毕达哥拉斯定理几何证明：面积与向量构型演示

GeoGebra 命令及参数

1. Point(xAxis) → C
2. Intersect(xAxis, yAxis) → B
3. Point(yAxis) → A
4. Polygon(A, C, 4) → poly1, f, g, h, i, D, E
5. Polygon(A, B, C) → t1, c, a, b
6. InteriorAngles(t1) → α, β, γ
7. Polygon(C, B, 4) → poly2, j, k, l, m, F, G
8. Polygon(B, A, 4) → poly3, n, p, q, r, H, I
9. Vector(E, ((1 - g3) * E) + (g3 * J)) → u
10. Translate(poly1, u) → poly1'
11. Translate(A, u) → A'
12. Translate(B, u) → B'
13. Translate(C, u) → C'
14. Polygon(A', B', C') → t1', c', a', b'
15. Midpoint(J, C') → K
16. Vector(C, ((1 - g1) * C) + (g1 * L)) → v
17. Translate(poly2, v) → poly2'
18. Translate(poly3, v) → poly3'
19. Translate(A, v) → A'_1
20. Translate(B, v) → B'_1
21. Translate(C, v) → C'_1
22. Polygon(A'_1, B'_1, C'_1) → t1'_1, c'_1, a'_1, b'_1
23. Midpoint(A'_1, L) → M
24. Sequence(Polygon[Rotate[A', (k * θ), K], Rotate[B', (k * θ), K], Rotate[C', (k * θ), K]], k, 1, 3) → l1
25. Point(v) → N
26. LineBisector(B'_1, A'_1) → s
27. LineBisector(N, B'_1) → t
28. Intersect(t, s) → P
29. Sequence(Polygon[Rotate[A'_1, (k * φ), Element[l2, k]], Rotate[B'_1, (k * φ), Element[l2, k]], Rotate[C'_1, (k * φ), Element[l2, k]]], k, 1, 3) → l3
30. Point(l3) → U
31. Point(Circle[Z, a + c]) → A_1
32. Segment(Z, A_1) → f_1
33. Polygon(Z, A_1, 4) → poly4, g_1, h_1, i_1, j_1, B_1, C_1
34. Sequence(((1 - g5) * Element[l5, k]) + (g5 * Element[l6, k]), k, 1, 4) → l8
35. Polygon(l8) → q2
36. Sequence(((1 - g5) * Element[l4, k]) + (g5 * Element[l6, k]), k, 1, 4) → l7
37. Polygon(l7) → q1