Archimedes Method for Calculating Pi

Archimedes Method for Calculating Pi
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2026-01-21 12:49
In collections Geometry - Area & Volume
This example demonstrates Archimedes' method for calculating pi. It involves the construction and analysis of geometric shapes, showing an approximation of pi. Key mathematical concepts include geometric construction, properties of circles, and approximating pi. The construction uses GeoGebra commands such as Segment, Circle, Rotate, Polygon, Intersect, Angle. Suitable for middle school math, geometry, and calculating pi.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Circle(B, 1) → c
  3. Rotate(A, (2 * pi / s), B) → A'
  4. Segment(A, A') → g
  5. Polygon(A, A', s) → poly1, h, r, p_5, q_5, r_5, s_5, t_5, a_5, b_5, c_5, d_5, e_5, t, f_6, g_6, h_6, i_6, j_6, k_6, l_6, m_6, n_6, p_6, b, q_6, r_6, s_6, t_6, a_6, b_6, c_6, d_6, e_6, f_7, d, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7, e, r_7, s_7, t_7, a_7, b_7, c_7, d_7, e_7, f_8, g_8, f_1, h_8, i_8, j_8, k_8, l_8, m_8, n_8, p_8, q_8, r_8, g_1, s_8, t_8, a_8, b_8, c_8, d_8, e_8, f_9, g_9, h_9, h_1, i_9, j_9, k_9, l_9, m_9, n_9, p_9, q_9, r_9, s_9, i_1, t_9, a_9, b_9, c_9, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}, j_1, j_{10}, k_{10}, l_{10}, s_{30}, t_{30}, a_{30}, b_{30}, c_{30}, d_{30}, e_{30}, i, k_1, f_{31}, g_{31}, h_{31}, i_{31}, j_{31}, k_{31}, l_{31}, m_{31}, n_{31}, p_{31}, l_1, q_{31}, r_{31}, s_{31}, t_{31}, a_{31}, b_{31}, c_{31}, d_{31}, e_{31}, f_{32}, m_1, g_{32}, h_{32}, i_{32}, j_{32}, k_{32}, l_{32}, m_{32}, n_{32}, p_{32}, q_{32}, n_1, r_{32}, s_{32}, t_{32}, a_{32}, b_{32}, c_{32}, d_{32}, e_{32}, f_{33}, g_{33}, p_1, h_{33}, i_{33}, j_{33}, k_{33}, l_{33}, m_{33}, n_{33}, p_{33}, q_{33}, r_{33}, q_1, s_{33}, t_{33}, a_{33}, b_{33}, c_{33}, d_{33}, e_{33}, f_{34}, g_{34}, h_{34}, r_1, i_{34}, j_{34}, k_{34}, l_{34}, m_{34}, n_{34}, p_{34}, q_{34}, r_{34}, s_{34}, s_1, t_{34}, a_{34}, b_{34}, c_{34}, d_{34}, e_{34}, f_{35}, g_{35}, h_{35}, i_{35}, t_1, j_{35}, k_{35}, l_{35}, m_{35}, n_{35}, p_{35}, q_{35}, r_{35}, s_{35}, t_{35}, a_1, a_{35}, b_{35}, c_{35}, d_{35}, e_{35}, f_{36}, g_{36}, h_{36}, i_{36}, j_{36}, j, b_1, k_{36}, l_{36}, m_{36}, n_{36}, p_{36}, q_{36}, r_{36}, s_{36}, t_{36}, a_{36}, c_1, b_{36}, c_{36}, d_{36}, e_{36}, f_{37}, g_{37}, h_{37}, i_{37}, j_{37}, k_{37}, d_1, l_{37}, m_{37}, n_{37}, p_{37}, q_{37}, r_{37}, s_{37}, t_{37}, a_{37}, b_{37}, e_1, c_{37}, d_{37}, e_{37}, f_{38}, g_{38}, h_{38}, i_{38}, j_{38}, k_{38}, l_{38}, f_2, m_{38}, n_{38}, p_{38}, q_{38}, r_{38}, s_{38}, t_{38}, a_{38}, b_{38}, c_{38}, g_2, d_{38}, e_{38}, f_{39}, g_{39}, h_{39}, i_{39}, j_{39}, k_{39}, l_{39}, m_{39}, h_2, n_{39}, p_{39}, q_{39}, r_{39}, s_{39}, t_{39}, a_{39}, b_{39}, c_{39}, d_{39}, i_2, e_{39}, f_{40}, g_{40}, h_{40}, i_{40}, j_{40}, k_{40}, l_{40}, m_{40}, n_{40}, j_2, p_{40}, q_{40}, r_{40}, s_{40}, t_{40}, C, D, E, F, G, k_2, H, I, J, K, L, M, N, O, P, Q, k, l_2, R, S, T, U, V, W, Z, A_1, B_1, C_1, m_2, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, n_2, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, p_2, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, q_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, r_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, s_2, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, t_2, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, a_2, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, b_2, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, U_4, l, c_2, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, d_2, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, e_2, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, f_3, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, g_3, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, h_3, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, I_7, i_3, J_7, K_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, j_3, T_7, U_7, V_7, W_7, Z_7, W_{23}, Z_{23}, A_{24}, B_{24}, C_{24}, k_3, D_{24}, E_{24}, F_{24}, G_{24}, H_{24}, I_{24}, J_{24}, K_{24}, L_{24}, M_{24}, l_3, N_{24}, O_{24}, P_{24}, Q_{24}, R_{24}, S_{24}, T_{24}, U_{24}, V_{24}, W_{24}, m, m_3, Z_{24}, A_{25}, B_{25}, C_{25}, D_{25}, E_{25}, F_{25}, G_{25}, H_{25}, I_{25}, n_3, J_{25}, K_{25}, L_{25}, M_{25}, N_{25}, O_{25}, P_{25}, Q_{25}, R_{25}, S_{25}, p_3, T_{25}, U_{25}, V_{25}, W_{25}, Z_{25}, A_{26}, B_{26}, C_{26}, D_{26}, E_{26}, q_3, F_{26}, G_{26}, H_{26}, I_{26}, J_{26}, K_{26}, L_{26}, M_{26}, N_{26}, O_{26}, r_3, P_{26}, Q_{26}, R_{26}, S_{26}, T_{26}, U_{26}, V_{26}, W_{26}, Z_{26}, A_{27}, s_3, B_{27}, C_{27}, D_{27}, E_{27}, F_{27}, G_{27}, H_{27}, I_{27}, J_{27}, K_{27}, t_3, L_{27}, M_{27}, N_{27}, O_{27}, P_{27}, Q_{27}, R_{27}, S_{27}, T_{27}, U_{27}, a_3, V_{27}, W_{27}, Z_{27}, A_{28}, B_{28}, C_{28}, D_{28}, E_{28}, F_{28}, G_{28}, b_3, H_{28}, I_{28}, J_{28}, K_{28}, L_{28}, M_{28}, N_{28}, O_{28}, P_{28}, Q_{28}, c_3, R_{28}, S_{28}, T_{28}, U_{28}, V_{28}, W_{28}, Z_{28}, A_{29}, B_{29}, C_{29}, n, d_3, D_{29}, E_{29}, F_{29}, G_{29}, H_{29}, I_{29}, J_{29}, K_{29}, L_{29}, M_{29}, e_3, N_{29}, O_{29}, P_{29}, Q_{29}, R_{29}, S_{29}, T_{29}, U_{29}, V_{29}, W_{29}, f_4, Z_{29}, A_{30}, B_{30}, C_{30}, D_{30}, E_{30}, F_{30}, G_{30}, H_{30}, I_{30}, g_4, J_{30}, K_{30}, L_{30}, M_{30}, N_{30}, O_{30}, P_{30}, Q_{30}, R_{30}, S_{30}, h_4, T_{30}, U_{30}, V_{30}, W_{30}, Z_{30}, A_{31}, B_{31}, C_{31}, D_{31}, E_{31}, i_4, F_{31}, G_{31}, H_{31}, I_{31}, J_{31}, K_{31}, L_{31}, M_{31}, N_{31}, O_{31}, j_4, P_{31}, Q_{31}, R_{31}, S_{31}, T_{31}, U_{31}, V_{31}, k_4, l_4, m_4, p, n_4, p_4, q_4, r_4, s_4, t_4, a_4, b_4, c_4, d_4, q, e_4, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5
  6. Rotate(A, (2 * pi / ((2 * s))), B) → o
  7. Segment(A, o) → m_{10}
  8. Polygon(A, o, (2 * s)) → poly2, n_{10}, d_{10}, s_{15}, P_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, U_{17}, V_{17}, W_{17}, Z_{17}, A_{18}, t_{15}, B_{18}, C_{18}, D_{18}, E_{18}, F_{18}, G_{18}, H_{18}, I_{18}, J_{18}, K_{18}, a_{15}, L_{18}, M_{18}, N_{18}, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}, U_{18}, b_{15}, V_{18}, W_{18}, Z_{18}, A_{19}, B_{19}, C_{19}, D_{19}, E_{19}, F_{19}, G_{19}, c_{15}, H_{19}, I_{19}, J_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}, P_{19}, Q_{19}, d_{15}, R_{19}, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, B_{20}, C_{20}, e_{15}, D_{20}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, K_{20}, L_{20}, M_{20}, f_{16}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}, V_{20}, W_{20}, g_{16}, Z_{20}, A_{21}, B_{21}, C_{21}, D_{21}, E_{21}, F_{21}, G_{21}, H_{21}, I_{21}, h_{16}, J_{21}, K_{21}, L_{21}, M_{21}, N_{21}, O_{21}, P_{21}, Q_{21}, R_{21}, S_{21}, e_{10}, i_{16}, T_{21}, U_{21}, V_{21}, W_{21}, Z_{21}, A_{22}, B_{22}, C_{22}, D_{22}, E_{22}, j_{16}, F_{22}, G_{22}, H_{22}, I_{22}, J_{22}, K_{22}, L_{22}, M_{22}, N_{22}, O_{22}, k_{16}, P_{22}, Q_{22}, R_{22}, S_{22}, T_{22}, U_{22}, V_{22}, W_{22}, Z_{22}, A_{23}, l_{16}, B_{23}, C_{23}, D_{23}, E_{23}, F_{23}, G_{23}, H_{23}, I_{23}, J_{23}, K_{23}, m_{16}, L_{23}, M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}, S_{23}, T_{23}, U_{23}, n_{16}, V_{23}, W_{31}, Z_{31}, A_{32}, B_{32}, C_{32}, D_{32}, E_{32}, F_{32}, G_{32}, p_{16}, H_{32}, I_{32}, J_{32}, K_{32}, L_{32}, M_{32}, N_{32}, O_{32}, P_{32}, Q_{32}, q_{16}, R_{32}, S_{32}, T_{32}, U_{32}, V_{32}, W_{32}, Z_{32}, A_{33}, B_{33}, C_{33}, r_{16}, D_{33}, E_{33}, F_{33}, G_{33}, H_{33}, I_{33}, J_{33}, K_{33}, L_{33}, M_{33}, s_{16}, N_{33}, O_{33}, P_{33}, Q_{33}, R_{33}, S_{33}, T_{33}, U_{33}, V_{33}, W_{33}, f_{11}, t_{16}, Z_{33}, A_{34}, B_{34}, C_{34}, D_{34}, E_{34}, F_{34}, G_{34}, H_{34}, I_{34}, a_{16}, J_{34}, K_{34}, L_{34}, M_{34}, N_{34}, O_{34}, P_{34}, Q_{34}, R_{34}, S_{34}, b_{16}, T_{34}, U_{34}, V_{34}, W_{34}, Z_{34}, A_{35}, B_{35}, C_{35}, D_{35}, E_{35}, c_{16}, F_{35}, G_{35}, H_{35}, I_{35}, J_{35}, K_{35}, L_{35}, M_{35}, N_{35}, O_{35}, d_{16}, P_{35}, Q_{35}, R_{35}, S_{35}, T_{35}, U_{35}, V_{35}, W_{35}, Z_{35}, A_{36}, e_{16}, B_{36}, C_{36}, D_{36}, E_{36}, F_{36}, G_{36}, H_{36}, I_{36}, J_{36}, K_{36}, f_{17}, L_{36}, M_{36}, N_{36}, O_{36}, P_{36}, Q_{36}, R_{36}, S_{36}, T_{36}, U_{36}, g_{17}, V_{36}, W_{36}, Z_{36}, A_{37}, B_{37}, C_{37}, D_{37}, E_{37}, F_{37}, G_{37}, h_{17}, H_{37}, I_{37}, J_{37}, K_{37}, L_{37}, M_{37}, N_{37}, O_{37}, P_{37}, Q_{37}, i_{17}, R_{37}, S_{37}, T_{37}, U_{37}, V_{37}, W_{37}, Z_{37}, A_{38}, B_{38}, C_{38}, g_{11}, j_{17}, D_{38}, E_{38}, F_{38}, G_{38}, H_{38}, I_{38}, J_{38}, K_{38}, L_{38}, M_{38}, k_{17}, N_{38}, O_{38}, P_{38}, Q_{38}, R_{38}, S_{38}, T_{38}, U_{38}, V_{38}, W_{38}, l_{17}, Z_{38}, A_{39}, B_{39}, C_{39}, D_{39}, E_{39}, F_{39}, G_{39}, H_{39}, I_{39}, m_{17}, J_{39}, K_{39}, L_{39}, M_{39}, N_{39}, O_{39}, P_{39}, Q_{39}, R_{39}, S_{39}, n_{17}, T_{39}, U_{39}, V_{39}, W_{39}, Z_{39}, A_{40}, B_{40}, C_{40}, D_{40}, E_{40}, p_{17}, F_{40}, G_{40}, H_{40}, I_{40}, J_{40}, K_{40}, L_{40}, M_{40}, N_{40}, O_{40}, q_{17}, P_{40}, Q_{40}, R_{40}, S_{40}, T_{40}, U_{40}, V_{40}, W_{40}, Z_{40}, A_{41}, r_{17}, B_{41}, C_{41}, D_{41}, E_{41}, F_{41}, G_{41}, H_{41}, I_{41}, J_{41}, K_{41}, s_{17}, L_{41}, M_{41}, N_{41}, O_{41}, P_{41}, Q_{41}, R_{41}, S_{41}, T_{41}, U_{41}, t_{17}, V_{41}, W_{41}, Z_{41}, A_{42}, B_{42}, C_{42}, D_{42}, E_{42}, F_{42}, G_{42}, h_{11}, a_{17}, H_{42}, I_{42}, J_{42}, K_{42}, L_{42}, M_{42}, N_{42}, O_{42}, P_{42}, Q_{42}, b_{17}, R_{42}, S_{42}, T_{42}, U_{42}, V_{42}, W_{42}, Z_{42}, A_{43}, B_{43}, C_{43}, c_{17}, D_{43}, E_{43}, F_{43}, G_{43}, H_{43}, I_{43}, J_{43}, K_{43}, L_{43}, M_{43}, d_{17}, N_{43}, O_{43}, P_{43}, Q_{43}, R_{43}, S_{43}, T_{43}, U_{43}, V_{43}, W_{43}, e_{17}, Z_{43}, A_{44}, B_{44}, C_{44}, D_{44}, E_{44}, F_{44}, G_{44}, H_{44}, I_{44}, f_{18}, J_{44}, K_{44}, L_{44}, M_{44}, N_{44}, O_{44}, P_{44}, Q_{44}, R_{44}, S_{44}, g_{18}, T_{44}, U_{44}, V_{44}, W_{44}, Z_{44}, A_{45}, B_{45}, C_{45}, D_{45}, E_{45}, h_{18}, F_{45}, G_{45}, H_{45}, I_{45}, J_{45}, K_{45}, L_{45}, M_{45}, N_{45}, O_{45}, i_{18}, P_{45}, Q_{45}, R_{45}, S_{45}, T_{45}, U_{45}, V_{45}, W_{45}, Z_{45}, A_{46}, j_{18}, B_{46}, C_{46}, D_{46}, E_{46}, F_{46}, G_{46}, H_{46}, I_{46}, J_{46}, K_{46}, i_{11}, k_{18}, L_{46}, M_{46}, N_{46}, O_{46}, P_{46}, Q_{46}, R_{46}, S_{46}, T_{46}, U_{46}, l_{18}, V_{46}, W_{46}, Z_{46}, A_{47}, B_{47}, C_{47}, D_{47}, E_{47}, F_{47}, G_{47}, m_{18}, H_{47}, I_{47}, J_{47}, K_{47}, L_{47}, M_{47}, N_{47}, O_{47}, P_{47}, Q_{47}, n_{18}, R_{47}, S_{47}, T_{47}, U_{47}, V_{47}, p_{18}, q_{18}, r_{18}, s_{18}, t_{18}, a_{18}, j_{11}, b_{18}, c_{18}, d_{18}, e_{18}, f_{19}, g_{19}, h_{19}, i_{19}, j_{19}, k_{19}, k_{11}, l_{19}, m_{19}, n_{19}, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, a_{19}, b_{19}, l_{11}, c_{19}, d_{19}, e_{19}, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, k_{20}, l_{20}, m_{11}, m_{20}, n_{20}, p_{20}, q_{20}, r_{20}, s_{20}, t_{20}, a_{20}, b_{20}, c_{20}, p_{10}, n_{11}, d_{20}, e_{20}, f_{21}, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, l_{21}, m_{21}, p_{11}, n_{21}, p_{21}, q_{21}, r_{21}, s_{21}, t_{21}, a_{21}, b_{21}, c_{21}, d_{21}, q_{11}, e_{21}, f_{22}, g_{22}, h_{22}, i_{22}, j_{22}, k_{22}, l_{22}, m_{22}, n_{22}, r_{11}, p_{22}, q_{22}, r_{22}, s_{22}, t_{22}, a_{22}, b_{22}, c_{22}, d_{22}, e_{22}, s_{11}, f_{23}, g_{23}, h_{23}, i_{23}, j_{23}, k_{23}, l_{23}, m_{23}, n_{23}, p_{23}, t_{11}, q_{23}, r_{23}, s_{23}, t_{23}, a_{23}, b_{23}, c_{23}, d_{23}, e_{23}, f_{24}, a_{11}, g_{24}, h_{24}, i_{24}, j_{24}, k_{24}, l_{24}, m_{24}, n_{24}, p_{24}, q_{24}, b_{11}, r_{24}, s_{24}, t_{24}, a_{24}, b_{24}, c_{24}, d_{24}, e_{24}, f_{25}, g_{25}, c_{11}, h_{25}, i_{25}, j_{25}, k_{25}, l_{25}, m_{25}, n_{25}, p_{25}, q_{25}, r_{25}, d_{11}, s_{25}, t_{25}, a_{25}, b_{25}, c_{25}, d_{25}, e_{25}, f_{26}, g_{26}, h_{26}, q_{10}, e_{11}, i_{26}, j_{26}, k_{26}, l_{26}, m_{26}, n_{26}, p_{26}, q_{26}, r_{26}, s_{26}, f_{12}, t_{26}, a_{26}, b_{26}, c_{26}, d_{26}, e_{26}, f_{27}, g_{27}, h_{27}, i_{27}, g_{12}, j_{27}, k_{27}, l_{27}, m_{27}, n_{27}, p_{27}, q_{27}, r_{27}, s_{27}, t_{27}, h_{12}, a_{27}, b_{27}, c_{27}, d_{27}, e_{27}, f_{28}, g_{28}, h_{28}, i_{28}, j_{28}, i_{12}, k_{28}, l_{28}, m_{28}, n_{28}, p_{28}, q_{28}, r_{28}, s_{28}, t_{28}, a_{28}, j_{12}, b_{28}, c_{28}, d_{28}, e_{28}, f_{29}, g_{29}, h_{29}, i_{29}, j_{29}, k_{29}, k_{12}, l_{29}, m_{29}, n_{29}, p_{29}, q_{29}, r_{29}, s_{29}, t_{29}, a_{29}, b_{29}, l_{12}, c_{29}, d_{29}, e_{29}, f_{30}, g_{30}, h_{30}, i_{30}, j_{30}, k_{30}, l_{30}, m_{12}, m_{30}, n_{30}, p_{30}, q_{30}, r_{30}, a_{40}, b_{40}, c_{40}, d_{40}, e_{40}, n_{12}, f_{41}, g_{41}, h_{41}, i_{41}, j_{41}, k_{41}, l_{41}, m_{41}, n_{41}, p_{41}, r_{10}, p_{12}, q_{41}, r_{41}, s_{41}, t_{41}, a_{41}, b_{41}, c_{41}, d_{41}, e_{41}, f_{42}, q_{12}, g_{42}, h_{42}, i_{42}, j_{42}, k_{42}, l_{42}, m_{42}, n_{42}, p_{42}, q_{42}, r_{12}, r_{42}, s_{42}, t_{42}, a_{42}, b_{42}, c_{42}, d_{42}, e_{42}, f_{43}, g_{43}, s_{12}, h_{43}, i_{43}, j_{43}, k_{43}, l_{43}, m_{43}, n_{43}, p_{43}, q_{43}, r_{43}, t_{12}, s_{43}, t_{43}, a_{43}, b_{43}, c_{43}, d_{43}, e_{43}, f_{44}, g_{44}, h_{44}, a_{12}, i_{44}, j_{44}, k_{44}, l_{44}, m_{44}, n_{44}, p_{44}, q_{44}, r_{44}, s_{44}, b_{12}, t_{44}, a_{44}, b_{44}, c_{44}, d_{44}, e_{44}, f_{45}, g_{45}, h_{45}, i_{45}, c_{12}, j_{45}, k_{45}, l_{45}, m_{45}, n_{45}, p_{45}, q_{45}, r_{45}, s_{45}, t_{45}, d_{12}, a_{45}, b_{45}, c_{45}, d_{45}, e_{45}, f_{46}, g_{46}, h_{46}, i_{46}, j_{46}, e_{12}, k_{46}, l_{46}, m_{46}, n_{46}, p_{46}, q_{46}, r_{46}, s_{46}, t_{46}, a_{46}, s_{10}, f_{13}, b_{46}, c_{46}, d_{46}, e_{46}, f_{47}, g_{47}, h_{47}, i_{47}, j_{47}, k_{47}, g_{13}, l_{47}, m_{47}, n_{47}, p_{47}, q_{47}, r_{47}, s_{47}, t_{47}, a_{47}, b_{47}, h_{13}, c_{47}, d_{47}, e_{47}, f_{48}, g_{48}, h_{48}, i_{48}, j_{48}, k_{48}, l_{48}, i_{13}, m_{48}, n_{48}, p_{48}, q_{48}, r_{48}, s_{48}, t_{48}, a_{48}, b_{48}, c_{48}, j_{13}, d_{48}, e_{48}, f_{49}, g_{49}, h_{49}, i_{49}, j_{49}, k_{49}, l_{49}, m_{49}, k_{13}, n_{49}, p_{49}, q_{49}, r_{49}, s_{49}, t_{49}, a_{49}, b_{49}, c_{49}, d_{49}, l_{13}, e_{49}, f_{50}, g_{50}, h_{50}, i_{50}, j_{50}, k_{50}, l_{50}, m_{50}, n_{50}, m_{13}, p_{50}, q_{50}, r_{50}, s_{50}, t_{50}, a_{50}, b_{50}, c_{50}, d_{50}, e_{50}, n_{13}, f_{51}, g_{51}, h_{51}, i_{51}, j_{51}, k_{51}, l_{51}, m_{51}, n_{51}, p_{51}, p_{13}, q_{51}, r_{51}, s_{51}, t_{51}, a_{51}, b_{51}, c_{51}, d_{51}, e_{51}, f_{52}, t_{10}, q_{13}, g_{52}, h_{52}, i_{52}, j_{52}, k_{52}, l_{52}, m_{52}, n_{52}, p_{52}, q_{52}, r_{13}, r_{52}, s_{52}, t_{52}, a_{52}, b_{52}, c_{52}, d_{52}, e_{52}, f_{53}, g_{53}, s_{13}, h_{53}, i_{53}, j_{53}, k_{53}, l_{53}, m_{53}, n_{53}, p_{53}, q_{53}, r_{53}, t_{13}, s_{53}, t_{53}, a_{53}, b_{53}, c_{53}, d_{53}, e_{53}, f_{54}, g_{54}, h_{54}, a_{13}, i_{54}, j_{54}, k_{54}, l_{54}, m_{54}, n_{54}, p_{54}, q_{54}, r_{54}, s_{54}, b_{13}, t_{54}, a_{54}, b_{54}, c_{54}, d_{54}, e_{54}, f_{55}, g_{55}, h_{55}, i_{55}, c_{13}, j_{55}, k_{55}, l_{55}, m_{55}, n_{55}, p_{55}, q_{55}, r_{55}, s_{55}, t_{55}, d_{13}, a_{55}, b_{55}, c_{55}, d_{55}, e_{55}, f_{56}, g_{56}, h_{56}, i_{56}, j_{56}, e_{13}, k_{56}, l_{56}, m_{56}, n_{56}, p_{56}, q_{56}, r_{56}, s_{56}, t_{56}, a_{56}, f_{14}, b_{56}, c_{56}, d_{56}, e_{56}, f_{57}, g_{57}, h_{57}, i_{57}, j_{57}, k_{57}, a_{10}, g_{14}, l_{57}, m_{57}, n_{57}, p_{57}, q_{57}, r_{57}, s_{57}, t_{57}, a_{57}, b_{57}, h_{14}, c_{57}, d_{57}, e_{57}, f_{58}, g_{58}, h_{58}, i_{58}, j_{58}, k_{58}, l_{58}, i_{14}, m_{58}, n_{58}, p_{58}, q_{58}, r_{58}, s_{58}, t_{58}, a_{58}, b_{58}, c_{58}, j_{14}, d_{58}, e_{58}, f_{59}, g_{59}, h_{59}, i_{59}, j_{59}, k_{59}, l_{59}, m_{59}, k_{14}, n_{59}, p_{59}, q_{59}, r_{59}, s_{59}, t_{59}, a_{59}, b_{59}, c_{59}, d_{59}, l_{14}, e_{59}, f_{60}, g_{60}, h_{60}, i_{60}, j_{60}, k_{60}, l_{60}, m_{60}, n_{60}, m_{14}, p_{60}, q_{60}, r_{60}, s_{60}, t_{60}, a_{60}, b_{60}, c_{60}, d_{60}, A_8, n_{14}, B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8, J_8, K_8, p_{14}, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, U_8, q_{14}, V_8, W_8, Z_8, A_9, B_9, C_9, D_9, E_9, F_9, G_9, b_{10}, r_{14}, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, s_{14}, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, t_{14}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, a_{14}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, b_{14}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, c_{14}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, d_{14}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, e_{14}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, f_{15}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, g_{15}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, c_{10}, h_{15}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}, i_{15}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, j_{15}, H_{14}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, k_{15}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, l_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, m_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, U_{15}, V_{15}, W_{15}, n_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, I_{16}, p_{15}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, R_{16}, S_{16}, q_{15}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}, B_{17}, C_{17}, D_{17}, E_{17}, r_{15}, F_{17}, G_{17}, H_{17}, I_{17}, J_{17}, K_{17}, L_{17}, M_{17}, N_{17}, O_{17}
  9. Segment(B, o) → e_{60}
  10. Intersect(e_{60}, g) → W_{47}
  11. Angle(B, W_{47}, A) → α

AI Drawing Prompt Reference

Draw a circle c with center B and radius 1. Then rotate point A around B by 2π/s to get point A'. Draw line segment AA', and use A and A' to construct a polygon, gradually increasing the number of sides to approximate pi.
The prompt above was compiled from the original drawing commands and is for reference only.