Exploring Symmetry and Translation with Cutouts and Folds

GeoGebra Commands & Parameters

1. Circle(Départ, b) → e
2. Line(Départ, xAxis) → d
3. Line(Départ, yAxis) → b_1
4. Intersect(e, b_1) → B, C
5. Line(B, d) → g
6. Circle(Départ, a) → c
7. Intersect(c, d) → D, E
8. Mirror(Départ, E) → A'
9. Line(E, b_1) → f
10. Intersect(g, f) → F
11. Vector(E, F) → u_2
12. CircleArc(F, Départ, A') → h
13. Point(h) → Move
14. Translate(Move, u_2) → G'
15. Midpoint(G', Move) → I
16. Polygon(G', F, E, Move) → poly1, g', f_1, e_1, g_1
17. Intersect(g_1, d) → H
18. Mirror(E, H) → E'
19. Translate(E', u_2) → E''
20. Polygon(E'', E', Move, G') → poly2, e'', e', g_2, g'_1
21. Angle(Départ, E, Move) → α
22. Vector(Départ, E) → u
23. Line(G', Move) → i_2
24. Intersect(i_2, d) → I_2
25. Vector(E, I_2) → v
26. Vector(E, E') → w
27. Sequence(Polygon[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]], Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre, 1) → liste2
28. Sequence(Polygon[Translate[G', Vector[(s * w)]], Translate[F, Vector[(s * w)]], Translate[E, Vector[(s * w)]], Translate[Move, Vector[(s * w)]]], s, 0, Nombre) → liste7
29. Segment(G', Move) → aa_1
30. PointIn(poly1) → J
31. PointIn(poly1) → K
32. PointIn(poly1) → L
33. PointIn(poly1) → M
34. PointIn(poly1) → N
35. PointIn(poly1) → O
36. PointIn(poly1) → P
37. PointIn(poly1) → Q
38. PointIn(poly1) → R
39. PointIn(poly1) → S
40. Polygon(J, K, M, O, P, S, R, Q, N, L) → poly3, j, l, k, m, o, p, s, r, q, n_1
41. Mirror(J, aa_1) → J'
42. Mirror(K, aa_1) → K'
43. Mirror(M, aa_1) → M'
44. Mirror(O, aa_1) → O'
45. Mirror(P, aa_1) → P'
46. Mirror(S, aa_1) → S'
47. Mirror(R, aa_1) → R'
48. Mirror(Q, aa_1) → Q'
49. Mirror(N, aa_1) → N'
50. Mirror(L, aa_1) → L'
51. Polygon(J', K', M', O', P', S', R', Q', N', L') → poly3', j', l', k', m', o', p', s', r', q', n'
52. Sequence(Polygon[Translate[J, Vector[(s * w)]], Translate[K, Vector[(s * w)]], Translate[M, Vector[(s * w)]], Translate[O, Vector[(s * w)]], Translate[P, Vector[(s * w)]], Translate[S, Vector[(s * w)]], Translate[R, Vector[(s * w)]], Translate[Q, Vector[(s * w)]], Translate[N, Vector[(s * w)]], Translate[L, Vector[(s * w)]]], s, 0, Nombre) → liste1
53. Sequence(Polygon[Translate[J', Vector[(s * w)]], Translate[K', Vector[(s * w)]], Translate[M', Vector[(s * w)]], Translate[O', Vector[(s * w)]], Translate[P', Vector[(s * w)]], Translate[S', Vector[(s * w)]], Translate[R', Vector[(s * w)]], Translate[Q', Vector[(s * w)]], Translate[N', Vector[(s * w)]], Translate[L', Vector[(s * w)]]], s, 0, Nombre) → liste3
54. Sequence(Segment[Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre) → liste4
55. Segment(F, E) → aa
56. Sequence(Segment[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]]], s, 0, Nombre) → liste5
57. Mirror(G', f_1) → G''
58. Mirror(F, f_1) → F'
59. Mirror(E, f_1) → E'_1
60. Mirror(G', f_1) → G''_1
61. Mirror(F, f_1) → F'_1
62. Mirror(E, f_1) → E'_2
63. Line(F, E) → i
64. Mirror(G', i) → G''_2
65. Mirror(F, i) → F'_2
66. Mirror(E, i) → E'_3
67. Mirror(Move, i) → G'_1
68. Polygon(G''_2, F'_2, E'_3, G'_1) → poly1', g''_2, f'_2, e'_3, g'_2
69. Mirror(J, i) → J'_1
70. Mirror(K, i) → K'_1
71. Mirror(M, i) → M'_1
72. Mirror(O, i) → O'_1
73. Mirror(P, i) → P'_1
74. Mirror(S, i) → S'_1
75. Mirror(R, i) → R'_1
76. Mirror(Q, i) → Q'_1
77. Mirror(N, i) → N'_1
78. Mirror(L, i) → L'_1
79. Polygon(J'_1, K'_1, M'_1, O'_1, P'_1, S'_1, R'_1, Q'_1, N'_1, L'_1) → poly3'_1, j'_1, l'_1, k'_1, m'_1, o'_1, p'_1, s'_1, r'_1, q'_1, n'_1
80. Ellipse(C_1, D_1, E_1) → c_1
81. Circle(F_1, G_1) → d_1
82. Circle(H_1, I_1) → h_1