无字证明：勾股定理的几何直观演示

GeoGebra 命令及参数

1. Point(yAxis) → A
2. Mirror(B, A) → B'
3. Semicircle(B, B') → c
4. Point(c) → C
5. Polygon(B, C, 4) → poly1, a, b, d, e, D, E
6. Polygon(C, B', 4) → poly2, f, g, h, i, F, G
7. Polygon(B', B, 4) → poly3, j, k, l, m, H, I
8. Line(C, j) → n
9. Segment(D, B) → p
10. Segment(G, B') → q
11. Intersect(n, p) → J
12. Intersect(n, q) → K
13. Polygon(D, J, C) → poly4, c_1, d_1, j_1
14. Polygon(B, J, C) → poly5, c_2, b_1, j_2
15. Polygon(C, K, G) → poly6, g_1, c_3, k_1
16. Polygon(K, B', C) → poly7, c_4, k_2, b'
17. Dilate(J, If[t ≤ 1, 1 - t, 0], K) → J'
18. Vector(J, J') → u
19. Translate(D, u) → D'
20. Translate(J, u) → J'_1
21. Translate(C, u) → C'
22. Polygon(D', J'_1, C') → poly4', c', d', j'_1
23. Translate(B, u) → B'_1
24. Translate(J, u) → J'_2
25. Translate(C, u) → C'_1
26. Polygon(B'_1, J'_2, C'_1) → poly5', c'_1, b'_1, j'_2
27. Midpoint(D, B) → L
28. Rotate(C, If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → C'_2
29. Rotate(K, If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → K'
30. Rotate(G, If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → G'
31. Polygon(C'_2, K', G') → poly6', g', c'_2, k'
32. Rotate(D', If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → D''
33. Rotate(J'_1, If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → M
34. Rotate(C', If[1 < t ≤ 2, ((-(t - 1)) * π / 2), -1.5707963267948966], L) → C''
35. Polygon(D'', M, C'') → poly4'', c'', d'', m_1
36. Dilate(C, If[2 < t ≤ 3, 3 - t, 0], B) → C'_3
37. Vector(C, C'_3) → v
38. Translate(K, v) → K'_1
39. Translate(B', v) → B''
40. Translate(C, v) → C'_4
41. Polygon(K'_1, B'', C'_4) → poly7', c'_4, k'_1, b''
42. Translate(B'_1, v) → N
43. Translate(J'_2, v) → O
44. Translate(C'_1, v) → P
45. Polygon(N, O, P) → poly5'', p_1, n_1, o
46. Midpoint(H, B') → Q
47. Rotate(D'', If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → D'''
48. Rotate(M, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → M'
49. Rotate(C'', If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → C'''
50. Polygon(D''', M', C''') → poly4''', c''', d''', m'
51. Rotate(C'_2, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → R
52. Rotate(K', If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → K''
53. Rotate(G', If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → G''
54. Polygon(R, K'', G'') → poly6'', g'', r, k''
55. Rotate(K'_1, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → S
56. Rotate(B'', If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → B'''
57. Rotate(C'_4, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → T
58. Polygon(S, B''', T) → poly7'', t_1, s, b'''
59. Rotate(N, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → N'
60. Rotate(O, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → O'
61. Rotate(P, If[3 < t ≤ 4, ((-(t - 3)) * π), -3.141592653589793], Q) → P'
62. Polygon(N', O', P') → poly5''', p', n', o'