毕达哥拉斯定理的铰接剖分证明

GeoGebra 命令及参数

1. If(t > 0.5, (2 * (t - 0.5)), 0) → t1
2. If(t < 0.5, (2 * t), 1) → t0
3. Midpoint(A, C - (3, 0)) → O
4. Rotate(O, 90°, A) → O'
5. Polygon(A, C, C - (3, 0), A - (3, 0)) → q1, f, g, h, i
6. Rotate(B, -90°, C) → B'
7. Vector(O', B') → u
8. Polygon(A, B, C) → t1_{1}, j, k, l
9. Line(O, k) → m
10. Intersect(m, g) → F
11. Intersect(m, i) → D
12. OrthogonalLine(O, m) → n
13. Intersect(n, l) → G
14. Intersect(n, h) → E
15. Polygon({O, D, H, E}) → q3
16. Polygon({A, B, B + (0, 2), A + (0, 2)}) → q2
17. Polygon({O, E, I, F}) → q4
18. Polygon({O, F, C, G}) → q5
19. Polygon({O, G, A, D}) → q6
20. Translate(Rotate[Rotate[Rotate[Rotate[q3, (180° * t0), E], (180° * t0), F], (180° * t0), G], (90° * t0), A], Vector[(t1 * u)]) → q3'
21. Translate(Rotate[Rotate[Rotate[q4, (180° * t0), F], (180° * t0), G], (90° * t0), A], Vector[(t1 * u)]) → q4'
22. Translate(Rotate[Rotate[q5, (180° * t0), G], (90° * t0), A], Vector[(t1 * u)]) → q5'
23. Translate(Rotate[q6, (90° * t0), A], Vector[(t1 * u)]) → q6'
24. Rotate(C, 90°, B) → C'
25. Polygon({B, C, B', C'}) → q7
26. Translate(q2, Vector[(t1 * u)]) → q2'
27. Translate(A, Vector[(t1 * u)]) → A'
28. Translate(Rotate[G, (90° * t0), A], Vector[(t1 * u)]) → J
29. Translate(Rotate[Rotate[F, (180° * t0), G], (90° * t0), A], Vector[(t1 * u)]) → K
30. Translate(Rotate[Rotate[Rotate[E, (180° * t0), F], (180° * t0), G], (90° * t0), A], Vector[(t1 * u)]) → L