Dynamic Relationship in Any Equilateral Triangle

GeoGebra Commands & Parameters

1. Polygon(A, B, 3) → poly1, f, g, h, C
2. Segment(A, B) → i
3. Point(i) → D
4. Line(C, D) → j
5. Rotate(B, π / 6, A) → B'
6. Angle(B, A, B') → α
7. Rotate(A, (-(π / 6)), B) → A'
8. Angle(A', B, A) → β
9. Ray(A, B') → k
10. Ray(B, A') → l
11. Angle(C, D, A) → γ
12. Rotate(C, γ / 2, D) → C'
13. Angle(C, D, C') → δ
14. Ray(D, C') → m
15. Rotate(B, (π - γ) / 2, D) → B'_1
16. Angle(B, D, B'_1) → ε
17. Ray(D, B'_1) → n
18. Intersect(k, m) → E
19. Intersect(l, n) → F
20. Segment(A, E) → p
21. Segment(E, D) → q
22. Segment(D, F) → r
23. Segment(B, F) → s
24. Min({p, q, r, s}) → a
25. Circle(A, (0.6 * a)) → c
26. Circle(B, (0.6 * a)) → d
27. Segment(A, B) → t
28. Segment(B, C) → b
29. Segment(C, A) → e
30. Intersect(c, k) → G,
31. Intersect(c, t) → H,
32. Intersect(d, b) → I,
33. Intersect(d, l) → J,
34. CircleSector(A, H, G) → c_1
35. CircleSector(B, I, J) → d_1
36. Circle(D, (0.6 * a)) → e_1
37. Intersect(e_1, j) → K, L
38. Intersect(e_1, m) → M,
39. Intersect(e_1, t) → N, O
40. Intersect(e_1, n) → P,
41. CircleSector(D, O, P) → f_1
42. CircleSector(D, K, M) → g_1
43. LineBisector(C, E) → h_1
44. LineBisector(F, C) → i_1
45. Intersect(i_1, h_1) → Q
46. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'_1
47. Segment(A, A'_1) → j_1
48. Rotate(A, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A'_2
49. Rotate(A'_1, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → R
50. Segment(A'_2, R) → k_1
51. Rotate(A, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → A'_3
52. Rotate(A'_1, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → S
53. Segment(A'_3, S) → l_1
54. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], D) → C'_1
55. Segment(C, C'_1) → m_1
56. Dilate(D, If[5 < o ≤ 6, 6 - o, 0], F) → D'
57. Dilate(D, If[5 < o ≤ 6, 6 - o, 0], E) → D'_1
58. Segment(D, D') → n_1
59. Segment(D, D'_1) → p_1
60. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], E) → A'_4
61. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], F) → B'_2
62. Segment(A, A'_4) → q_1
63. Segment(B, B'_2) → r_1
64. Rotate(c_1, If[8 < o ≤ 9, ((o - 8) * π / 6), π / 6], A) → s_1
65. Rotate(g_1, If[9 < o ≤ 10, ((o - 9) * δ), δ], D) → t_1
66. Rotate(f_1, If[10 < o ≤ 11, ((o - 10) * ε), ε], D) → c_2
67. Rotate(d_1, If[11 < o ≤ 12, ((o - 11) * π / 6), π / 6], B) → d_2
68. Dilate(Q, If[14 < o ≤ 15, 15 - o, 0], F) → Q'
69. Circle(Q, Q') → e_2
70. Polygon(E, F, Q) → poly2, q_2, e_3, f_2
71. Dilate(E, If[15 < o ≤ 16, 16 - o, 0], F) → E'
72. Segment(E, E') → a_1
73. Rotate(E, If[16 < o ≤ 17, ((o - 16) * π / 3), π / 3], E) → E'_1
74. Rotate(E', If[16 < o ≤ 17, ((o - 16) * π / 3), π / 3], E) → E''
75. Segment(E'_1, E'') → b_1
76. Rotate(E, If[17 < o ≤ 18, ((-(o - 17)) * π / 3), ((-π)) / 3], F) → E'_2
77. Rotate(E', If[17 < o ≤ 18, ((-(o - 17)) * π / 3), ((-π)) / 3], F) → E''_1
78. Segment(E'_2, E''_1) → g_2