Deriving Pi with Polygon Areas

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Circle(A, radius) → c
3. Rotate(B, a, A) → B'
4. Angle(B, A, B') → α
5. Polygon(B, B', n) → poly1, b, l, q_{10}, t_{10}, a_{11}, d_{11}, e_{11}, f_{11}, g_{11}, l_{11}, m_{11}, q_{11}, m, r_{11}, a_{12}, b_{12}, c_{12}, d_{12}, i_{12}, j_{12}, k_{12}, l_{12}, r_{12}, p, s_{12}, t_{12}, d_{13}, e_{13}, f_{13}, j_{13}, k_{13}, n_{13}, p_{13}, q_{13}, q, a_{14}, c_{14}, d_{14}, g_{14}, h_{14}, k_{14}, l_{14}, p_{14}, q_{14}, t_{14}, s, a_{15}, d_{15}, f_{15}, h_{15}, i_{15}, j_{15}, k_{15}, q_{15}, r_{15}, s_{15}, t, t_{15}, e_{16}, f_{16}, i_{16}, k_{16}, m_{16}, p_{16}, q_{16}, t_{16}, a_{17}, a_1, d_{17}, e_{17}, f_{17}, j_{17}, l_{17}, m_{17}, q_{17}, r_{17}, s_{17}, t_{17}, b_1, a_{18}, g_{18}, h_{18}, i_{18}, j_{18}, p_{18}, r_{18}, s_{18}, t_{18}, d_{19}, c_1, e_{19}, f_{19}, g_{19}, h_{19}, n_{19}, p_{19}, q_{19}, r_{19}, c_{20}, d_{20}, d_1, e_{20}, f_{20}, g_{20}, m_{20}, n_{20}, p_{20}, t_{20}, a_{21}, b_{21}, c_{21}, d, e_1, h_{21}, i_{21}, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, c_{22}, d_{22}, e_{22}, f_1, f_{22}, g_{22}, h_{22}, i_{22}, r_{22}, s_{22}, t_{22}, d_{23}, f_{23}, g_{23}, g_1, h_{23}, i_{23}, n_{23}, p_{23}, s_{23}, t_{23}, c_{24}, d_{24}, g_{24}, h_{24}, h_1, i_{24}, m_{24}, n_{24}, p_{24}, t_{24}, a_{25}, d_{25}, f_{25}, g_{25}, h_{25}, i_1, l_{25}, n_{25}, p_{25}, s_{25}, t_{25}, c_{26}, d_{26}, g_{26}, h_{26}, k_{26}, j_1, m_{26}, p_{26}, r_{26}, t_{26}, b_{27}, d_{27}, e_{27}, h_{27}, j_{27}, l_{27}, k_1, n_{27}, q_{27}, r_{27}, a_{28}, b_{28}, e_{28}, g_{28}, i_{28}, j_{28}, k_{28}, l_1, l_{28}, m_{28}, n_{28}, b_{29}, c_{29}, d_{29}, e_{29}, f_{29}, g_{29}, n_{29}, m_1, p_{29}, q_{29}, r_{29}, s_{29}, t_{29}, a_{30}, i_{30}, j_{30}, k_{30}, l_{30}, n_1, m_{30}, n_{30}, p_{30}, q_{30}, f_{31}, g_{31}, h_{31}, i_{31}, n_{31}, p_{31}, e, p_1, q_{31}, a_{32}, b_{32}, c_{32}, d_{32}, e_{32}, k_{32}, l_{32}, m_{32}, n_{32}, l_3, p_{32}, b_{33}, c_{33}, d_{33}, e_{33}, f_{33}, l_{33}, m_{33}, n_{33}, p_{33}, n_3, a_{34}, b_{34}, c_{34}, d_{34}, e_{34}, f_{34}, m_{34}, n_{34}, p_{34}, q_{34}, p_3, r_{34}, d_{35}, e_{35}, f_{35}, g_{35}, l_{35}, m_{35}, n_{35}, p_{35}, q_{35}, s_3, c_{36}, d_{36}, e_{36}, f_{36}, k_{36}, l_{36}, m_{36}, r_{36}, s_{36}, b_{37}, a_4, c_{37}, d_{37}, h_{37}, i_{37}, j_{37}, n_{37}, p_{37}, s_{37}, t_{37}, a_{38}, c_4, b_{38}, c_{38}, d_{38}, e_{38}, f_{38}, g_{38}, h_{38}, i_{38}, b_{39}, c_{39}, e_4, d_{39}, e_{39}, f_{39}, l_{39}, m_{39}, q_{39}, r_{39}, a_{40}, b_{40}, c_{40}, g_4, g_{40}, h_{40}, i_{40}, m_{40}, p_{40}, r_{40}, s_{40}, t_{40}, a_{41}, f_{41}, i_4, g_{41}, h_{41}, i_{41}, j_{41}, k_{41}, l_{41}, m_{41}, n_{41}, p_{41}, q_{41}, f, j_4, r_{41}, s_{41}, t_{41}, p_{42}, q_{42}, r_{42}, s_{42}, t_{42}, a_{43}, b_{43}, k_4, c_{43}, d_{43}, e_{43}, f_{43}, g_{43}, h_{43}, i_{43}, j_{43}, g_{44}, h_{44}, p_4, i_{44}, j_{44}, k_{44}, l_{44}, m_{44}, b_{45}, c_{45}, d_{45}, e_{45}, f_{45}, q_4, g_{45}, h_{45}, i_{45}, j_{45}, k_{45}, c_{46}, d_{46}, e_{46}, f_{46}, g_{46}, r_4, h_{46}, i_{46}, j_{46}, k_{46}, l_{46}, m_{46}, n_{46}, p_{46}, q_{46}, r_{46}, b_5, s_{46}, t_{46}, a_{47}, a_{48}, b_{48}, c_{48}, d_{48}, e_{48}, f_{48}, g_{48}, c_5, p_{48}, q_{48}, r_{48}, s_{48}, t_{48}, a_{49}, h_{49}, i_{49}, j_{49}, k_{49}, d_5, l_{49}, m_{49}, a_{50}, b_{50}, c_{50}, d_{50}, e_{50}, k_{50}, l_{50}, m_{50}, e_5, r_{50}, s_{50}, t_{50}, a_{51}, b_{51}, h_{51}, i_{51}, j_{51}, k_{51}, l_{51}, j_5, m_{51}, a_{52}, b_{52}, c_{52}, d_{52}, i_{52}, j_{52}, k_{52}, l_{52}, m_{52}, g, k_5, n_{52}, C, D, E, F, G, H, I, J, K, n_5, L, M, N, O, P, Q, R, S, T, U, p_5, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, M_2, q_5, O_2, P_2, S_2, U_2, W_2, A_3, C_3, E_3, F_3, G_3, r_5, K_3, L_3, M_3, Q_3, R_3, S_3, T_3, A_4, B_4, E_4, c_6, F_4, G_4, H_4, M_4, N_4, Q_4, R_4, S_4, W_4, Z_4, d_6, C_5, D_5, G_5, H_5, K_5, M_5, N_5, Q_5, R_5, U_5, g_6, W_5, Z_5, C_6, D_6, G_6, H_6, K_6, L_6, M_6, Q_6, h_6, R_6, U_6, V_6, A_7, B_7, E_7, F_7, G_7, K_7, L_7, i_6, O_7, P_7, S_7, T_7, W_7, A_8, B_8, E_8, F_8, I_8, h, m_6, J_8, M_8, N_8, O_8, P_8, U_8, V_8, A_9, B_9, E_9, n_6, F_9, G_9, H_9, M_9, N_9, O_9, P_9, U_9, V_9, W_9, r_6, C_{10}, D_{10}, E_{10}, I_{10}, J_{10}, M_{10}, N_{10}, O_{10}, S_{10}, U_{10}, s_6, V_{10}, A_{11}, B_{11}, E_{11}, F_{11}, I_{11}, J_{11}, M_{11}, N_{11}, Q_{11}, b_7, S_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, E_{12}, F_{12}, G_{12}, H_{12}, M_{12}, c_7, N_{12}, Q_{12}, S_{12}, U_{12}, W_{12}, Z_{12}, C_{13}, D_{13}, G_{13}, H_{13}, f_7, I_{13}, M_{13}, O_{13}, P_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, E_{14}, h_7, F_{14}, G_{14}, H_{14}, M_{14}, O_{14}, P_{14}, Q_{14}, U_{14}, V_{14}, W_{14}, i_7, Z_{14}, A_{15}, G_{15}, H_{15}, I_{15}, J_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, l_7, S_{15}, A_{16}, B_{16}, C_{16}, G_{16}, H_{16}, I_{16}, J_{16}, O_{16}, P_{16}, i, m_7, S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}, q_7, J_{17}, K_{17}, S_{17}, T_{17}, U_{17}, A_{18}, C_{18}, D_{18}, E_{18}, F_{18}, s_7, K_{18}, L_{18}, O_{18}, P_{18}, S_{18}, T_{18}, W_{18}, Z_{18}, A_{19}, E_{19}, t_7, F_{19}, G_{19}, K_{19}, L_{19}, O_{19}, Q_{19}, R_{19}, S_{19}, W_{19}, A_{20}, c_8, B_{20}, E_{20}, F_{20}, I_{20}, J_{20}, M_{20}, N_{20}, Q_{20}, S_{20}, U_{20}, d_8, W_{20}, A_{21}, C_{21}, E_{21}, F_{21}, I_{21}, K_{21}, M_{21}, O_{21}, Q_{21}, g_8, R_{21}, U_{21}, V_{21}, A_{22}, C_{22}, E_{22}, F_{22}, G_{22}, H_{22}, I_{22}, h_8, J_{22}, Q_{22}, R_{22}, S_{22}, T_{22}, U_{22}, V_{22}, E_{23}, F_{23}, G_{23}, k_8, H_{23}, I_{23}, J_{23}, K_{23}, S_{23}, T_{23}, U_{23}, V_{23}, W_{23}, Z_{23}, l_8, A_{24}, B_{24}, K_{24}, L_{24}, M_{24}, N_{24}, S_{24}, T_{24}, U_{24}, A_{25}, j, m_8, B_{25}, C_{25}, D_{25}, E_{25}, K_{25}, L_{25}, M_{25}, N_{25}, O_{25}, U_{25}, r_8, V_{25}, W_{25}, Z_{25}, A_{26}, G_{26}, H_{26}, I_{26}, J_{26}, O_{26}, P_{26}, s_8, Q_{26}, R_{26}, S_{26}, T_{26}, C_{27}, D_{27}, E_{27}, F_{27}, G_{27}, M_{27}, b_9, N_{27}, O_{27}, P_{27}, U_{27}, V_{27}, W_{27}, Z_{27}, A_{28}, G_{28}, H_{28}, c_9, I_{28}, J_{28}, O_{28}, P_{28}, Q_{28}, U_{28}, V_{28}, A_{29}, B_{29}, C_{29}, f_9, G_{29}, H_{29}, I_{29}, M_{29}, N_{29}, Q_{29}, R_{29}, S_{29}, T_{29}, U_{29}, g_9, V_{29}, W_{29}, Z_{29}, A_{30}, B_{30}, C_{30}, O_{30}, P_{30}, Q_{30}, R_{30}, j_9, S_{30}, A_{31}, B_{31}, E_{31}, F_{31}, I_{31}, J_{31}, K_{31}, O_{31}, P_{31}, k_9, Q_{31}, U_{31}, W_{31}, A_{32}, B_{32}, C_{32}, D_{32}, I_{32}, J_{32}, K_{32}, l_9, L_{32}, M_{32}, N_{32}, O_{32}, P_{32}, Q_{32}, R_{32}, S_{32}, T_{32}, U_{32}, k, q_9, V_{32}, M_{33}, N_{33}, O_{33}, P_{33}, Q_{33}, R_{33}, S_{33}, T_{33}, U_{33}, r_9, V_{33}, W_{33}, Z_{33}, A_{34}, B_{34}, C_{34}, S_{34}, T_{34}, U_{34}, V_{34}, a_{10}, W_{34}, Z_{34}, A_{35}, I_{35}, J_{35}, K_{35}, L_{35}, M_{35}, N_{35}, O_{35}, b_{10}, P_{35}, Q_{35}, R_{35}, E_{36}, F_{36}, G_{36}, H_{36}, I_{36}, J_{36}, K_{36}, e_{10}, L_{36}, M_{36}, N_{36}, O_{36}, P_{36}, Q_{36}, R_{36}, S_{36}, T_{36}, U_{36}, f_{10}, V_{36}, Q_{37}, R_{37}, S_{37}, T_{37}, U_{37}, V_{37}, W_{37}, G_{38}, H_{38}, i_{10}, I_{38}, J_{38}, K_{38}, L_{38}, S_{38}, T_{38}, U_{38}, V_{38}, W_{38}, Z_{38}, k_{10}, G_{39}, H_{39}, I_{39}, J_{39}, K_{39}, Q_{39}, R_{39}, S_{39}, W_{39}, Z_{39}, l_{10}, A_{40}, B_{40}, C_{40}, I_{40}, J_{40}, K_{40}, L_{40}, M_{40}, N_{40}, U_{40}, p_{10}, V_{40}, W_{40}, Z_{40}, E_{41}, F_{41}, G_{41}, H_{41}, I_{41}, J_{41}
6. Tangent(B, c) → q_1,
7. Tangent(B', c) → r_1,
8. Tangent(C, c) → s_1,
9. Tangent(B, c) → t_1,
10. Intersect(r_1, t_1) → G_1
11. Intersect(r_1, s_1) → H_1
12. Polygon(G_1, H_1, n) → poly2, a_2, j_2, s_{10}, b_{11}, c_{11}, h_{11}, i_{11}, j_{11}, k_{11}, n_{11}, p_{11}, s_{11}, k_2, t_{11}, e_{12}, f_{12}, g_{12}, h_{12}, m_{12}, n_{12}, p_{12}, q_{12}, a_{13}, l_2, b_{13}, c_{13}, g_{13}, h_{13}, i_{13}, l_{13}, m_{13}, r_{13}, s_{13}, t_{13}, m_2, b_{14}, e_{14}, f_{14}, i_{14}, j_{14}, m_{14}, n_{14}, r_{14}, s_{14}, b_{15}, n_2, c_{15}, e_{15}, g_{15}, l_{15}, m_{15}, n_{15}, p_{15}, a_{16}, b_{16}, c_{16}, p_2, d_{16}, g_{16}, h_{16}, j_{16}, l_{16}, n_{16}, r_{16}, s_{16}, b_{17}, c_{17}, q_2, g_{17}, h_{17}, i_{17}, k_{17}, n_{17}, p_{17}, b_{18}, c_{18}, d_{18}, e_{18}, r_2, f_{18}, k_{18}, l_{18}, m_{18}, n_{18}, q_{18}, a_{19}, b_{19}, c_{19}, i_{19}, s_2, j_{19}, k_{19}, l_{19}, m_{19}, s_{19}, t_{19}, a_{20}, b_{20}, h_{20}, i_{20}, t_2, j_{20}, k_{20}, l_{20}, q_{20}, r_{20}, s_{20}, d_{21}, e_{21}, f_{21}, g_{21}, b_2, a_3, j_{21}, k_{21}, r_{21}, s_{21}, t_{21}, a_{22}, b_{22}, j_{22}, k_{22}, l_{22}, b_3, m_{22}, n_{22}, p_{22}, q_{22}, a_{23}, b_{23}, c_{23}, e_{23}, j_{23}, k_{23}, c_3, l_{23}, m_{23}, q_{23}, r_{23}, a_{24}, b_{24}, e_{24}, f_{24}, j_{24}, k_{24}, d_3, l_{24}, q_{24}, r_{24}, s_{24}, b_{25}, c_{25}, e_{25}, i_{25}, j_{25}, k_{25}, e_3, m_{25}, q_{25}, r_{25}, a_{26}, b_{26}, e_{26}, f_{26}, i_{26}, j_{26}, l_{26}, f_3, n_{26}, q_{26}, s_{26}, a_{27}, c_{27}, f_{27}, g_{27}, i_{27}, k_{27}, m_{27}, g_3, p_{27}, s_{27}, t_{27}, c_{28}, d_{28}, f_{28}, h_{28}, p_{28}, q_{28}, r_{28}, h_3, s_{28}, t_{28}, a_{29}, h_{29}, i_{29}, j_{29}, k_{29}, l_{29}, m_{29}, b_{30}, i_3, c_{30}, d_{30}, e_{30}, f_{30}, g_{30}, h_{30}, r_{30}, s_{30}, t_{30}, a_{31}, j_3, b_{31}, c_{31}, d_{31}, e_{31}, j_{31}, k_{31}, l_{31}, m_{31}, r_{31}, s_{31}, c_2, k_3, t_{31}, f_{32}, g_{32}, h_{32}, i_{32}, j_{32}, q_{32}, r_{32}, s_{32}, t_{32}, m_3, a_{33}, g_{33}, h_{33}, i_{33}, j_{33}, k_{33}, q_{33}, r_{33}, s_{33}, t_{33}, q_3, g_{34}, h_{34}, i_{34}, j_{34}, k_{34}, l_{34}, s_{34}, t_{34}, a_{35}, b_{35}, r_3, c_{35}, h_{35}, i_{35}, j_{35}, k_{35}, r_{35}, s_{35}, t_{35}, a_{36}, b_{36}, t_3, g_{36}, h_{36}, i_{36}, j_{36}, n_{36}, p_{36}, q_{36}, t_{36}, a_{37}, e_{37}, b_4, f_{37}, g_{37}, k_{37}, l_{37}, m_{37}, q_{37}, r_{37}, j_{38}, k_{38}, l_{38}, d_4, m_{38}, n_{38}, p_{38}, q_{38}, r_{38}, s_{38}, t_{38}, a_{39}, g_{39}, h_{39}, f_4, i_{39}, j_{39}, k_{39}, n_{39}, p_{39}, s_{39}, t_{39}, d_{40}, e_{40}, f_{40}, h_4, j_{40}, k_{40}, l_{40}, n_{40}, q_{40}, b_{41}, c_{41}, d_{41}, e_{41}, a_{42}, l_4, b_{42}, c_{42}, d_{42}, e_{42}, f_{42}, g_{42}, h_{42}, i_{42}, j_{42}, k_{42}, d_2, m_4, l_{42}, m_{42}, n_{42}, k_{43}, l_{43}, m_{43}, n_{43}, p_{43}, q_{43}, r_{43}, n_4, s_{43}, t_{43}, a_{44}, b_{44}, c_{44}, d_{44}, e_{44}, f_{44}, n_{44}, p_{44}, s_4, q_{44}, r_{44}, s_{44}, t_{44}, a_{45}, l_{45}, m_{45}, n_{45}, p_{45}, q_{45}, t_4, r_{45}, s_{45}, t_{45}, a_{46}, b_{46}, b_{47}, c_{47}, d_{47}, e_{47}, f_{47}, a_5, g_{47}, h_{47}, i_{47}, j_{47}, k_{47}, l_{47}, m_{47}, n_{47}, p_{47}, q_{47}, f_5, r_{47}, s_{47}, t_{47}, h_{48}, i_{48}, j_{48}, k_{48}, l_{48}, m_{48}, n_{48}, g_5, b_{49}, c_{49}, d_{49}, e_{49}, f_{49}, g_{49}, n_{49}, p_{49}, q_{49}, r_{49}, h_5, s_{49}, t_{49}, f_{50}, g_{50}, h_{50}, i_{50}, j_{50}, n_{50}, p_{50}, q_{50}, i_5, c_{51}, d_{51}, e_{51}, f_{51}, g_{51}, n_{51}, p_{51}, q_{51}, r_{51}, s_{51}, l_5, t_{51}, e_{52}, f_{52}, g_{52}, h_{52}, p_{52}, q_{52}, r_{52}, s_{52}, t_{52}, e_2, m_5, a_{53}, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, s_5, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, t_5, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, N_2, a_6, Q_2, R_2, T_2, V_2, Z_2, B_3, D_3, H_3, I_3, J_3, b_6, N_3, O_3, P_3, U_3, V_3, W_3, Z_3, C_4, D_4, I_4, e_6, J_4, K_4, L_4, O_4, P_4, T_4, U_4, V_4, A_5, B_5, f_6, E_5, F_5, I_5, J_5, L_5, O_5, P_5, S_5, T_5, V_5, j_6, A_6, B_6, E_6, F_6, I_6, J_6, N_6, O_6, P_6, S_6, k_6, T_6, W_6, Z_6, C_7, D_7, H_7, I_7, J_7, M_7, N_7, l_6, Q_7, R_7, U_7, V_7, Z_7, C_8, D_8, G_8, H_8, K_8, f_2, p_6, L_8, Q_8, R_8, S_8, T_8, W_8, Z_8, C_9, D_9, I_9, q_6, J_9, K_9, L_9, Q_9, R_9, S_9, T_9, Z_9, A_{10}, B_{10}, t_6, F_{10}, G_{10}, H_{10}, K_{10}, L_{10}, P_{10}, Q_{10}, R_{10}, T_{10}, W_{10}, a_7, Z_{10}, C_{11}, D_{11}, G_{11}, H_{11}, K_{11}, L_{11}, O_{11}, P_{11}, R_{11}, d_7, T_{11}, A_{12}, B_{12}, C_{12}, D_{12}, I_{12}, J_{12}, K_{12}, L_{12}, O_{12}, e_7, P_{12}, R_{12}, T_{12}, V_{12}, A_{13}, B_{13}, E_{13}, F_{13}, J_{13}, K_{13}, g_7, L_{13}, N_{13}, Q_{13}, R_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, I_{14}, j_7, J_{14}, K_{14}, L_{14}, N_{14}, R_{14}, S_{14}, T_{14}, B_{15}, C_{15}, D_{15}, k_7, E_{15}, F_{15}, K_{15}, L_{15}, M_{15}, N_{15}, T_{15}, U_{15}, V_{15}, W_{15}, n_7, Z_{15}, D_{16}, E_{16}, F_{16}, K_{16}, L_{16}, M_{16}, N_{16}, Q_{16}, R_{16}, g_2, p_7, Z_{16}, A_{17}, B_{17}, C_{17}, D_{17}, L_{17}, M_{17}, N_{17}, O_{17}, P_{17}, r_7, Q_{17}, R_{17}, V_{17}, W_{17}, Z_{17}, B_{18}, G_{18}, H_{18}, I_{18}, J_{18}, a_8, M_{18}, N_{18}, Q_{18}, R_{18}, U_{18}, V_{18}, B_{19}, C_{19}, D_{19}, H_{19}, b_8, I_{19}, J_{19}, M_{19}, N_{19}, P_{19}, T_{19}, U_{19}, V_{19}, Z_{19}, C_{20}, e_8, D_{20}, G_{20}, H_{20}, K_{20}, L_{20}, O_{20}, P_{20}, R_{20}, T_{20}, V_{20}, f_8, Z_{20}, B_{21}, D_{21}, G_{21}, H_{21}, J_{21}, L_{21}, N_{21}, P_{21}, S_{21}, i_8, T_{21}, W_{21}, Z_{21}, B_{22}, D_{22}, K_{22}, L_{22}, M_{22}, N_{22}, O_{22}, j_8, P_{22}, W_{22}, Z_{22}, A_{23}, B_{23}, C_{23}, D_{23}, L_{23}, M_{23}, N_{23}, n_8, O_{23}, P_{23}, Q_{23}, R_{23}, C_{24}, D_{24}, E_{24}, F_{24}, G_{24}, H_{24}, p_8, I_{24}, J_{24}, O_{24}, P_{24}, Q_{24}, R_{24}, V_{24}, W_{24}, Z_{24}, F_{25}, h_2, q_8, G_{25}, H_{25}, I_{25}, J_{25}, P_{25}, Q_{25}, R_{25}, S_{25}, T_{25}, B_{26}, t_8, C_{26}, D_{26}, E_{26}, F_{26}, K_{26}, L_{26}, M_{26}, N_{26}, U_{26}, V_{26}, a_9, W_{26}, Z_{26}, A_{27}, B_{27}, H_{27}, I_{27}, J_{27}, K_{27}, L_{27}, Q_{27}, d_9, R_{27}, S_{27}, T_{27}, B_{28}, C_{28}, D_{28}, E_{28}, F_{28}, K_{28}, L_{28}, e_9, M_{28}, N_{28}, R_{28}, S_{28}, T_{28}, W_{28}, Z_{28}, D_{29}, E_{29}, F_{29}, h_9, J_{29}, K_{29}, L_{29}, O_{29}, P_{29}, D_{30}, E_{30}, F_{30}, G_{30}, H_{30}, i_9, I_{30}, J_{30}, K_{30}, L_{30}, M_{30}, N_{30}, T_{30}, U_{30}, V_{30}, W_{30}, m_9, Z_{30}, C_{31}, D_{31}, G_{31}, H_{31}, L_{31}, M_{31}, N_{31}, R_{31}, S_{31}, n_9, T_{31}, V_{31}, Z_{31}, E_{32}, F_{32}, G_{32}, H_{32}, W_{32}, Z_{32}, A_{33}, p_9, B_{33}, C_{33}, D_{33}, E_{33}, F_{33}, G_{33}, H_{33}, I_{33}, J_{33}, K_{33}, i_2, s_9, L_{33}, D_{34}, E_{34}, F_{34}, G_{34}, H_{34}, I_{34}, J_{34}, K_{34}, L_{34}, t_9, M_{34}, N_{34}, O_{34}, P_{34}, Q_{34}, R_{34}, B_{35}, C_{35}, D_{35}, E_{35}, c_{10}, F_{35}, G_{35}, H_{35}, S_{35}, T_{35}, U_{35}, V_{35}, W_{35}, Z_{35}, A_{36}, d_{10}, B_{36}, C_{36}, D_{36}, W_{36}, Z_{36}, A_{37}, B_{37}, C_{37}, D_{37}, E_{37}, g_{10}, F_{37}, G_{37}, H_{37}, I_{37}, J_{37}, K_{37}, L_{37}, M_{37}, N_{37}, O_{37}, h_{10}, P_{37}, Z_{37}, A_{38}, B_{38}, C_{38}, D_{38}, E_{38}, F_{38}, M_{38}, N_{38}, j_{10}, O_{38}, P_{38}, Q_{38}, R_{38}, A_{39}, B_{39}, C_{39}, D_{39}, E_{39}, F_{39}, m_{10}, L_{39}, M_{39}, N_{39}, O_{39}, P_{39}, T_{39}, U_{39}, V_{39}, D_{40}, E_{40}, n_{10}, F_{40}, G_{40}, H_{40}, O_{40}, P_{40}, Q_{40}, R_{40}, S_{40}, T_{40}, A_{41}, r_{10}, B_{41}, C_{41}, D_{41}, K_{41}, L_{41}, M_{41}, N_{41}, O_{41}, P_{41}