Tangram Geometry with Rotations and Constructions

GeoGebra Commands & Parameters

1. Circle(A, a) → c
2. Point(c) → B
3. Line(A, B) → f
4. OrthogonalLine(B, f) → g_{4}
5. Circle(B, A) → d
6. Intersect(d, g_{4}, 2) → C
7. Polygon(A, B, C) → t1, c_1, a_1, b_{3}
8. Circle(D, a) → e
9. Point(e) → E
10. Line(D, E) → h
11. OrthogonalLine(E, h) → i
12. Circle(E, D) → k
13. Intersect(k, i, 2) → F
14. Polygon(D, E, F) → t2, f_1, d_1, e_1
15. Circle(G, a / 2) → p
16. Point(p) → H
17. Line(G, H) → j
18. OrthogonalLine(H, j) → l
19. Circle(H, G) → q
20. Intersect(q, l, 2) → I
21. OrthogonalLine(G, j) → m
22. OrthogonalLine(I, m) → n
23. Intersect(m, n) → J
24. Polygon(G, H, I, J) → q1, g_1, h_1, i_1, j_1
25. Circle(N, a / 2) → p_1
26. Point(p_1) → O
27. Line(N, O) → n_1
28. OrthogonalLine(O, n_1) → q_1
29. Circle(O, N) → r_1
30. Intersect(r_1, q_1, 1) → P
31. Polygon(O, N, P) → t4, p_2, o_1, n_2
32. Circle(Q, (sqrt(2) / 2 * a)) → s_1
33. Point(s_1) → R
34. Line(Q, R) → t_1
35. Rotate(R, ((-π)) / 4, Q) → R'
36. Rotate(R, π / 4, Q) → R'_{1}
37. Ray(Q, R') → b_1
38. Circle(Q, a / 2) → d_2
39. Intersect(d_2, b_1, 1) → S
40. Line(S, t_1) → f_2
41. Circle(S, (sqrt(2) / 2 * a)) → c_2
42. Intersect(c_2, f_2, 2) → T
43. Polygon(Q, S, T, R) → q2, q_2, s_2, t_2, r_2
44. Ray(Q, R'_{1}) → g_2
45. Intersect(d_2, g_2, 1) → U
46. Line(U, t_1) → h_2
47. Circle(U, (sqrt(2) / 2 * a)) → e_2
48. Intersect(e_2, h_2, 2) → V
49. Polygon(Q, R, V, U) → q3, q_3, r_3, v, u
50. Point(Circle[W, a / 2]) → Z
51. Segment(W, Z) → i_2
52. Rotate(Z, ((-π)) / 2, W) → Z'
53. Polygon(Z, W, Z') → t5, z', z_1, w
54. Point(Circle[A_1, a]) → B_1
55. Segment(A_1, B_1) → j_2
56. Rotate(B_1, ((-π)) / 4, A_1) → C_1
57. Rotate(A_1, π / 4, B_1) → D_1
58. Ray(B_1, D_1) → m_2
59. Ray(A_1, C_1) → a_2
60. Intersect(m_2, a_2) → E_1
61. Polygon(B_1, A_1, E_1) → t6, b_2, f_3, g_3
62. If(o ≟ 1, (sqrt(2) / 32 * a), o ≟ 2, a / 32) → r_{4}