正多边形现象探索

GeoGebra 命令及参数

1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
2. Polygon(D, C, 10) → poly2, k, a, F, G, H, I, J, K, L, M, l, m, n, p, q, r, s, t
3. Segment(E, H) → b
4. Segment(E, M) → c
5. Segment(M, H) → j_1
6. Angle(E, M, H) → α
7. Angle(H, E, M) → δ
8. Segment(E, D) → e
9. Segment(D, C) → f_1
10. Segment(C, B) → g_1
11. Segment(B, A) → h_1
12. Segment(A, E) → i_1
13. Segment(C, F) → k_1
14. Segment(F, G) → l_1
15. Segment(G, H) → m_1
16. Segment(H, I) → n_1
17. Segment(I, J) → p_1
18. Segment(J, K) → q_1
19. Segment(K, L) → r_1
20. Segment(L, M) → s_1
21. Midpoint(j_1) → N
22. Polygon(G, F, 6) → poly3, t_1, R, a_1, b_1, c_1, d_1, e_1, O, P, Q
23. Segment(M, D) → f_2
24. Segment(B, R) → r_2
25. Segment(F, O) → g_2
26. Segment(O, P) → h_2
27. Segment(P, Q) → i_2
28. Segment(Q, R) → j_2
29. Segment(R, G) → k_2
30. Dilate(E, If[0 < u ≤ 1, 1 - u, 0], M) → E'
31. Segment(E, E') → l_2
32. Dilate(M, If[1 < u ≤ 2, 2 - u, 0], N) → M'
33. Segment(M, M') → m_2
34. Dilate(N, If[2 < u ≤ 3, 3 - u, 0], H) → N'
35. Segment(N, N') → n_2
36. Rotate(E, If[4 < u ≤ 5, (((u - 4) * 3) * π / 5), (3 * π / 5)], M) → E'_1
37. Rotate(E', If[4 < u ≤ 5, (((u - 4) * 3) * π / 5), (3 * π / 5)], M) → E''
38. Segment(E'_1, E'') → p_2
39. Rotate(E'_1, If[5 < u ≤ 6, ((u - 5) * π), π], E'_1) → S
40. Rotate(E'', If[5 < u ≤ 6, ((u - 5) * π), π], E'_1) → E'''
41. Segment(S, E''') → q_2
42. Dilate(B, If[6 < u ≤ 7, 7 - u, 0], R) → B'
43. Segment(B, B') → s_2
44. Dilate(H, If[8 < u ≤ 9, 9 - u, 0], R) → H'
45. Vector(H, H') → v
46. Line(R, q_2) → t_2
47. Point(t_2) → T
48. Angle(T, R, B) → ε
49. Translate(S, v) → S'
50. Translate(E''', v) → U
51. Segment(S', U) → a_2
52. Translate(E'_1, v) → V
53. Translate(E'', v) → E'''_1
54. Segment(V, E'''_1) → b_2
55. Rotate(S', If[8 < u ≤ 9, ((u - 8) * ε), ε], U) → S''
56. Rotate(U, If[8 < u ≤ 9, ((u - 8) * ε), ε], U) → U'
57. Segment(S'', U') → c_2
58. Rotate(V, If[8 < u ≤ 9, ((u - 8) * ε), ε], U) → V'
59. Rotate(E'''_1, If[8 < u ≤ 9, ((u - 8) * ε), ε], U) → W
60. Segment(V', W) → d_2