勾股定理的剪切证明 by Markus Hohenwarter

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Semicircle(A, B) → h
4. Midpoint(A, B) → O
5. Circle(O, B) → o
6. Point(h) → C
7. Rotate(C, 90*°, A) → D
8. Rotate(A, 270*°, C) → E
9. Line(D, E) → m
10. Vector(D, E) → v_b
11. Length(v_b) → k_b
12. Rotate(C, 270*°, B) → F
13. Rotate(B, 90*°, C) → G
14. Line(F, G) → n
15. Intersect(m, n) → H
16. Line(H, yAxis) → hc
17. Vector(E, H) → u_a
18. Length(u_a) → ku_b
19. Vector(G, H) → u_b
20. Length(u_b) → ku_a
21. Vector(F, G) → v_a
22. Length(v_a) → k_a
23. Rotate(B, 270*°, A) → I
24. Vector(A, I) → v_c
25. Length(v_c) → k_c
26. Circle(H, (ku_a * ku_b / k_c)) → d
27. Intersect(d, hc) → K, L
28. Vector(H, L) → v_h
29. Rotate(A, 90*°, B) → J
30. If(a < ka_1, Point[F, Vector[(a / ka_1 * u_b)]], If[a < ka_2, Point[F, u_b], Point[F, Vector[u_b + ((a - ka_2) / (1 - ka_2) * v_c)]]]) → F'
31. Polygon(B, C, G, F) → P, b_1, c, g, f
32. If(a < ka_1, Point[G, Vector[(a / ka_1 * u_b)]], If[a < ka_2, Point[H, Vector[((a - ka_1) / (ka_2 - ka_1) * v_h)]], Point[L, Vector[((a - ka_2) / (1 - ka_2) * v_c)]]]) → G'
33. If(a < ka_1, C, If[a < ka_2, Point[C, Vector[((a - ka_1) / (ka_2 - ka_1) * v_h)]], Point[C, Vector[v_h + ((a - ka_2) / (1 - ka_2) * v_c)]]]) → Ca'
34. Vector(G', Ca') → u
35. If(a < ka_1, B, If[a < ka_2, B, Point[B, Vector[((a - ka_2) / (1 - ka_2) * v_c)]]]) → B'
36. Vector(F', B') → v
37. Polygon(B', Ca', G', F') → Q, b', c', g', f'
38. If(b < kb_1, Point[E, Vector[(b / kb_1 * u_a)]], If[b < kb_2, Point[H, Vector[((b - kb_1) / (kb_2 - kb_1) * v_h)]], Point[L, Vector[((b - kb_2) / (1 - kb_2) * v_c)]]]) → E'
39. If(b < kb_1, Point[D, Vector[(b / kb_1 * u_a)]], If[b < kb_2, Point[D, u_a], Point[D, Vector[u_a + ((b - kb_2) / (1 - kb_2) * v_c)]]]) → D'
40. If(b < kb_1, C, If[b < kb_2, Point[C, Vector[((b - kb_1) / (kb_2 - kb_1) * v_h)]], Point[C, Vector[v_h + ((b - kb_2) / (1 - kb_2) * v_c)]]]) → Cb'
41. If(b < kb_1, A, If[b < kb_2, A, Point[A, Vector[((b - kb_2) / (1 - kb_2) * v_c)]]]) → A'
42. Polygon(A, C, E, D) → R, a_1, c_1, e, d_1
43. Polygon(A', Cb', E', D') → S, a', cb', e', d'
44. Polygon(A, B, J, I) → T, a_2, b_2, j, i
45. Angle(A, C, B) → α
46. Midpoint(C, B) → M
47. Midpoint(A, C) → N
48. Midpoint(a_2) → U