有趣三角形现象：旋转与分形几何的视觉探索

GeoGebra 命令及参数

1. Rotate(A, (a * π / 180), B) → A'
2. Angle(A, B, A') → α
3. Ray(B, A') → g
4. Point(g) → C
5. Segment(A, C) → j
6. Circle(B, j) → d
7. Rotate(B, (-(π - α)), C) → B'
8. Ray(C, B') → h
9. Intersect(d, h, 1) → D
10. Midpoint(A, D) → N
11. Segment(A, B) → f
12. Angle(B', C, B) → γ
13. Segment(B, D) → i
14. Angle(C, A, B) → β
15. Angle(B, D, C) → δ
16. Ray(C, B) → k
17. Min({f, j, i, Distance[C, D]}) → b
18. Circle(B, (0.25 * b)) → c
19. Circle(A, (0.25 * b)) → e
20. Polygon(A, C, D, B) → q1, a_1, c_1, d_1, b_1
21. Segment(C, D) → m
22. Intersect(c, f, 1) → E
23. Rotate(E, If[0 < l ≤ 1, ((-l) * γ), (-γ)], B) → E'
24. CircleSector(B, E', E) → p
25. Semicircle(B, C) → q
26. Midpoint(C, B) → F
27. Rotate(B, If[2 < l ≤ 3, ((-(l - 2)) * π), (-π)], F) → B'_{1}
28. Vector(B, B'_{1}) → u
29. Translate(p, u) → p'
30. Line(B, m) → n
31. Rotate(p', If[2 < l ≤ 3, ((-(l - 2)) * γ), (-γ)], B'_{1}) → p''
32. Circle(B, E) → r
33. Intersect(r, k) → G, H
34. CircleArc(B, H, E) → s
35. Dilate(A, If[3 < l ≤ 4, 4 - l, 0], C) → A'_{1}
36. Vector(A, A'_{1}) → v
37. Segment(A, A'_{1}) → t
38. Dilate(C, If[4 < l ≤ 5, 5 - l, 0], D) → C'
39. Vector(C, C') → w
40. Translate(A, w) → A'_{2}
41. Translate(A'_{1}, w) → I
42. Segment(A'_{2}, I) → t'
43. Line(B, D) → f_1
44. Line(C, f_1) → g_1
45. Point(g_1) → J
46. Angle(A, C, J) → ε
47. Rotate(A'_{2}, If[4 < l ≤ 5, ((l - 4) * ε), ε], C') → K
48. Rotate(I, If[4 < l ≤ 5, ((l - 4) * ε), ε], C') → I'
49. Segment(K, I') → t''
50. Intersect(e, Segment[A, C]) → L,
51. Rotate(L, If[6 < l ≤ 7, ((l - 6) * β), β], A) → L'
52. CircleSector(A, L, L') → e_1
53. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], N) → A'_{3}
54. Vector(A, A'_{3}) → u_1
55. Translate(e_1, u_1) → h_1
56. Intersect(e, f, 1) → M
57. Line(N, t'') → i_1
58. Line(A, t'') → j_1
59. Point(j_1) → O
60. Angle(O, A, C) → ζ
61. Rotate(h_1, If[9 < l ≤ 10, ((-(l - 9)) * ζ), (-ζ)], N) → k_1
62. Dilate(N, If[10 < l ≤ 11, 11 - l, 0], D) → N'
63. Vector(N, N') → v_1
64. Translate(k_1, v_1) → p_1
65. Rotate(E, (a / 2 * π / 180), B) → E'_{1}