直角三角形勾股定理无字证明

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. Point(Segment[C, (0, 1)]) → E
3. Rotate(F, π / 2) → F'
4. Rotate(E, π / 2) → E'
5. Line(E', E) → l_1
6. Line(E', F') → l
7. Angle(xAxis, l) → α
8. Line(C, l) → n
9. OrthogonalLine(C, n) → h_1
10. AngularBisector(h_1, n) → i_1, j_1
11. Line(A, D) → p
12. Intersect(n, p) → L
13. LineBisector(L, C) → t
14. Intersect(t, j_1) → T
15. Line(D, B) → r
16. Circle(G, Segment[T, C]) → c_1
17. Intersect(c_1, r) → U, V
18. Rotate(r, γ, U) → r'
19. LineBisector(L, D) → q
20. Intersect(q, r) → N
21. Polygon(E', G, E, D) → q1, e', g_1, e, d
22. Polygon(E', A, F, G) → q2, j, a, f_1, g_2
23. Polygon(F, B, F', G) → q3, f_2, b, f', g_3
24. Polygon(G, F', C, E) → q4, g_4, k, c, e_1
25. Line(F, E) → m
26. Midpoint(L, D) → M
27. Midpoint(L, C) → S
28. Line(A, C) → k_1
29. Intersect(c_1, k_1) → W, Z
30. Intersect(l, e') → H
31. Intersect(r', l_1) → K
32. Intersect(l, e') → I
33. If(0 < o ≤ 1, Polygon[Rotate[E', ((o - 0) * (π + α)), K], Rotate[G, ((o - 0) * (π + α)), K], Rotate[E, ((o - 0) * (π + α)), K], Rotate[D, ((o - 0) * (π + α)), K]], If[o > 1, Polygon[Rotate[E', π + α, K], Rotate[G, π + α, K], Rotate[E, π + α, K], Rotate[D, π + α, K]]]) → q6
34. Midpoint(G, E) → J
35. Circle(G, Segment[N, L]) → s
36. Rotate(K, π / 2, (0, 0)) → K'
37. Rotate(K, π, (0, 0)) → K'_1
38. Rotate(K, (3 * π / 2), (0, 0)) → K'_2
39. If(2 < o ≤ 3, Polygon[Rotate[E', ((o - 2) * (π + α)), K'], Rotate[A, ((o - 2) * (π + α)), K'], Rotate[F, ((o - 2) * (π + α)), K'], Rotate[G, ((o - 2) * (π + α)), K']], If[o > 3, Polygon[Rotate[E', π + α, K'], Rotate[A, π + α, K'], Rotate[F, π + α, K'], Rotate[G, π + α, K']]]) → q5
40. If(4 < o ≤ 5, Polygon[Rotate[F, ((o - 4) * (π + α)), K'_1], Rotate[B, ((o - 4) * (π + α)), K'_1], Rotate[F', ((o - 4) * (π + α)), K'_1], Rotate[G, ((o - 4) * (π + α)), K'_1]], If[o > 5, Polygon[Rotate[F, π + α, K'_1], Rotate[B, π + α, K'_1], Rotate[F', π + α, K'_1], Rotate[G, π + α, K'_1]]]) → q7
41. If(6 < o ≤ 7, Polygon[Rotate[G, ((o - 6) * (π + α)), K'_2], Rotate[F', ((o - 6) * (π + α)), K'_2], Rotate[C, ((o - 6) * (π + α)), K'_2], Rotate[E, ((o - 6) * (π + α)), K'_2]], If[o > 7, Polygon[Rotate[G, π + α, K'_2], Rotate[F', π + α, K'_2], Rotate[C, π + α, K'_2], Rotate[E, π + α, K'_2]]]) → q8
42. Angle(K, U, G) → β
43. Intersect(r', l_1) → O