Interactive Definition of Regular Polygons

GeoGebra Commands & Parameters

1. Rotate(A, 108°, B) → A'
2. Ray(B, A') → g
3. Ray(B, A) → f
4. Point(f) → C
5. Segment(C, B) → n
6. Circle(C, n) → d_1
7. Rotate(B, (-(108°)), C) → B'
8. Ray(C, B') → h
9. Intersect(d_1, h, 1) → G
10. Circle(G, n) → e_1
11. Point(h) → D
12. Rotate(C, (-(108°)), D) → C'
13. Ray(D, C') → i
14. Point(i) → E
15. Rotate(D, (-(108°)), E) → D'
16. Ray(E, D') → j
17. Intersect(g, j) → F
18. Segment(F, E) → k
19. Segment(E, D) → l
20. Line(G, l) → g_1
21. Intersect(e_1, g_1, 1) → J
22. Line(J, k) → h_1
23. Intersect(h_1, g) → K
24. Angle(A, B, A') → α
25. Angle(B', C, B) → β
26. Angle(C', D, C) → γ
27. Angle(D', E, D) → δ
28. Segment(D, C) → m
29. Segment(B, F) → p
30. Min(list) → a
31. Circle(B, (0.2 * n)) → q
32. Intersect(q, p) → H,
33. Intersect(q, n) → I,
34. CircleSector(B, I, H) → r
35. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], C) → B'_1
36. Vector(B, B'_1) → u
37. Translate(r, u) → r'
38. Rotate(r', If[1 < o ≤ 2, (((o - 1) * 2) * π / 5), (2 * π / 5)], C) → r''
39. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], G) → C'_1
40. Vector(C, C'_1) → v
41. Translate(r'', v) → r'''
42. Rotate(r''', If[3 < o ≤ 4, (((o - 3) * 2) * π / 5), (2 * π / 5)], G) → s
43. Dilate(G, If[4 < o ≤ 5, 5 - o, 0], J) → D'_1
44. Vector(G, D'_1) → w
45. Translate(s, w) → s'
46. Rotate(s', If[5 < o ≤ 6, (((o - 5) * 2) * π / 5), (2 * π / 5)], J) → s''
47. Dilate(J, If[6 < o ≤ 7, 7 - o, 0], K) → E'
48. Vector(J, E') → t
49. Translate(s'', t) → s'''
50. Circle(J, n) → k_1
51. Rotate(s''', If[7 < o ≤ 8, (((o - 7) * 2) * π / 5), (2 * π / 5)], K) → c_1
52. Segment(B, B'_1) → b
53. Segment(C, C'_1) → c
54. Segment(G, D'_1) → d
55. Segment(J, E') → e
56. Dilate(K, If[8 < o ≤ 9, 9 - o, 0], B) → K'
57. Segment(K, K') → f_1
58. Polygon(B, C, G, J, K) → poly1, b_1, c_2, g_2, j_1, k_2
59. Rotate(B, If[9 < o ≤ 10, ((-(o - 9)) * α), (-α)], C) → B'_2
60. Rotate(B'_1, If[9 < o ≤ 10, ((-(o - 9)) * α), (-α)], C) → L
61. Segment(B'_2, L) → b'
62. Rotate(B'_2, If[10 < o ≤ 11, ((-(o - 10)) * α), (-α)], G) → M
63. Rotate(L, If[10 < o ≤ 11, ((-(o - 10)) * α), (-α)], G) → L'
64. Segment(M, L') → b''
65. Rotate(M, If[11 < o ≤ 12, ((-(o - 11)) * α), (-α)], J) → M'
66. Rotate(L', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], J) → L''
67. Segment(M', L'') → b'''
68. Rotate(M', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], K) → M''
69. Rotate(L'', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], K) → L'''
70. Segment(M'', L''') → i_1