勾股定理的图形化证明

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Polygon(A, D, G, C) → q1, a_1, d, g, c_1
3. Polygon(C, F, E, B) → q2, f, h, i, j
4. Line(D, G) → k
5. Line(F, E) → l
6. Intersect(k, l) → H
7. Line(H, C) → m
8. Intersect(m, c) → I
9. Vector(H, C) → u
10. Translate(I, u) → I'
11. Line(I', c) → n
12. Point(n) → J
13. Polygon(J, A, B, K) → q3, j_1, a_2, b_1, k_1
14. Segment(H, C) → p
15. Segment(I, I') → q
16. If(0 < o ≤ 1, Polygon[A, C, Dilate[G, 1 - o, H], Dilate[G, 1 - o, H] + A - C], Polygon[A, C, H, H + A - C]) → q4
17. If(2 < o ≤ 3, Polygon[A, Dilate[C, 3 - o, I], Dilate[C, 3 - o, I] + H - C, A + H - C], Polygon[A, I, I + H - C, A + H - C]) → q5
18. If(4 < o ≤ 5, Polygon[Dilate[I, 5 - o, I'], Dilate[I, 5 - o, I'] + H - C, A + H - C + Dilate[I, 5 - o, I'] - I, A + Dilate[I, 5 - o, I'] - I], Polygon[A, I, I', A + I' - I]) → q6
19. If(6 < o ≤ 7, Polygon[B, C, Dilate[F, 7 - o, H], Dilate[F, 7 - o, H] + E - F], Polygon[B, C, H, H + E - F]) → q7
20. If(8 < o ≤ 9, Polygon[B + H - C, B, Dilate[C, 9 - o, I], Dilate[C, 9 - o, I] + H - C], Polygon[B, I, I + H - C, B + H - C]) → q8
21. If(10 < o ≤ 11, Polygon[Dilate[I, 11 - o, I'], B + Dilate[I, 11 - o, I'] - I, B + Dilate[I, 11 - o, I'] - I + H - C, Dilate[I, 11 - o, I'] + H - C], Polygon[I', I, B, B + I' - I]) → q9
22. If(12 < o ≤ 13, Polygon[I, B, Dilate[B + I' - I, 13 - o, K], Dilate[B + I' - I, 13 - o, K] + I - B], Polygon[I, B, K, K + I - B]) → q10
23. If(12 < o ≤ 13, p) → r
24. If(12 < o ≤ 13, Polygon[I, A, Dilate[A + I' - I, 13 - o, J], Dilate[A + I' - I, 13 - o, J] + I - A], Polygon[A, J, J + I - A, I]) → q11