45-45-90三角形证明：几何图形与数学概念的结合

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Circle(A, B) → c
4. Intersect(c, yAxis, 2) → C
5. Polygon(B, A, 4) → poly1, f, g, h, i, D, E
6. Polygon(A, C, 4) → poly2, j, k, l, m, F, G
7. Polygon(C, B, 4) → poly3, p, q, r, s, H, I
8. Polygon(G, C, F) → t1, f_1, g_1, c_1
9. Polygon(G, A, C) → t2, c_2, g_2, a
10. Midpoint(h) → J
11. Midpoint(g) → K
12. Midpoint(f) → L
13. Midpoint(i) → M
14. Centroid(poly1) → N
15. Polygon(D, K, N, J) → q1, d, k_1, n_1, j_1
16. Polygon(K, L, A) → t3, a_1, k_2, l_1
17. Polygon(K, L, B, N) → q2, k_3, l_2, b, n_2
18. Polygon(E, N, B) → t4, b_1, e, n_3
19. Polygon(J, N, E) → t5, e_1, j_2, n_4
20. If(0 ≤ n < 1, Rotate[Polygon[Translate[G, (n * (I - G))], Translate[C, (n * (I - G))], Translate[F, (n * (I - G))]], (n * π / 2), (n * (I - G))], If[1 ≤ n, Rotate[Polygon[Translate[G, (1 * (I - G))], Translate[C, (1 * (I - G))], Translate[F, (1 * (I - G))]], (1 * π / 2), (1 * (I - G))]]) → t6
21. If(2 ≤ n < 3, Polygon[Translate[G, ((n - 2) * (I - C))], Translate[A, ((n - 2) * (I - C))], Translate[C, ((n - 2) * (I - C))]], If[n ≥ 3, Polygon[Translate[G, I - C], Translate[A, I - C], Translate[C, I - C]], Polygon[G, C, A]]) → t7
22. If(4 ≤ n < 5, Polygon[Translate[K, ((n - 4) * (H - B))], Translate[L, ((n - 4) * (H - B))], Translate[B, ((n - 4) * (H - B))], Translate[N, ((n - 4) * (H - B))]], If[n ≥ 5, Polygon[Translate[K, H - B], Translate[L, H - B], Translate[B, H - B], Translate[N, H - B]], Polygon[K, L, B, N]]) → q3
23. If(6 ≤ n < 7, Polygon[Translate[K, ((n - 6) * (H - B))], Translate[L, ((n - 6) * (H - B))], Translate[A, ((n - 6) * (H - B))]], If[n ≥ 7, Polygon[Translate[K, H - B], Translate[L, H - B], Translate[A, H - B]], Polygon[K, L, A]]) → t8
24. Midpoint(C, H) → O
25. If(8 ≤ n < 9, Polygon[Translate[D, ((n - 8) * (O - N))], Translate[K, ((n - 8) * (O - N))], Translate[N, ((n - 8) * (O - N))], Translate[J, ((n - 8) * (O - N))]], If[n ≥ 9, Polygon[Translate[D, O - N], Translate[K, O - N], Translate[N, O - N], Translate[J, O - N]], Polygon[K, N, J, D]]) → q4
26. If(10 ≤ n < 11, Rotate[Polygon[Translate[E, ((n - 10) * (B - N))], Translate[N, ((n - 10) * (B - N))], Translate[B, ((n - 10) * (B - N))]], ((n - 10) * π / 2), B], If[n ≥ 11, Rotate[Polygon[Translate[E, B - N], Translate[N, B - N], Translate[B, B - N]], π / 2, B], Polygon[B, N, E]]) → t9
27. Midpoint(C, O) → P
28. Midpoint(C, B) → Q
29. If(12 ≤ n < 13, Rotate[Polygon[Translate[J, ((n - 12) * (P - J))], Translate[N, ((n - 12) * (P - J))], Translate[E, ((n - 12) * (P - J))]], ((n - 12) * π), Translate[J, ((n - 12) * (P - J))]], If[n ≥ 13, Polygon[C, P, Q], Polygon[N, J, E]]) → t10