第7个皮亚哥拉定理探索：互动几何作图与谜题

GeoGebra 命令及参数

1. Distance(A, B) → nc
2. Semicircle(A, B) → z
3. Point(z) → C
4. Polygon(C, B, 4) → poly4, c_3, b_2, h, i, H, I
5. Line(H, I) → k
6. Polygon(A, C, 4) → poly3, a_2, c_2, f, g, F, G
7. Line(G, F) → j
8. Intersect(j, k) → J
9. Circle(J, If[n ≤ 0, -n, n]) → s
10. Segment(J, I) → q
11. Line(J, C) → l
12. Polygon(A, B, C) → poly1, c, a, b
13. Intersect(c, l) → K
14. Segment(J, K) → p
15. Intersect(s, If[n ≤ 0, q, p], 1) → I_1
16. If(n ≤ 0, (x(C), y(C)), Translate[I_1, Vector[J, C]]) → C_1
17. If(n ≤ nc, Translate[I_1, Vector[C, B]], (x(B), y(B))) → H_1
18. If(n ≤ 0, (x(B), y(B)), Translate[H_1, Vector[J, C]]) → B_1
19. Polygon(B, A, 4) → poly2, b_1, a_1, d, e, D, E
20. Midpoint(A, B) → L
21. Segment(J, F) → r
22. Distance(C, K) → hc
23. Distance(B, C) → na
24. Distance(C, A) → nb
25. If(a > b, -a, -b) → nmin
26. Polygon(I_1, C_1, B_1, H_1) → poly5, m, t, c_1, d_1
27. Intersect(s, If[n ≤ 0, r, p], 1) → F_1
28. If(n ≤ nc, Translate[F_1, Vector[C, A]], (x(A), y(A))) → G_1
29. If(n ≤ 0, (x(C), y(C)), Translate[F_1, Vector[J, C]]) → C1
30. If(n ≤ 0, (x(A), y(A)), Translate[G_1, Vector[J, C]]) → A_1
31. Polygon(G_1, A_1, C1, F_1) → poly6, g_1, a_3, c1, f_1
32. Angle(A, C, B) → α