用半角正弦计算圆周率π

GeoGebra 命令及参数

1. Rotate(A, α, B) → A'
2. Rotate(A, (-α), B) → A'_1
3. Segment(A', A'_1) → f
4. Polygon(A'_1, A', (4 * 2^(a - 1))) → poly1, g, q, r_5, s_5, t_5, a_5, b_5, c_5, d_5, e_5, f_6, g_6, r, h_6, i_6, j_6, k_6, l_6, m_6, n_6, p_6, q_6, r_6, s, s_6, t_6, a_6, b_6, c_6, d_6, e_6, f_7, g_7, h_7, t, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7, r_7, s_7, b, t_7, a_7, b_7, c_7, d_7, e_7, f_8, g_8, h_8, i_8, d, j_8, k_8, l_8, m_8, n_8, p_8, q_8, r_8, s_8, t_8, e, a_8, b_8, c_8, d_8, e_8, f_9, g_9, h_9, i_9, j_9, f_1, k_9, l_9, m_9, n_9, p_9, q_9, r_9, s_9, t_9, a_9, g_1, b_9, c_9, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, h_1, l_{10}, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}, s_{10}, t_{10}, a_{10}, b_{10}, h, i_1, c_{10}, d_{10}, e_{10}, f_{11}, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, j_1, m_{11}, n_{11}, p_{11}, q_{11}, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, c_{11}, k_1, d_{11}, e_{11}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, l_1, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}, t_{12}, a_{12}, b_{12}, c_{12}, d_{12}, m_1, e_{12}, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, n_1, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}, a_{13}, b_{13}, C, D, E, p_1, F, G, H, I, J, K, L, M, N, O, q_1, P, Q, R, S, T, U, V, W, Z, A_1, r_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, s_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, i, t_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, a_1, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, T_2, b_1, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, c_1, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, d_1, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, e_1, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, f_2, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, U_4, V_4, g_2, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5, h_2, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, i_2, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, D_6, j, j_2, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6, k_2, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, l_2, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, I_7, J_7, m_2, K_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, n_2, U_7, V_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, p_2, G_8, H_8, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8, q_2, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, r_2, C_9, D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, s_2, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_9, U_9, V_9, t_2, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, k, a_2, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, b_2, S_{10}, c_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, l, k_3, l_3, m_3, n_3, p_3, a_3, b_3, c_3, d_3, e_3, m, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, p_4, n, q_4, r_4, s_4, t_4, a_4, b_4, c_4, d_4, e_4, f_5, p, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5, p_5, q_5
5. Segment(B, A'_1) → q_3
6. Segment(B, A') → r_3
7. OrthogonalLine(B, f) → s_3
8. Intersect(f, g) → Q_2
9. Intersect(f, g) → R_2
10. Intersect(f, s_3) → S_2
11. Segment(B, S_2) → t_3
12. Angle(B, S_2, A'_1) → β