毕达哥拉斯定理无言证明的几何构造演示

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Line(A, C) → t
3. Point(h) → E
4. Line(A, E) → j
5. OrthogonalLine(D, j) → k
6. Intersect(j, k) → F
7. Line(C, k) → l
8. Line(A, D) → m
9. Intersect(l, m) → H
10. LineBisector(H, C) → n
11. Rotate(l, 45°, H) → l'
12. Intersect(n, l') → J
13. Line(D, B) → s
14. Circle(O, Segment[J, H]) → q
15. Intersect(q, t) → M, N
16. Circle(M, Segment[F, D]) → s_1
17. LineBisector(M, F) → h_1
18. Intersect(q, s) → K, L
19. OrthogonalLine(K, xAxis) → q_1
20. OrthogonalLine(M, q_1) → t_1
21. Intersect(s_1, t_1, 1) → A_1
22. LineBisector(D, A_1) → b_1
23. Circle(K, Segment[F, E]) → p_1
24. Intersect(p_1, q_1) → V, W
25. LineBisector(V, E) → r_1
26. LineBisector(K, F) → r
27. Polygon(D, F, E) → t1, e, d, f_1
28. Polygon(D, A, F) → t2, f_2, d_1, a
29. Intersect(k, g) → G
30. Polygon(E, C, G, F) → q1, e_1, c, g_1, f_3
31. Polygon(A, F, G, B) → q2, a_1, f_4, g_2, b
32. LineBisector(D, H) → p
33. Rotate(m, 45°, D) → m'
34. Intersect(p, m') → I
35. Intersect(r_1, r) → P
36. Intersect(b_1, h_1) → Q
37. Angle(H, C, D) → α
38. LineBisector(L, F) → i_1
39. LineBisector(N, F) → j_1
40. If(0 < o ≤ 1, Polygon[Rotate[D, ((o - 0) * (π + α)), P], Rotate[F, ((o - 0) * (π + α)), P], Rotate[E, ((o - 0) * (π + α)), P]], If[o > 1, Polygon[Rotate[D, π + α, P], Rotate[F, π + α, P], Rotate[E, π + α, P]]]) → t3
41. If(2 < o ≤ 3, Polygon[Rotate[D, ((o - 2) * (π + α)), Q], Rotate[A, ((o - 2) * (π + α)), Q], Rotate[F, ((o - 2) * (π + α)), Q]], If[o > 2, Polygon[Rotate[D, π + α, Q], Rotate[A, π + α, Q], Rotate[F, π + α, Q]]]) → t4
42. Polygon(P, Q, 4) → poly2, k_1, l_1, m_1, n_1, T, U
43. If(4 < o ≤ 5, Polygon[Rotate[A, ((o - 4) * (π + α)), T], Rotate[F, ((o - 4) * (π + α)), T], Rotate[G, ((o - 4) * (π + α)), T], Rotate[B, ((o - 4) * (π + α)), T]], If[o > 5, Polygon[Rotate[A, π + α, T], Rotate[F, π + α, T], Rotate[G, π + α, T], Rotate[B, π + α, T]]]) → q5
44. If(6 < o ≤ 7, Polygon[Rotate[E, ((o - 6) * (π + α)), U], Rotate[C, ((o - 6) * (π + α)), U], Rotate[G, ((o - 6) * (π + α)), U], Rotate[F, ((o - 6) * (π + α)), U]], If[o > 7, Polygon[Rotate[E, π + α, U], Rotate[C, π + α, U], Rotate[G, π + α, U], Rotate[F, π + α, U]]]) → q3
45. Centroid(poly2) → R
46. Intersect(h_1, r) → S
47. Circle(R, P) → c_1
48. Intersect(r_1, r) → Z
49. Intersect(b_1, h_1) → B_1