勾股定理的图形证明 by Steve Phelps

GeoGebra 命令及参数

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Semicircle(A, B) → c
4. Point(c) → C
5. Polygon(A, C, 4) → poly1, f, g, h, i, D, E
6. Polygon(C, B, 4) → poly2, j, k, l, m, F, G
7. Polygon(B, A, 4) → poly3, n, p, q, r, H, I
8. Centroid(poly2) → J
9. Centroid(poly3) → K
10. Centroid(poly1) → L
11. OrthogonalLine(J, n) → s
12. OrthogonalLine(J, s) → t
13. OrthogonalLine(J, m) → a
14. OrthogonalLine(J, a) → b
15. Intersect(s, j) → M
16. OrthogonalLine(M, a) → d
17. Intersect(a, d) → N
18. Intersect(t, k) → O
19. Polygon(M, N, J, O, B) → p1, m_1, n_1, j_1, o_1, b_1
20. Rotate(M, π / 2, J) → M'
21. Rotate(N, π / 2, J) → N'
22. Rotate(J, π / 2, J) → J'
23. Rotate(O, π / 2, J) → O'
24. Rotate(B, π / 2, J) → B'
25. Polygon(M', N', J', O', B') → p2, m', n', j', o', b'
26. Rotate(M, π, J) → M'_1
27. Rotate(N, π, J) → N'_1
28. Rotate(J, π, J) → J'_1
29. Rotate(O, π, J) → O'_1
30. Rotate(B, π, J) → B'_1
31. Polygon(M'_1, N'_1, J'_1, O'_1, B'_1) → p3, m'_1, n'_1, j'_1, o'_1, b'_1
32. Rotate(M, ((-π)) / 2, J) → M'_2
33. Rotate(N, ((-π)) / 2, J) → N'_2
34. Rotate(J, ((-π)) / 2, J) → J'_2
35. Rotate(O, ((-π)) / 2, J) → O'_2
36. Rotate(B, ((-π)) / 2, J) → B'_2
37. Polygon(M'_2, N'_2, J'_2, O'_2, B'_2) → p4, m'_2, n'_2, j'_2, o'_2, b'_2
38. If(0 < o ≤ 1, Polygon[Translate[M, Vector[J, Dilate[J, 1 - o, A]]], Translate[N, Vector[J, Dilate[J, 1 - o, A]]], Translate[J, Vector[J, Dilate[J, 1 - o, A]]], Translate[O, Vector[J, Dilate[J, 1 - o, A]]], Translate[B, Vector[J, Dilate[J, 1 - o, A]]]], Polygon[Translate[M, A - J], Translate[N, A - J], Translate[J, A - J], Translate[O, A - J], Translate[B, A - J]]) → poly4
39. If(2 < o ≤ 3, Polygon[Translate[M', Vector[J, Dilate[J, 3 - o, H]]], Translate[N', Vector[J, Dilate[J, 3 - o, H]]], Translate[J', Vector[J, Dilate[J, 3 - o, H]]], Translate[O', Vector[J, Dilate[J, 3 - o, H]]], Translate[B', Vector[J, Dilate[J, 3 - o, H]]]], Polygon[Translate[M', H - J], Translate[N', H - J], Translate[J', H - J], Translate[O', H - J], Translate[B', H - J]]) → poly5
40. If(4 < o ≤ 5, Polygon[Translate[M'_1, Vector[J, Dilate[J, 5 - o, I]]], Translate[N'_1, Vector[J, Dilate[J, 5 - o, I]]], Translate[J'_1, Vector[J, Dilate[J, 5 - o, I]]], Translate[O'_1, Vector[J, Dilate[J, 5 - o, I]]], Translate[B'_1, Vector[J, Dilate[J, 5 - o, I]]]], Polygon[Translate[M'_1, I - J], Translate[N'_1, I - J], Translate[J'_1, I - J], Translate[O'_1, I - J], Translate[B'_1, I - J]]) → poly6
41. If(6 < o ≤ 7, Polygon[Translate[M'_2, Vector[J, Dilate[J, 7 - o, B]]], Translate[N'_2, Vector[J, Dilate[J, 7 - o, B]]], Translate[J'_2, Vector[J, Dilate[J, 7 - o, B]]], Translate[O'_2, Vector[J, Dilate[J, 7 - o, B]]], Translate[B'_2, Vector[J, Dilate[J, 7 - o, B]]]], Polygon[Translate[M'_2, B - J], Translate[N'_2, B - J], Translate[J'_2, B - J], Translate[O'_2, B - J], Translate[B'_2, B - J]]) → poly7
42. Polygon(M, N, J) → t1, j_2, m_2, n_2
43. Polygon(O'_1, N'_2, J) → t2, j_3, e, f_1
44. Polygon(O', N'_1, J) → t3, j_4, g_1, h_1
45. Polygon(O, N', J) → t4, j_5, o_2, i_1
46. If(8 < o ≤ 9, Polygon[Translate[M, Vector[J, Dilate[J, 9 - o, A]]], Translate[N, Vector[J, Dilate[J, 9 - o, A]]], Translate[J, Vector[J, Dilate[J, 9 - o, A]]]], Polygon[Translate[M, A - J], Translate[N, A - J], Translate[J, A - J]]) → t5
47. If(10 < o ≤ 11, Polygon[Translate[O'_1, Vector[J, Dilate[J, 11 - o, B]]], Translate[N'_2, Vector[J, Dilate[J, 11 - o, B]]], Translate[J, Vector[J, Dilate[J, 11 - o, B]]]], Polygon[Translate[O'_1, B - J], Translate[N'_2, B - J], Translate[J, B - J]]) → t6
48. If(12 < o ≤ 13, Polygon[Translate[O', Vector[J, Dilate[J, 13 - o, I]]], Translate[N'_1, Vector[J, Dilate[J, 13 - o, I]]], Translate[J, Vector[J, Dilate[J, 13 - o, I]]]], Polygon[Translate[O', I - J], Translate[N'_1, I - J], Translate[J, I - J]]) → t7
49. If(14 < o ≤ 15, Polygon[Translate[O, Vector[J, Dilate[J, 15 - o, H]]], Translate[N', Vector[J, Dilate[J, 15 - o, H]]], Translate[J, Vector[J, Dilate[J, 15 - o, H]]]], Polygon[Translate[O, H - J], Translate[N', H - J], Translate[J, H - J]]) → t8
50. Polygon(A, E, D, C) → q1, a_1, e_1, d_1, c_1
51. If(16 < o ≤ 17, Polygon[Translate[A, Vector[L, Dilate[L, 17 - o, K]]], Translate[E, Vector[L, Dilate[L, 17 - o, K]]], Translate[D, Vector[L, Dilate[L, 17 - o, K]]], Translate[C, Vector[L, Dilate[L, 17 - o, K]]]], Polygon[Translate[A, K - L], Translate[E, K - L], Translate[D, K - L], Translate[C, K - L]]) → q2
52. Angle(B, C, A) → α