Regular Pentagon Wonder: GoGeometry Action 192!

GeoGebra Commands & Parameters

1. Circle(A, B) → c
2. Point(c) → C
3. Rotate(C, (2 * π / 5), A) → C'
4. Polygon(C, C', 5) → poly1, f, g, h, i, j, D, E, F
5. CircleArc(A, E, F) → d
6. CircleArc(A, F, E) → e
7. Point(d) → G
8. Dilate(G, If[0 < a ≤ 2, 1 - (0.5 * a), 0], F) → G'
9. Dilate(G, If[0 < a ≤ 2, 1 - (0.5 * a), 0], C) → G'_{1}
10. Dilate(G, If[0 < a ≤ 2, 1 - (0.5 * a), 0], C') → G'_{2}
11. Dilate(G, If[0 < a ≤ 2, 1 - (0.5 * a), 0], D) → G'_{3}
12. Dilate(G, If[0 < a ≤ 2, 1 - (0.5 * a), 0], E) → G'_{4}
13. Segment(G, G') → k
14. Segment(G, G'_{1}) → l
15. Segment(G, G'_{2}) → m
16. Segment(G, G'_{3}) → n
17. Segment(G, G'_{4}) → p
18. Segment(D, E) → r
19. Segment(E, F) → s
20. Segment(F, C) → t
21. Segment(C, C') → b
22. Segment(C', D) → f_1
23. Dilate(F, If[4 < a ≤ 5, 5 - a, 0], H) → F'
24. Vector(F, F') → u
25. Translate(G, u) → G'_{5}
26. Translate(G', u) → G''
27. Segment(G'_{5}, G'') → k'
28. Point(h_1) → J
29. Angle(J, F', G'_{5}) → α
30. Rotate(G'_{5}, If[4 < a ≤ 5, ((-(a - 4)) * α), (-α)], G'') → K
31. Rotate(G'', If[4 < a ≤ 5, ((-(a - 4)) * α), (-α)], G'') → G'''
32. Segment(K, G''') → k''
33. Dilate(G, If[5 < a ≤ 6, 6 - a, 0], K) → G'_{6}
34. Vector(G, G'_{6}) → v
35. Point(p_1) → L
36. Angle(C', G, L) → β
37. Translate(G, v) → G'_{7}
38. Translate(G'_{2}, v) → M
39. Segment(G'_{7}, M) → m'
40. Rotate(G'_{7}, If[5 < a ≤ 6, ((a - 5) * β), β], G'_{6}) → N
41. Rotate(M, If[5 < a ≤ 6, ((a - 5) * β), β], G'_{6}) → M'
42. Segment(N, M') → m''
43. Dilate(G, If[6 < a ≤ 7, 7 - a, 0], M') → G'_{8}
44. Vector(G, G'_{8}) → w
45. Translate(G, w) → G'_{9}
46. Translate(G'_{4}, w) → O
47. Segment(G'_{9}, O) → p'
48. Angle(E, G, L) → γ
49. Rotate(G'_{9}, If[6 < a ≤ 7, ((a - 6) * γ), γ], G'_{9}) → P
50. Rotate(O, If[6 < a ≤ 7, ((a - 6) * γ), γ], G'_{9}) → O'
51. Segment(P, O') → p''
52. Dilate(C, If[9 < a ≤ 10, 10 - a, 0], I) → C'_{1}
53. Vector(C, C'_{1}) → u_1
54. Translate(G, u_1) → G'_{10}
55. Translate(G'_{1}, u_1) → Q
56. Segment(G'_{10}, Q) → l'
57. Point(q_1) → R
58. Angle(R, C, G) → δ
59. Rotate(G'_{10}, If[9 < a ≤ 10, ((-(a - 9)) * δ), (-δ)], Q) → S
60. Rotate(Q, If[9 < a ≤ 10, ((-(a - 9)) * δ), (-δ)], Q) → Q'
61. Segment(S, Q') → l''
62. Dilate(G, If[10 < a ≤ 11, 11 - a, 0], S) → G'_{11}
63. Vector(G, G'_{11}) → v_1
64. Translate(G, v_1) → G'_{12}
65. Translate(G'_{3}, v_1) → T
66. Segment(G'_{12}, T) → n'
67. Angle(D, G, L) → ε
68. Rotate(G'_{12}, If[10 < a ≤ 11, ((a - 10) * ε), ε], G'_{12}) → U
69. Rotate(T, If[10 < a ≤ 11, ((a - 10) * ε), ε], G'_{12}) → T'
70. Segment(U, T') → n''
71. Dilate(I, If[13 < a ≤ 14, 14 - a, 0], H) → I'
72. Vector(I, I') → w_1
73. Translate(S, w_1) → S'
74. Translate(Q', w_1) → Q''
75. Segment(S', Q'') → l'''
76. Translate(U, w_1) → U'
77. Translate(T', w_1) → T''
78. Segment(U', T'') → n'''