Can Four Pieces Fit into a Square?

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
3. Midpoint(D, A) → E
4. Midpoint(A, B) → F
5. Midpoint(B, C) → G
6. Midpoint(C, D) → H
7. Midpoint(H, D) → I
8. Midpoint(D, E) → J
9. Midpoint(E, A) → K
10. Midpoint(A, F) → L
11. Midpoint(F, B) → M
12. Midpoint(B, G) → N
13. Midpoint(G, C) → O
14. Midpoint(C, H) → P
15. Segment(I, L) → j
16. Segment(H, F) → k
17. Segment(P, M) → l
18. Segment(J, O) → m
19. Segment(E, G) → n
20. Segment(K, N) → p
21. Polygon(A, L, 4) → poly2, q, r, s, t, Q, R
22. Polygon(F, M, 4) → poly3, a, b, c, d, S, T
23. Polygon(Q, T, 4) → poly4, e, f_1, g_1, h_1, U, V
24. Polygon(E, V, 4) → poly5, i_1, j_1, k_1, l_1, W, Z
25. Polygon(I, W, 4) → poly6, m_1, n_1, p_1, q_1, A_1, B_1
26. Polygon(A_1, U, 4) → poly7, r_1, s_1, t_1, a_1, C_1, D_1
27. Polygon(C_1, S, 4) → poly8, b_1, c_1, d_1, e_1, E_1, F_1
28. Polygon(P, D_1, 4) → poly9, f_2, g_2, h_2, i_2, G_1, H_1
29. Point(Circle[I_1, 2]) → J_1
30. Segment(I_1, J_1) → j_2
31. Midpoint(j_2) → K_1
32. Polygon(I_1, K_1, 4) → whiteS2, k_2, l_2, m_2, n_2, L_1, M_1
33. Polygon(K_1, J_1, 4) → poly11, p_2, q_2, r_2, s_2, N_1, O_1
34. Polygon(L_1, N_1, 4) → whiteS1, t_2, a_2, b_2, c_2, P_1, Q_1
35. Polygon(P_1, N_1, 4) → poly13, d_2, e_2, f_3, g_3, R_1, S_1
36. Polygon(I_1, J_1, N_1, R_1, S_1, Q_1, L_1, M_1) → Sborder_0, i_3, j_3, n_3, r_3, s_3, q_3, l_3, m_3
37. Polygon(M_1, I_1, J_1, N_1, R_1, S_1, Q_1, L_1) → Sborder_2, m_4, i_4, j_4, n_4, r_4, s_4, q_4, l_4
38. Segment(L_1, K_1) → h_3
39. Segment(P_1, N_1) → k_3
40. Segment(L_1, N_1) → p_3
41. Point(Circle[T_1, 2]) → U_1
42. Segment(T_1, U_1) → t_3
43. Midpoint(t_3) → V_1
44. Polygon(T_1, V_1, 4) → poly10, a_3, b_3, c_3, d_3, W_1, Z_1
45. Polygon(V_1, U_1, 4) → whiteL1, e_3, f_4, g_4, h_4, A_2, B_2
46. Polygon(Z_1, W_1, 4) → whiteL2, k_4, p_4, t_4, a_4, C_2, D_2
47. Polygon(D_2, C_2, 4) → poly15, b_4, c_4, d_4, e_4, E_2, F_2
48. Polygon(F_2, T_1, U_1, A_2, W_1, E_2) → Lborder_0, f_5, t_5, u_1, a_5, w_1, e_5
49. Segment(D_2, C_2) → g_5
50. Segment(Z_1, W_1) → h_5
51. Segment(W_1, V_1) → i_5
52. Polygon(F_2, T_1, U_1, A_2, W_1, E_2) → Lborder_2, f_6, t_6, u_2, a_6, w_2, e_6
53. Point(Circle[G_2, 3]) → H_2
54. Segment(G_2, H_2) → j_5
55. Circle(G_2, 1) → c_5
56. Circle(H_2, 1) → d_5
57. Intersect(c_5, j_5, 1) → I_2
58. Intersect(d_5, j_5, 1) → J_2
59. Polygon(G_2, I_2, 4) → poly14, k_5, l_5, m_5, n_5, K_2, L_2
60. Polygon(I_2, J_2, 4) → whiteT1, p_5, q_5, r_5, s_5, M_2, N_2
61. Polygon(J_2, H_2, 4) → poly17, b_5, g_6, h_6, i_6, O_2, P_2
62. Polygon(K_2, M_2, 4) → poly18, j_6, k_6, l_6, m_6, Q_2, R_2
63. Polygon(G_2, H_2, O_2, M_2, Q_2, R_2, K_2, L_2) → Tborder_0, g_7, h_7, o_2, m_7, q_6, r_6, k_7, l_7
64. Segment(K_2, I_2) → n_6
65. Segment(K_2, M_2) → p_6
66. Segment(M_2, J_2) → s_6
67. Polygon(G_2, H_2, O_2, M_2, Q_2, R_2, K_2, L_2) → Tborder_2, g_8, h_8, o_1, m_8, q_7, r_7, k_8, l_8
68. Point(Circle[S_2, 4]) → T_2
69. Segment(S_2, T_2) → b_6
70. Midpoint(b_6) → U_2
71. Midpoint(S_2, U_2) → V_2
72. Midpoint(U_2, T_2) → W_2
73. Polygon(S_2, V_2, 4) → whiteI1, c_6, d_6, f_7, i_7, Z_2, A_3
74. Polygon(V_2, U_2, 4) → poly19, j_7, n_7, p_7, s_7, B_3, C_3
75. Polygon(U_2, W_2, 4) → whiteI2, t_7, a_7, b_7, c_7, D_3, E_3
76. Polygon(W_2, T_2, 4) → Iborder_1, d_7, e_7, f_8, i_8, F_3, G_3
77. Polygon(A_3, S_2, T_2, F_3) → Iborder_0, a_8, s_8, t_8, f_9
78. Segment(Z_2, V_2) → j_8
79. Segment(B_3, U_2) → n_8
80. Segment(D_3, W_2) → p_8
81. Polygon(A_3, S_2, T_2, F_3) → Iborder_2, a_9, s_9, t_9, f_{10}