Pythagoras证明剪切：几何作图与参数曲线

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Segment(A, C) → a
3. OrthogonalLine(C, a) → b
4. Intersect(b, xAxis) → D
5. Polygon(A, D, 4) → poly1, a_1, d, c, e, B, E
6. OrthogonalLine(C, a_1) → j
7. Polygon(D, C, 4) → poly2, d_1, c_1, f, g, F, G
8. Ray(G, F) → r
9. Intersect(j, r) → L
10. Segment(F, L) → m
11. Polygon(C, A, 4) → poly3, c_2, a_2, h, i, H, I
12. Point(m) → J
13. Segment(I, L) → l
14. Ray(H, I) → k
15. Point(l) → K
16. Vector(C, K) → v
17. Vector(F, J) → w
18. Translate(F, w) → F'
19. Translate(G, w) → G'
20. Segment(F', G') → f'
21. Polygon(D, G', J, C) → poly4, d_2, g', j_1, c_3
22. Vector(I, K) → u
23. Translate(H, u) → H'
24. Translate(I, u) → I'
25. Segment(H', I') → h'
26. Polygon(A, H', K, C) → poly5, a_3, h'_1, k_1, c_4
27. Intersect(a_1, j) → M
28. Segment(M, C) → n
29. Point(n) → N
30. Vector(M, N) → z
31. Vector(C, N) → p
32. Translate(J, p) → J'
33. Translate(C, p) → C'
34. Segment(J', C') → q
35. Polygon(A, N, D, G', J', H') → poly6, a_4, n_1, d_3, g'_1, j', h'_2
36. Polygon(A, C, D) → poly7, d_4, a_5, c_5
37. Intersect(j, c_5) → O