C', C) → f
13. Polygon(C', C, 4) → poly1, g, h, i, j, F, G
14. Polygon(C, E, 4) → poly2, k, l, m, n, H, I
15. Polygon(E, C', 4) → poly3, p, q, r, s, J, K
16. Midpoint(E, J) → L
17. OrthogonalLine(L, i) → t
18. OrthogonalLine(L, t) → a_1
19. Intersect(a_1, s) → M
20. Intersect(t, r) → N
21. Intersect(a_1, q) → O
22. Intersect(t, e) → P
23. Polygon(M, L, N, K) → poly4, m_1, l_1, n_1, k_1
24. Polygon(L, N, J, O) → poly5, l_2, n_2, j_1, o
25. Polygon(L, P, C', O) → poly6, l_3, p_1, c', o_1
26. Polygon(P, L, M, E) → poly7, p_2, l_4, m_2, e_1
27. Vector(L, C) → u
28. Vector(L, F) → v
29. Vector(L, C') → w
30. Vector(L, G) → u_1
31. Centroid(poly4) → Q
32. Centroid(poly5) → R
33. Centroid(poly6) → S
34. Centroid(poly7) → T
35. Translate(T, w) → T'
36. Translate(S, u) → S'
37. Translate(R, v) → R'
38. Translate(Q, u_1) → Q'
39. Segment(Q, Q') → b_1
40. Segment(R, R') → c_1
41. Segment(S, S') → d_1
42. Segment(T, T') → f_1
43. Point(b_1) → U
44. Point(c_1) → V
45. Point(d_1) → W
46. Point(f_1) → Z
47. Vector(Q, U) → v_1
48. Vector(R, V) → w_1
49. Vector(S, W) → g_1
50. Vector(T, Z) → h_1
51. Translate(L, w_1) → L'
52. Translate(N, w_1) → N'
53. Translate(J, w_1) → J'
54. Translate(O, w_1) → O'
55. Polygon(L', N', J', O') → poly5', l', n', j', o'
56. Translate(M, v_1) → M'
57. Translate(L, v_1) → L'_1
58. Translate(N, v_1) → N'_1
59. Translate(K, v_1) → K'
60. Polygon(M', L'_1, N'_1, K') → poly4', m', l'_1, n'_1, k'
61. Translate(L, g_1) → L'_2
62. Translate(P, g_1) → P'
63. Translate(C', g_1) → C''
64. Translate(O, g_1) → O'_1
65. Polygon(L'_2, P', C'', O'_1) → poly6', l'_2, p', c'', o'_1
66. Translate(P, h_1) → P'_1
67. Translate(L, h_1) → L'_3
68. Translate(M, h_1) → M'_1
69. Translate(E, h_1) → E'
70. Polygon(P'_1, L'_3, M'_1, E') → poly7', p'_1, l'_3, m'_1, e'
71. Midpoint(H, C) → A_1
72. Midpoint(C, G) → B_1
73. Segment(A_1, B_1) → i_1
74. Point(i_1) → C_1
75. Vector(A_1, C_1) → q_1
76. Translate(poly2, q_1) → poly2'