毕达哥拉斯定理无字证明

GeoGebra 命令及参数

1. Point(yAxis) → A
2. Point(yAxis) → B
3. Polygon(B, A, 3) → poly3, l, m, n, F
4. Semicircle(A, B) → c
5. Point(c) → C
6. Polygon(C, B, 3) → poly2, i, j, k, E
7. Midpoint(j) → K
8. Centroid(poly2) → H
9. LineBisector(i) → q
10. Mirror(A, i) → A'
11. Line(B, A') → p
12. Intersect(p, q) → G
13. Rotate(G, 120°, H) → G'
14. Angle(G', B, G) → aa
15. Rotate(Translate[K, F - B], (-aa), F) → M
16. Polygon(A, C, 3) → poly1, f, g, h, D
17. Rotate(G', 120°, H) → G''
18. Midpoint(i) → I
19. Midpoint(k) → J
20. Polygon(H, G, B, K) → q1, h_1, g_1, b_2, k_1
21. Polygon(H, G', E, J) → q2, h_2, g', e, j_1
22. Polygon(H, G'', C, I) → q3, h_3, g'', c_1, i_1
23. Angle(G, B, A) → a
24. If(0 < o ≤ 1, Rotate[Polygon[Translate[H, Vector[B, Dilate[B, 1 - o, F]]], Translate[G, Vector[B, Dilate[B, 1 - o, F]]], Translate[B, Vector[B, Dilate[B, 1 - o, F]]], Translate[K, Vector[B, Dilate[B, 1 - o, F]]]], ((-(o - 0)) * aa), Dilate[B, 1 - o, F]], Rotate[Polygon[Translate[H, F - B], Translate[G, F - B], Translate[B, F - B], Translate[K, F - B]], (-aa), F]) → q4
25. If(2 < o ≤ 3, Rotate[Polygon[Translate[H, Vector[E, Dilate[E, 3 - o, B]]], Translate[G', Vector[E, Dilate[E, 3 - o, B]]], Translate[E, Vector[E, Dilate[E, 3 - o, B]]], Translate[J, Vector[E, Dilate[E, 3 - o, B]]]], ((-(o - 2)) * aa), Dilate[E, 3 - o, B]], Rotate[Polygon[Translate[H, B - E], Translate[G', B - E], Translate[E, B - E], Translate[J, B - E]], (-aa), B]) → q5
26. If(4 < o ≤ 5, Rotate[Polygon[Translate[H, Vector[C, Dilate[C, 5 - o, A]]], Translate[G'', Vector[C, Dilate[C, 5 - o, A]]], Translate[C, Vector[C, Dilate[C, 5 - o, A]]], Translate[I, Vector[C, Dilate[C, 5 - o, A]]]], ((-(o - 4)) * aa), Dilate[C, 5 - o, A]], Rotate[Polygon[Translate[H, A - C], Translate[G'', A - C], Translate[C, A - C], Translate[I, A - C]], (-aa), A]) → q6
27. Polygon(G, I, B) → t1, b_1, g_2, i_2
28. Polygon(G', K, E) → t2, e_1, r, k_2
29. Polygon(G'', J, C) → t3, c_2, s, j_2
30. Line(B, G) → t
31. OrthogonalLine(B, l) → d
32. Point(d) → L
33. If(6 < o ≤ 7, Rotate[Polygon[Translate[G, Vector[B, Dilate[B, 7 - o, F]]], Translate[I, Vector[B, Dilate[B, 7 - o, F]]], Translate[B, Vector[B, Dilate[B, 7 - o, F]]]], ((-(o - 6)) * b), Dilate[B, 7 - o, F]], Rotate[Polygon[Translate[G, F - B], Translate[I, F - B], Translate[B, F - B]], (-b), F]) → t4
34. Rotate(Translate[K, F - B], (-aa), F) → N
35. If(8 < o ≤ 9, Rotate[Polygon[Translate[G', Vector[E, Dilate[E, 9 - o, B]]], Translate[K, Vector[E, Dilate[E, 9 - o, B]]], Translate[E, Vector[E, Dilate[E, 9 - o, B]]]], ((-(o - 8)) * b), Dilate[E, 9 - o, B]], Rotate[Polygon[Translate[G', B - E], Translate[K, B - E], Translate[E, B - E]], (-b), B]) → t5
36. If(10 < o ≤ 11, Rotate[Polygon[Translate[G'', Vector[C, Dilate[C, 11 - o, A]]], Translate[J, Vector[C, Dilate[C, 11 - o, A]]], Translate[C, Vector[C, Dilate[C, 11 - o, A]]]], ((-(o - 10)) * b), Dilate[C, 11 - o, A]], Rotate[Polygon[Translate[G'', A - C], Translate[J, A - C], Translate[C, A - C]], (-b), A]) → t6
37. Centroid(poly3) → O
38. Centroid(poly1) → P
39. Polygon(A, D, C) → t7, c_3, a_1, d_1
40. If(12 < o ≤ 13, Rotate[Polygon[Translate[A, Vector[P, Dilate[P, 13 - o, O]]], Translate[D, Vector[P, Dilate[P, 13 - o, O]]], Translate[C, Vector[P, Dilate[P, 13 - o, O]]]], ((-(o - 12)) * b), Dilate[P, 13 - o, O]], Rotate[Polygon[Translate[A, O - P], Translate[D, O - P], Translate[C, O - P]], (-b), O]) → t8
41. Angle(A, C, B) → α