毕达哥拉斯定理“无字证明”几何拼图演示

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Polygon(A, B, 3) → poly1, f, g, h, C
3. Centroid(poly1) → D
4. Midpoint(h) → E
5. Midpoint(g) → F
6. Midpoint(f) → G
7. Point(Segment[A, G]) → H
8. Line(C, H) → i
9. Segment(E, D) → j
10. Intersect(i, j) → I
11. Angle(A, C, H) → α
12. Polygon(C, E, I) → t1, i_1, c, e
13. Polygon(C, I, D, F) → q1, c_1, i_2, d, f_1
14. Line(A, B) → k
15. Rotate(k, α, B) → k'
16. Intersect(k', yAxis) → J
17. Polygon(B, J, 3) → poly2, l, m, n, K
18. Centroid(poly2) → L
19. Circle(D, Segment[L, B]) → p
20. Line(D, C) → q
21. Line(D, A) → r
22. Line(D, B) → s
23. Intersect(p, r, 2) → M
24. Intersect(p, s, 2) → N
25. Intersect(p, q, 2) → O
26. LineBisector(C, O) → t
27. Midpoint(O, M) → P
28. LineBisector(I, E) → a
29. Intersect(t, a) → Q
30. If(0 ≤ o ≤ 1, Polygon[Rotate[C, ((-o) * α), Q], Rotate[I, ((-o) * α), Q], Rotate[D, ((-o) * α), Q], Rotate[F, ((-o) * α), Q]]) → q2
31. If(0 ≤ o ≤ 1, Rotate[I, ((-o) * α), Q]) → R
32. Rotate(If[0 ≤ o ≤ 1, Polygon[Rotate[C, ((-o) * α), Q], Rotate[E, ((-o) * α), Q], Rotate[I, ((-o) * α), Q]]], (o * π), R) → t2
33. Rotate(If[0 ≤ o ≤ 1, Rotate[E, ((-o) * α), Q]], (o * π), R) → S
34. Rotate(I, (2 * π / 3), D) → I'
35. Rotate(I, (-2 * π / 3), D) → I'_1
36. Polygon(A, E, D, I') → q3, a_1, e_1, d_1, i'
37. Rotate(Rotate[If[0 ≤ o ≤ 1, Polygon[Rotate[A, ((-o) * α), Q], Rotate[E, ((-o) * α), Q], Rotate[D, ((-o) * α), Q], Rotate[I', ((-o) * α), Q]]], (o * π), R], ((-o) * π), S) → q4
38. Rotate(Rotate[If[0 ≤ o ≤ 1, Rotate[I', ((-o) * α), Q]], (o * π), R], ((-o) * π), S) → T
39. Polygon(A, I', G) → t3, g_1, a_2, b
40. Rotate(Rotate[Rotate[If[0 ≤ o ≤ 1, Polygon[Rotate[A, ((-o) * α), Q], Rotate[I', ((-o) * α), Q], Rotate[G, ((-o) * α), Q]]], (o * π), R], ((-o) * π), S], (o * π), T) → t4
41. Polygon(B, G, D, I'_1) → q5, b_1, g_2, d_2, i'_1
42. Rotate(Rotate[Rotate[If[0 ≤ o ≤ 1, Rotate[G, ((-o) * α), Q]], (o * π), R], ((-o) * π), S], (o * π), T) → U
43. Rotate(Rotate[Rotate[Rotate[If[0 ≤ o ≤ 1, Polygon[Rotate[B, ((-o) * α), Q], Rotate[G, ((-o) * α), Q], Rotate[D, ((-o) * α), Q], Rotate[I'_1, ((-o) * α), Q]]], (o * π), R], ((-o) * π), S], (o * π), T], ((-o) * π), U) → q6
44. Polygon(B, I'_1, F) → t5, f_2, b_2, h_1
45. Rotate(Rotate[Rotate[Rotate[If[0 ≤ o ≤ 1, Rotate[I'_1, ((-o) * α), Q]], (o * π), R], ((-o) * π), S], (o * π), T], ((-o) * π), U) → V
46. Rotate(Rotate[Rotate[Rotate[Rotate[If[0 ≤ o ≤ 1, Polygon[Rotate[B, ((-o) * α), Q], Rotate[I'_1, ((-o) * α), Q], Rotate[F, ((-o) * α), Q]]], (o * π), R], ((-o) * π), S], (o * π), T], ((-o) * π), U], (o * π), V) → t6