从正多边形中寻找圆周率

从正多边形中寻找圆周率
几何画板及绘图内容加载中,请稍等……
2019-08-15 08:29
①本范例通过演示正多边形边数增加时其周长与外接圆周长的比值变化,直观展示圆周率的计算过程;②涉及核心数学概念包括正多边形、周长、圆周率、极限、三角函数等;③作图要点提炼自GeoGebra命令:Segment(线段)、Circle(圆)、Rotate(旋转)、Polygon(多边形)、Tangent(切线)、Angle(角度)、Intersect(交点)、Line(直线);④适合高中数学学生及对几何与极限概念感兴趣的学习者,可用于理解圆周率的历史推导方法。

GeoGebra 命令及参数

  1. Segment(A, B) → ab
  2. Circle(A, B) → c
  3. Rotate(B, (360 * ° / num), A) → B'
  4. Polygon(B, B', num) → poly1, a, p, q_{10}, t_{104}, C_1, E, F, G, H, I, J, K, L, s_{10}, Z, B_1, D_1, F_1, H_1, J_1, L_1, N_1, P_1, R_1, a_{11}, T_1, V_1, Z_1, B_2, D_2, F_2, H_2, J_2, L_2, N_2, b_{11}, P_2, R_2, T_2, V_2, Z_2, B_3, D_3, F_3, H_3, J_3, c_{11}, L_3, N_3, P_3, R_3, T_3, V_3, Z_3, B_4, D_4, F_4, g_{11}, H_4, J_4, L_4, N_4, P_4, R_4, T_4, V_4, Z_4, B_5, i_{11}, D_5, E_5, F_5, G_5, L_5, M_5, N_5, O_5, P_5, Q_5, k_{11}, R_5, S_5, T_5, F_6, G_6, H_6, I_6, J_6, K_6, L_6, m_{11}, T_6, U_6, V_6, B_7, C_7, D_7, H_7, I_7, J_7, K_7, p_{11}, L_7, R_7, T_7, V_7, Z_7, B_8, D_8, F_8, H_8, J_8, q, r_{11}, L_8, M_8, N_8, R_8, T_8, V_8, Z_8, B_9, D_9, F_9, t_{11}, H_9, J_9, K_9, N_9, O_9, P_9, Q_9, V_9, W_9, B_{10}, b_{12}, D_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, R_{10}, S_{10}, T_{10}, d_{12}, Z_{10}, A_{11}, D_{11}, E_{11}, F_{11}, J_{11}, L_{11}, M_{11}, P_{11}, R_{11}, e_{12}, S_{11}, T_{11}, Z_{11}, B_{12}, D_{12}, F_{12}, G_{12}, H_{12}, L_{12}, M_{12}, h_{12}, N_{12}, R_{12}, T_{12}, V_{12}, Z_{12}, B_{13}, D_{13}, E_{13}, H_{13}, I_{13}, i_{12}, L_{13}, M_{13}, P_{13}, R_{13}, T_{13}, V_{13}, Z_{13}, B_{14}, D_{14}, F_{14}, j_{12}, H_{14}, J_{14}, L_{14}, N_{14}, O_{14}, R_{14}, T_{14}, V_{14}, Z_{14}, B_{15}, k_{12}, C_{15}, F_{15}, G_{15}, J_{15}, L_{15}, M_{15}, P_{15}, Q_{15}, R_{15}, V_{15}, q_{12}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, k_1, r_{12}, T_{16}, U_{16}, V_{16}, W_{16}, D_{17}, E_{17}, H_{17}, J_{17}, K_{17}, L_{17}, a_{13}, M_{17}, R_{17}, S_{17}, T_{17}, U_{17}, V_{17}, W_{17}, F_{18}, G_{18}, J_{18}, c_{13}, L_{18}, M_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}, B_{19}, C_{19}, D_{19}, e_{13}, H_{19}, J_{19}, K_{19}, N_{19}, O_{19}, P_{19}, Q_{19}, R_{19}, Z_{19}, A_{20}, f_{13}, B_{20}, F_{20}, G_{20}, J_{20}, K_{20}, L_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, g_{13}, T_{20}, U_{20}, V_{20}, F_{21}, G_{21}, H_{21}, I_{21}, J_{21}, K_{21}, L_{21}, h_{13}, M_{21}, N_{21}, O_{21}, P_{21}, Q_{21}, R_{21}, S_{21}, T_{21}, U_{21}, N_{22}, i_{13}, O_{22}, P_{22}, Q_{22}, V_{22}, Z_{22}, A_{23}, B_{23}, C_{23}, D_{23}, E_{23}, j_{13}, L_{23}, M_{23}, N_{23}, O_{23}, P_{23}, Q_{23}, R_{23}, S_{23}, T_{23}, F_{24}, r_{13}, G_{24}, H_{24}, L_{24}, M_{24}, N_{24}, O_{24}, P_{24}, V_{24}, W_{24}, Z_{24}, m_1, s_{13}, D_{25}, E_{25}, H_{25}, J_{25}, K_{25}, N_{25}, P_{25}, R_{25}, T_{25}, V_{25}, t_{13}, W_{25}, B_{26}, D_{26}, F_{26}, H_{26}, J_{26}, L_{26}, N_{26}, O_{26}, P_{26}, d_{14}, T_{26}, V_{26}, Z_{26}, B_{27}, D_{27}, F_{27}, H_{27}, I_{27}, L_{27}, M_{27}, e_{14}, P_{27}, Q_{27}, T_{27}, V_{27}, Z_{27}, A_{28}, D_{28}, E_{28}, H_{28}, J_{28}, h_{14}, L_{28}, N_{28}, O_{28}, R_{28}, S_{28}, T_{28}, Z_{28}, B_{29}, C_{29}, F_{29}, i_{14}, G_{29}, J_{29}, K_{29}, N_{29}, O_{29}, P_{29}, Q_{29}, V_{29}, W_{29}, L_{30}, j_{14}, N_{30}, O_{30}, R_{30}, T_{30}, V_{30}, W_{30}, B_{31}, C_{31}, D_{31}, H_{31}, n_{14}, I_{31}, J_{31}, K_{31}, P_{31}, Q_{31}, R_{31}, S_{31}, T_{31}, B_{32}, C_{32}, q_{14}, D_{32}, E_{32}, F_{32}, G_{32}, N_{32}, O_{32}, P_{32}, Q_{32}, R_{32}, S_{32}, r_{14}, T_{32}, D_{33}, E_{33}, F_{33}, J_{33}, K_{33}, L_{33}, M_{33}, N_{33}, O_{33}, p_1, a_{15}, V_{33}, W_{33}, Z_{33}, A_{34}, B_{34}, H_{34}, I_{34}, J_{34}, K_{34}, P_{34}, c_{15}, Q_{34}, R_{34}, S_{34}, Z_{34}, A_{35}, B_{35}, F_{35}, G_{35}, H_{35}, I_{35}, d_{15}, J_{35}, P_{35}, Q_{35}, R_{35}, S_{35}, T_{35}, U_{35}, V_{35}, W_{35}, Z_{35}, e_{15}, A_{36}, B_{36}, C_{36}, P_{36}, Q_{36}, R_{36}, S_{36}, T_{36}, U_{36}, V_{36}, i_{15}, W_{36}, Z_{36}, A_{37}, B_{37}, C_{37}, D_{37}, E_{37}, F_{37}, G_{37}, H_{37}, k_{15}, I_{37}, J_{37}, K_{37}, L_{37}, J_{38}, K_{38}, L_{38}, M_{38}, N_{38}, O_{38}, m_{15}, P_{38}, Q_{38}, R_{38}, S_{38}, T_{38}, U_{38}, J_{39}, L_{39}, M_{39}, N_{39}, p_{15}, O_{39}, P_{39}, Q_{39}, R_{39}, B_{40}, C_{40}, D_{40}, E_{40}, F_{40}, G_{40}, q_{15}, H_{40}, I_{40}, R_{40}, S_{40}, T_{40}, U_{40}, V_{40}, W_{40}, Z_{40}, A_{41}, r_{15}, B_{41}, C_{41}, D_{41}, E_{41}, F_{41}, G_{41}, V_{41}, W_{41}, Z_{41}, A_{42}, r_1, b_{16}, B_{42}, C_{42}, D_{42}, E_{42}, F_{42}, G_{42}, H_{42}, I_{42}, J_{42}, K_{42}, c_{16}, L_{42}, M_{42}, F_{43}, G_{43}, H_{43}, I_{43}, J_{43}, K_{43}, L_{43}, M_{43}, d_{16}, N_{43}, O_{43}, P_{43}, Q_{43}, R_{43}, S_{43}, T_{43}, U_{43}, V_{43}, W_{43}, h_{16}, Z_{43}, A_{44}, B_{44}, C_{44}, D_{44}, E_{44}, F_{44}, G_{44}, H_{44}, I_{44}, j_{16}, N_{45}, O_{45}, P_{45}, Q_{45}, R_{45}, S_{45}, T_{45}, U_{45}, V_{45}, W_{45}, l_{16}, Z_{45}, A_{46}, B_{46}, C_{46}, D_{46}, T_{46}, U_{46}, V_{46}, B_{47}, C_{47}, n_{16}, F_{47}, G_{47}, H_{47}, I_{47}, N_{47}, O_{47}, P_{47}, Q_{47}, R_{47}, S_{47}, q_{16}, T_{47}, D_{48}, E_{48}, F_{48}, G_{48}, H_{48}, I_{48}, P_{48}, Q_{48}, R_{48}, s_{16}, S_{48}, Z_{48}, A_{49}, B_{49}, C_{49}, D_{49}, J_{49}, K_{49}, L_{49}, M_{49}, t_{16}, N_{49}, O_{49}, P_{49}, Q_{49}, R_{49}, S_{49}, T_{49}, U_{49}, J_{50}, K_{50}, t_1, c_{17}, L_{50}, M_{50}, N_{50}, O_{50}, P_{50}, Q_{50}, R_{50}, S_{50}, T_{50}, U_{50}, d_{17}, V_{50}, W_{50}, Z_{50}, A_{51}, B_{51}, C_{51}, D_{51}, Z_{51}, A_{52}, B_{52}, g_{17}, C_{52}, D_{52}, E_{52}, F_{52}, G_{52}, H_{52}, I_{52}, J_{52}, K_{52}, L_{52}, h_{17}, M_{52}, N_{52}, O_{52}, P_{52}, Q_{52}, R_{52}, S_{52}, T_{52}, U_{52}, V_{52}, k_{17}, W_{52}, Z_{52}, B_{54}, C_{54}, D_{54}, E_{54}, F_{54}, G_{54}, H_{54}, I_{54}, m_{17}, J_{54}, K_{54}, L_{54}, M_{54}, N_{54}, O_{54}, P_{54}, Q_{54}, R_{54}, S_{54}, p_{17}, T_{54}, U_{54}, V_{54}, W_{54}, Z_{54}, A_{55}, B_{55}, C_{55}, D_{55}, E_{55}, r_{17}, F_{55}, L_{56}, M_{56}, N_{56}, O_{56}, P_{56}, Q_{56}, R_{56}, S_{56}, T_{56}, t_{17}, U_{56}, V_{56}, W_{56}, Z_{56}, A_{57}, B_{57}, C_{57}, D_{57}, E_{57}, F_{57}, b_{18}, G_{57}, H_{57}, I_{57}, J_{57}, K_{57}, L_{57}, M_{57}, N_{57}, O_{57}, P_{57}, b_2, d_{18}, Q_{57}, R_{57}, S_{57}, T_{57}, U_{57}, V_{57}, W_{57}, Z_{57}, A_{58}, B_{58}, f_{18}, C_{58}, D_{58}, E_{58}, F_{58}, G_{58}, H_{58}, I_{58}, H_{60}, I_{60}, J_{60}, h_{18}, K_{60}, L_{60}, M_{60}, N_{60}, O_{60}, P_{60}, Q_{60}, R_{60}, S_{60}, T_{60}, j_{18}, U_{60}, V_{60}, W_{60}, Z_{60}, A_{61}, B_{61}, C_{61}, D_{61}, E_{61}, F_{61}, l_{18}, G_{61}, H_{61}, I_{61}, J_{61}, K_{61}, L_{61}, R_{62}, S_{62}, V_{62}, W_{62}, n_{18}, Z_{62}, A_{63}, B_{63}, C_{63}, D_{63}, E_{63}, F_{63}, G_{63}, H_{63}, I_{63}, p_{18}, V_{63}, W_{63}, Z_{63}, A_{64}, B_{64}, C_{64}, D_{64}, E_{64}, F_{64}, G_{64}, s_{18}, H_{64}, I_{64}, V_{64}, W_{64}, Z_{64}, A_{65}, B_{65}, C_{65}, D_{65}, E_{65}, a_{19}, F_{65}, G_{65}, H_{65}, I_{65}, J_{65}, K_{65}, L_{65}, M_{65}, N_{65}, O_{65}, c_{19}, P_{65}, Q_{65}, R_{65}, S_{65}, T_{65}, T_{66}, U_{66}, V_{66}, W_{66}, Z_{66}, d_2, e_{19}, A_{67}, B_{67}, C_{67}, D_{67}, E_{67}, F_{67}, G_{67}, T_{67}, U_{67}, V_{67}, g_{19}, W_{67}, Z_{67}, A_{68}, B_{68}, C_{68}, D_{68}, E_{68}, F_{68}, G_{68}, H_{68}, h_{19}, I_{68}, J_{68}, K_{68}, L_{68}, M_{68}, N_{68}, O_{68}, P_{68}, Q_{68}, R_{68}, k_{19}, S_{68}, T_{68}, U_{68}, V_{68}, W_{68}, Z_{68}, A_{69}, B_{69}, C_{69}, D_{69}, l_{19}, E_{69}, F_{69}, G_{69}, H_{69}, I_{69}, J_{69}, K_{69}, L_{69}, M_{69}, N_{69}, p_{19}, O_{69}, P_{69}, Q_{69}, R_{69}, S_{69}, T_{69}, V_{71}, W_{71}, Z_{71}, A_{72}, r_{19}, B_{72}, C_{72}, D_{72}, E_{72}, F_{72}, G_{72}, H_{72}, I_{72}, J_{72}, K_{72}, s_{19}, L_{72}, M_{72}, N_{72}, O_{72}, P_{72}, Q_{72}, R_{72}, S_{72}, T_{72}, U_{72}, b_{20}, V_{72}, W_{72}, Z_{72}, A_{73}, B_{73}, C_{73}, D_{73}, E_{73}, N_{74}, O_{74}, c_{20}, P_{74}, Q_{74}, R_{74}, S_{74}, T_{74}, U_{74}, V_{74}, W_{74}, Z_{74}, A_{75}, f_2, d_{20}, B_{75}, C_{75}, D_{75}, E_{75}, F_{75}, G_{75}, H_{75}, I_{75}, J_{75}, K_{75}, h_{20}, L_{75}, M_{75}, N_{75}, O_{75}, P_{75}, Q_{75}, R_{75}, S_{75}, T_{75}, U_{75}, i_{20}, V_{75}, W_{75}, Z_{75}, A_{76}, B_{76}, C_{76}, D_{76}, E_{76}, F_{76}, G_{76}, j_{20}, H_{76}, I_{76}, J_{76}, K_{76}, L_{76}, M_{76}, N_{76}, O_{76}, P_{76}, Q_{76}, k_{20}, R_{76}, S_{76}, T_{76}, D_{79}, E_{79}, F_{79}, G_{79}, H_{79}, I_{79}, J_{79}, l_{20}, K_{79}, L_{79}, M_{79}, N_{79}, O_{79}, P_{79}, Q_{79}, R_{79}, S_{79}, L_{80}, m_{20}, N_{80}, O_{80}, P_{80}, Q_{80}, R_{80}, S_{80}, T_{80}, D_{81}, E_{81}, F_{81}, a_{21}, G_{81}, H_{81}, I_{81}, J_{81}, K_{81}, L_{81}, M_{81}, N_{81}, O_{81}, P_{81}, b_{21}, Q_{81}, R_{81}, S_{81}, T_{81}, U_{81}, V_{81}, W_{81}, Z_{81}, V_{82}, W_{82}, c_{21}, Z_{82}, A_{83}, B_{83}, C_{83}, D_{83}, E_{83}, F_{83}, G_{83}, H_{83}, b, h_2, d_{21}, e_{21}, k_{21}, l_{21}, m_{21}, n_{21}, t_{21}, a_{22}, d_{22}, f_{22}, j_2, g_{22}, h_{22}, i_{22}, n_{22}, p_{22}, q_{22}, r_{22}, s_{22}, t_{22}, g_{23}, l_2, h_{23}, k_{23}, m_{23}, n_{23}, r_{23}, s_{23}, t_{23}, a_{24}, b_{24}, h_{24}, n_2, i_{24}, j_{24}, n_{24}, q_{24}, r_{24}, a_{25}, b_{25}, c_{25}, d_{25}, e_{25}, q_2, k_{25}, l_{25}, m_{25}, r_{25}, s_{25}, b_{26}, c_{26}, d_{26}, h_{26}, i_{26}, s_2, j_{26}, k_{26}, l_{26}, m_{26}, n_{26}, c_{27}, d_{27}, e_{27}, f_{27}, g_{27}, a_3, h_{27}, i_{27}, j_{27}, k_{27}, l_{27}, m_{27}, n_{27}, p_{27}, q_{27}, r_{27}, c_3, s_{27}, q_{28}, r_{28}, s_{28}, t_{28}, e_{29}, g_{29}, h_{29}, i_{29}, j_{29}, e_3, k_{29}, l_{29}, t_{29}, a_{30}, b_{30}, c_{30}, d_{30}, e_{30}, f_{30}, g_{30}, g_3, h_{30}, s_{30}, t_{30}, a_{31}, e_{31}, f_{31}, g_{31}, h_{31}, i_{31}, p_{31}, d, i_3, q_{31}, r_{31}, b_{32}, c_{32}, f_{32}, h_{32}, i_{32}, l_{32}, n_{32}, q_{32}, k_3, s_{32}, a_{33}, b_{33}, e_{33}, g_{33}, i_{33}, k_{33}, m_{33}, p_{33}, r_{33}, m_3, s_{33}, t_{33}, d_{34}, f_{34}, h_{34}, j_{34}, l_{34}, n_{34}, q_{34}, r_{34}, p_3, a_{35}, b_{35}, e_{35}, f_{35}, i_{35}, k_{35}, m_{35}, n_{35}, r_{35}, s_{35}, r_3, b_{36}, d_{36}, f_{36}, h_{36}, i_{36}, l_{36}, m_{36}, n_{36}, s_{36}, a_{37}, t_3, b_{37}, e_{37}, f_{37}, i_{37}, j_{37}, m_{37}, n_{37}, p_{37}, q_{37}, b_{38}, b_4, c_{38}, e_{38}, g_{38}, h_{38}, k_{38}, m_{38}, p_{38}, q_{38}, t_{38}, a_{39}, d_4, b_{39}, f_{39}, g_{39}, h_{39}, i_{39}, n_{39}, p_{39}, q_{39}, r_{39}, s_{39}, f_4, e_{40}, f_{40}, g_{40}, h_{40}, i_{40}, j_{40}, r_{40}, s_{40}, t_{40}, a_{41}, h_4, b_{41}, c_{41}, d_{41}, l_{41}, m_{41}, n_{41}, s_{41}, t_{41}, a_{42}, b_{42}, e, j_4, c_{42}, d_{42}, k_{42}, l_{42}, m_{42}, n_{42}, p_{42}, b_{43}, c_{43}, d_{43}, l_4, e_{43}, j_{43}, k_{43}, l_{43}, m_{43}, s_{43}, t_{43}, a_{44}, e_{44}, f_{44}, n_4, g_{44}, h_{44}, i_{44}, p_{44}, q_{44}, r_{44}, s_{44}, t_{44}, a_{45}, b_{45}, q_4, c_{45}, d_{45}, e_{45}, f_{45}, g_{45}, a_{46}, b_{46}, c_{46}, d_{46}, e_{46}, s_4, f_{46}, g_{46}, h_{46}, i_{46}, j_{46}, k_{46}, l_{46}, m_{46}, n_{46}, p_{46}, a_5, q_{46}, r_{46}, s_{46}, t_{46}, a_{47}, b_{47}, e_{48}, f_{48}, g_{48}, h_{48}, c_5, i_{48}, j_{48}, k_{48}, l_{48}, m_{48}, n_{48}, p_{48}, q_{48}, j_{49}, l_{49}, e_5, m_{49}, n_{49}, p_{49}, q_{49}, r_{49}, s_{49}, g_{50}, h_{50}, i_{50}, j_{50}, g_5, k_{50}, l_{50}, m_{50}, n_{50}, d_{51}, e_{51}, f_{51}, g_{51}, h_{51}, i_{51}, i_5, j_{51}, k_{51}, l_{51}, m_{51}, n_{51}, p_{51}, q_{51}, r_{51}, m_{52}, n_{52}, j, k_5, p_{52}, q_{52}, r_{52}, s_{52}, t_{52}, a_{53}, b_{53}, c_{53}, d_{53}, e_{53}, m_5, f_{53}, g_{53}, h_{53}, i_{53}, g_{54}, h_{54}, i_{54}, j_{54}, k_{54}, l_{54}, p_5, m_{54}, n_{54}, p_{54}, q_{54}, r_{54}, s_{54}, t_{54}, a_{55}, b_{55}, c_{55}, r_5, d_{55}, e_{55}, f_{55}, g_{55}, h_{55}, i_{55}, j_{55}, k_{55}, l_{55}, m_{55}, t_5, n_{55}, p_{55}, f_{57}, g_{57}, h_{57}, i_{57}, j_{57}, k_{57}, l_{57}, m_{57}, b_6, n_{57}, p_{57}, q_{57}, r_{57}, s_{57}, t_{57}, a_{58}, r_{58}, s_{58}, t_{58}, d_6, d_{59}, e_{59}, h_{59}, i_{59}, j_{59}, k_{59}, q_{59}, r_{59}, s_{59}, t_{59}, f_6, a_{60}, b_{60}, c_{60}, k_{60}, l_{60}, m_{60}, n_{60}, p_{60}, q_{60}, d_{61}, h_6, e_{61}, f_{61}, g_{61}, l_{61}, m_{61}, n_{61}, p_{61}, q_{61}, c_{62}, d_{62}, j_6, e_{62}, f_{62}, g_{62}, h_{62}, i_{62}, j_{62}, k_{62}, l_{62}, m_{62}, n_{62}, k, l_6, h_{63}, i_{63}, j_{63}, k_{63}, l_{63}, m_{63}, n_{63}, p_{63}, q_{63}, r_{63}, n_6, s_{63}, t_{63}, a_{64}, b_{64}, c_{64}, d_{64}, e_{64}, f_{64}, g_{64}, h_{65}, q_6, i_{65}, j_{65}, k_{65}, l_{65}, m_{65}, n_{65}, p_{65}, q_{65}, r_{65}, s_{65}, r_6, t_{65}, a_{66}, b_{66}, c_{66}, d_{66}, e_{66}, f_{66}, g_{66}, h_{66}, i_{66}, s_6, j_{66}, k_{66}, l_{66}, m_{66}, a_{68}, b_{68}, c_{68}, d_{68}, e_{68}, f_{68}, t_6, g_{68}, h_{68}, i_{68}, j_{68}, k_{68}, l_{68}, m_{68}, n_{68}, p_{68}, q_{68}, e_7, r_{68}, s_{68}, t_{68}, a_{69}, b_{69}, c_{69}, d_{69}, e_{69}, f_{69}, g_{69}, f_7, h_{69}, i_{69}, j_{69}, b_{71}, c_{71}, d_{71}, e_{71}, f_{71}, g_{71}, h_{71}, g_7, i_{71}, j_{71}, k_{71}, l_{71}, m_{71}, n_{71}, p_{71}, q_{71}, r_{71}, s_{71}, h_7, t_{71}, a_{72}, b_{72}, c_{72}, d_{72}, e_{72}, f_{72}, g_{72}, h_{72}, i_{72}, l, i_7, j_{72}, k_{72}, l_{72}, m_{72}, n_{72}, p_{72}, q_{72}, r_{72}, s_{72}, t_{72}, j_7, a_{73}, b_{73}, c_{73}, d_{73}, e_{73}, f_{73}, g_{73}, h_{73}, i_{73}, s_{75}, k_7, t_{75}, a_{76}, b_{76}, c_{76}, d_{76}, e_{76}, f_{76}, g_{76}, h_{76}, i_{76}, l_7, j_{76}, k_{76}, l_{76}, m_{76}, n_{76}, p_{76}, q_{76}, r_{76}, s_{76}, t_{76}, m_7, a_{77}, b_{77}, c_{77}, d_{77}, e_{77}, f_{77}, g_{77}, h_{77}, t_{78}, a_{79}, d_8, d_{79}, e_{79}, f_{79}, g_{79}, h_{79}, i_{79}, j_{79}, k_{79}, l_{79}, m_{79}, e_8, n_{79}, p_{79}, i_{80}, j_{80}, k_{80}, l_{80}, m_{80}, n_{80}, p_{80}, q_{80}, f_8, r_{80}, s_{80}, t_{80}, a_{81}, n_{81}, p_{81}, q_{81}, r_{81}, s_{81}, t_{81}, g_8, a_{82}, b_{82}, c_{82}, d_{82}, e_{82}, f_{82}, g_{82}, h_{82}, i_{82}, j_{82}, h_8, k_{82}, l_{82}, m_{82}, n_{82}, p_{82}, q_{82}, r_{82}, c_{84}, d_{84}, e_{84}, m, i_8, f_{84}, g_{84}, h_{84}, i_{84}, j_{84}, k_{84}, l_{84}, m_{84}, n_{84}, h_{85}, j_8, i_{85}, j_{85}, k_{85}, l_{85}, m_{85}, n_{85}, p_{85}, q_{85}, r_{85}, s_{85}, s_8, t_{85}, a_{86}, b_{86}, c_{86}, d_{86}, e_{86}, f_{86}, g_{86}, h_{86}, i_{86}, t_8, j_{86}, k_{86}, l_{86}, m_{86}, n_{86}, p_{86}, q_{86}, r_{86}, s_{86}, t_{86}, a_9, a_{87}, b_{87}, c_{87}, d_{87}, e_{87}, f_{87}, g_{87}, h_{87}, i_{87}, j_{87}, e_9, k_{87}, l_{87}, m_{87}, n_{87}, p_{87}, q_{87}, r_{87}, s_{87}, k_{90}, l_{90}, f_9, m_{90}, n_{90}, p_{90}, q_{90}, r_{90}, s_{90}, t_{90}, a_{91}, b_{91}, c_{91}, g_9, d_{91}, e_{91}, f_{91}, g_{91}, h_{91}, i_{91}, j_{91}, k_{91}, l_{91}, m_{91}, k_9, n_{91}, p_{91}, q_{91}, r_{91}, s_{91}, t_{91}, a_{92}, b_{92}, c_{92}, d_{92}, l_9, s_{93}, t_{93}, a_{94}, b_{94}, c_{94}, d_{94}, e_{94}, f_{94}, g_{94}, h_{94}, n, m_9, i_{94}, j_{94}, k_{94}, l_{94}, m_{94}, n_{94}, p_{94}, q_{94}, r_{94}, s_{94}, n_9, t_{94}, a_{95}, b_{95}, c_{95}, d_{95}, e_{95}, f_{95}, g_{95}, h_{95}, i_{95}, p_9, j_{95}, k_{95}, l_{95}, m_{95}, n_{95}, p_{95}, q_{95}, r_{95}, s_{95}, t_{95}, b_{10}, a_{96}, b_{96}, c_{96}, d_{96}, e_{96}, f_{96}, g_{96}, h_{96}, i_{96}, j_{96}, d_{10}, k_{96}, l_{96}, m_{96}, n_{96}, p_{96}, n_{99}, p_{99}, q_{99}, r_{99}, s_{99}, f_{10}, t_{99}, a_{100}, b_{100}, c_{100}, d_{100}, e_{100}, f_{100}, g_{100}, h_{100}, i_{100}, h_{10}, j_{100}, h_{101}, j_{101}, k_{101}, l_{101}, m_{101}, n_{101}, p_{101}, q_{101}, e_{102}, j_{10}, f_{102}, g_{102}, h_{102}, i_{102}, j_{102}, k_{102}, l_{102}, m_{102}, n_{102}, p_{102}, l_{10}, q_{102}, r_{102}, s_{102}, t_{102}, a_{103}, b_{103}, c_{103}, d_{103}, e_{103}, f_{103}, n_{10}, i_{104}, j_{104}, k_{104}, l_{104}, m_{104}, n_{104}, p_{104}, q_{104}, r_{104}, s_{104}
  5. Tangent(b, c) → h, i
  6. Angle(B, A, B') → α
  7. Tangent(a, c) → f, g
  8. Intersect(i, g) → D
  9. Line(A, B) → t
  10. Intersect(g, t) → C
  11. Polygon(C, D, num) → poly2, a_1, r, p_{10}, k_{105}, M, N, O, P, Q, R, S, T, U, r_{10}, V, W, A_1, E_1, G_1, I_1, K_1, M_1, O_1, Q_1, t_{10}, S_1, U_1, W_1, A_2, C_2, E_2, G_2, I_2, K_2, M_2, d_{11}, O_2, Q_2, S_2, U_2, W_2, A_3, C_3, E_3, G_3, I_3, e_{11}, K_3, M_3, O_3, Q_3, S_3, U_3, W_3, A_4, C_4, E_4, f_{11}, G_4, I_4, K_4, M_4, O_4, Q_4, S_4, U_4, W_4, A_5, h_{11}, C_5, H_5, I_5, J_5, K_5, U_5, V_5, W_5, Z_5, A_6, j_{11}, B_6, C_6, D_6, E_6, M_6, N_6, O_6, P_6, Q_6, R_6, l_{11}, S_6, W_6, Z_6, A_7, E_7, F_7, G_7, M_7, N_7, O_7, n_{11}, P_7, Q_7, S_7, U_7, W_7, A_8, C_8, E_8, G_8, I_8, s, q_{11}, K_8, O_8, P_8, Q_8, S_8, U_8, W_8, A_9, C_9, E_9, s_{11}, G_9, I_9, L_9, M_9, R_9, S_9, T_9, U_9, Z_9, A_{10}, a_{12}, C_{10}, E_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, U_{10}, V_{10}, c_{12}, W_{10}, B_{11}, C_{11}, G_{11}, H_{11}, I_{11}, K_{11}, N_{11}, O_{11}, Q_{11}, f_{12}, U_{11}, V_{11}, W_{11}, A_{12}, C_{12}, E_{12}, I_{12}, J_{12}, K_{12}, O_{12}, g_{12}, P_{12}, Q_{12}, S_{12}, U_{12}, W_{12}, A_{13}, C_{13}, F_{13}, G_{13}, J_{13}, l_{12}, K_{13}, N_{13}, O_{13}, Q_{13}, S_{13}, U_{13}, W_{13}, A_{14}, C_{14}, E_{14}, m_{12}, G_{14}, I_{14}, K_{14}, M_{14}, P_{14}, Q_{14}, S_{14}, U_{14}, W_{14}, A_{15}, n_{12}, D_{15}, E_{15}, H_{15}, I_{15}, K_{15}, N_{15}, O_{15}, S_{15}, T_{15}, U_{15}, p_{12}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, I_{16}, O_{16}, P_{16}, Q_{16}, R_{16}, j_1, s_{12}, S_{16}, Z_{16}, A_{17}, B_{17}, C_{17}, F_{17}, G_{17}, I_{17}, N_{17}, O_{17}, t_{12}, P_{17}, Q_{17}, Z_{17}, A_{18}, B_{18}, C_{18}, D_{18}, E_{18}, H_{18}, I_{18}, b_{13}, K_{18}, N_{18}, O_{18}, U_{18}, V_{18}, W_{18}, Z_{18}, A_{19}, E_{19}, F_{19}, d_{13}, G_{19}, I_{19}, L_{19}, M_{19}, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, C_{20}, k_{13}, D_{20}, E_{20}, H_{20}, I_{20}, M_{20}, N_{20}, O_{20}, W_{20}, Z_{20}, A_{21}, l_{13}, B_{21}, C_{21}, D_{21}, E_{21}, V_{21}, W_{21}, Z_{21}, A_{22}, B_{22}, C_{22}, m_{13}, D_{22}, E_{22}, F_{22}, G_{22}, H_{22}, I_{22}, J_{22}, K_{22}, L_{22}, M_{22}, n_{13}, R_{22}, S_{22}, T_{22}, U_{22}, W_{22}, F_{23}, G_{23}, H_{23}, I_{23}, J_{23}, p_{13}, K_{23}, U_{23}, V_{23}, W_{23}, Z_{23}, A_{24}, B_{24}, C_{24}, D_{24}, E_{24}, q_{13}, I_{24}, J_{24}, K_{24}, Q_{24}, R_{24}, S_{24}, T_{24}, U_{24}, A_{25}, B_{25}, l_1, a_{14}, C_{25}, F_{25}, G_{25}, I_{25}, L_{25}, M_{25}, O_{25}, Q_{25}, S_{25}, U_{25}, b_{14}, Z_{25}, A_{26}, C_{26}, E_{26}, G_{26}, I_{26}, K_{26}, M_{26}, Q_{26}, R_{26}, c_{14}, S_{26}, U_{26}, W_{26}, A_{27}, C_{27}, E_{27}, G_{27}, J_{27}, K_{27}, N_{27}, f_{14}, O_{27}, R_{27}, S_{27}, U_{27}, W_{27}, B_{28}, C_{28}, F_{28}, G_{28}, I_{28}, g_{14}, K_{28}, M_{28}, P_{28}, Q_{28}, U_{28}, V_{28}, W_{28}, A_{29}, D_{29}, E_{29}, k_{14}, H_{29}, I_{29}, L_{29}, M_{29}, R_{29}, S_{29}, T_{29}, U_{29}, Z_{29}, M_{30}, l_{14}, P_{30}, Q_{30}, S_{30}, U_{30}, Z_{30}, A_{31}, E_{31}, F_{31}, G_{31}, L_{31}, m_{14}, M_{31}, N_{31}, O_{31}, U_{31}, V_{31}, W_{31}, Z_{31}, A_{32}, H_{32}, I_{32}, p_{14}, J_{32}, K_{32}, L_{32}, M_{32}, U_{32}, V_{32}, W_{32}, Z_{32}, A_{33}, B_{33}, s_{14}, C_{33}, G_{33}, H_{33}, I_{33}, P_{33}, Q_{33}, R_{33}, S_{33}, T_{33}, U_{33}, n_1, t_{14}, C_{34}, D_{34}, E_{34}, F_{34}, G_{34}, L_{34}, M_{34}, N_{34}, O_{34}, T_{34}, b_{15}, U_{34}, V_{34}, W_{34}, C_{35}, D_{35}, E_{35}, K_{35}, L_{35}, M_{35}, N_{35}, f_{15}, O_{35}, D_{36}, E_{36}, F_{36}, G_{36}, H_{36}, I_{36}, J_{36}, K_{36}, L_{36}, g_{15}, M_{36}, N_{36}, O_{36}, M_{37}, N_{37}, O_{37}, P_{37}, Q_{37}, R_{37}, S_{37}, h_{15}, T_{37}, U_{37}, V_{37}, W_{37}, Z_{37}, A_{38}, B_{38}, C_{38}, D_{38}, E_{38}, j_{15}, F_{38}, G_{38}, H_{38}, I_{38}, V_{38}, W_{38}, Z_{38}, A_{39}, B_{39}, C_{39}, l_{15}, D_{39}, E_{39}, F_{39}, G_{39}, H_{39}, I_{39}, K_{39}, S_{39}, T_{39}, U_{39}, n_{15}, V_{39}, W_{39}, Z_{39}, A_{40}, J_{40}, K_{40}, L_{40}, M_{40}, N_{40}, O_{40}, s_{15}, P_{40}, Q_{40}, H_{41}, I_{41}, J_{41}, K_{41}, L_{41}, M_{41}, N_{41}, O_{41}, t_{15}, P_{41}, Q_{41}, R_{41}, S_{41}, T_{41}, U_{41}, N_{42}, O_{42}, P_{42}, Q_{42}, q_1, a_{16}, R_{42}, S_{42}, T_{42}, U_{42}, V_{42}, W_{42}, Z_{42}, A_{43}, B_{43}, C_{43}, e_{16}, D_{43}, E_{43}, J_{44}, K_{44}, L_{44}, M_{44}, N_{44}, O_{44}, P_{44}, Q_{44}, f_{16}, R_{44}, S_{44}, T_{44}, U_{44}, V_{44}, W_{44}, Z_{44}, A_{45}, B_{45}, C_{45}, g_{16}, D_{45}, E_{45}, F_{45}, G_{45}, H_{45}, I_{45}, J_{45}, K_{45}, L_{45}, M_{45}, i_{16}, E_{46}, F_{46}, G_{46}, H_{46}, I_{46}, J_{46}, K_{46}, L_{46}, M_{46}, N_{46}, k_{16}, O_{46}, P_{46}, Q_{46}, R_{46}, S_{46}, W_{46}, Z_{46}, A_{47}, D_{47}, E_{47}, m_{16}, J_{47}, K_{47}, L_{47}, M_{47}, U_{47}, V_{47}, W_{47}, Z_{47}, A_{48}, B_{48}, p_{16}, C_{48}, J_{48}, K_{48}, L_{48}, M_{48}, N_{48}, O_{48}, T_{48}, U_{48}, V_{48}, r_{16}, W_{48}, E_{49}, F_{49}, G_{49}, H_{49}, I_{49}, V_{49}, W_{49}, Z_{49}, A_{50}, a_{17}, B_{50}, C_{50}, D_{50}, E_{50}, F_{50}, G_{50}, H_{50}, I_{50}, E_{51}, F_{51}, s_1, b_{17}, G_{51}, H_{51}, I_{51}, J_{51}, K_{51}, L_{51}, M_{51}, N_{51}, O_{51}, P_{51}, e_{17}, Q_{51}, R_{51}, S_{51}, T_{51}, U_{51}, V_{51}, W_{51}, A_{53}, B_{53}, C_{53}, f_{17}, D_{53}, E_{53}, F_{53}, G_{53}, H_{53}, I_{53}, J_{53}, K_{53}, L_{53}, M_{53}, i_{17}, N_{53}, O_{53}, P_{53}, Q_{53}, R_{53}, S_{53}, T_{53}, U_{53}, V_{53}, W_{53}, j_{17}, Z_{53}, A_{54}, G_{55}, H_{55}, I_{55}, J_{55}, K_{55}, L_{55}, M_{55}, N_{55}, l_{17}, O_{55}, P_{55}, Q_{55}, R_{55}, S_{55}, T_{55}, U_{55}, V_{55}, W_{55}, Z_{55}, n_{17}, A_{56}, B_{56}, C_{56}, D_{56}, E_{56}, F_{56}, G_{56}, H_{56}, I_{56}, J_{56}, q_{17}, K_{56}, J_{58}, K_{58}, L_{58}, M_{58}, N_{58}, O_{58}, P_{58}, Q_{58}, R_{58}, s_{17}, S_{58}, T_{58}, U_{58}, V_{58}, W_{58}, Z_{58}, A_{59}, B_{59}, C_{59}, D_{59}, a_{18}, E_{59}, F_{59}, G_{59}, H_{59}, I_{59}, J_{59}, K_{59}, L_{59}, M_{59}, N_{59}, a_2, c_{18}, O_{59}, P_{59}, Q_{59}, R_{59}, S_{59}, T_{59}, U_{59}, V_{59}, W_{59}, Z_{59}, e_{18}, A_{60}, B_{60}, C_{60}, D_{60}, E_{60}, F_{60}, G_{60}, M_{61}, N_{61}, O_{61}, g_{18}, P_{61}, Q_{61}, R_{61}, S_{61}, T_{61}, U_{61}, V_{61}, W_{61}, Z_{61}, A_{62}, i_{18}, B_{62}, C_{62}, D_{62}, E_{62}, F_{62}, G_{62}, H_{62}, I_{62}, J_{62}, K_{62}, k_{18}, L_{62}, M_{62}, N_{62}, O_{62}, P_{62}, Q_{62}, T_{62}, U_{62}, J_{63}, K_{63}, m_{18}, L_{63}, M_{63}, N_{63}, O_{63}, P_{63}, Q_{63}, R_{63}, S_{63}, T_{63}, U_{63}, q_{18}, J_{64}, K_{64}, L_{64}, M_{64}, N_{64}, O_{64}, P_{64}, Q_{64}, R_{64}, S_{64}, r_{18}, T_{64}, U_{64}, U_{65}, V_{65}, W_{65}, Z_{65}, A_{66}, B_{66}, C_{66}, D_{66}, t_{18}, E_{66}, F_{66}, G_{66}, H_{66}, I_{66}, J_{66}, K_{66}, L_{66}, M_{66}, N_{66}, b_{19}, O_{66}, P_{66}, Q_{66}, R_{66}, S_{66}, H_{67}, I_{67}, J_{67}, K_{67}, L_{67}, c_2, d_{19}, M_{67}, N_{67}, O_{67}, P_{67}, Q_{67}, R_{67}, S_{67}, U_{69}, V_{69}, W_{69}, f_{19}, Z_{69}, A_{70}, B_{70}, C_{70}, D_{70}, E_{70}, F_{70}, G_{70}, H_{70}, I_{70}, i_{19}, J_{70}, K_{70}, L_{70}, M_{70}, N_{70}, O_{70}, P_{70}, Q_{70}, R_{70}, S_{70}, j_{19}, T_{70}, U_{70}, V_{70}, W_{70}, Z_{70}, A_{71}, B_{71}, C_{71}, D_{71}, E_{71}, m_{19}, F_{71}, G_{71}, H_{71}, I_{71}, J_{71}, K_{71}, L_{71}, M_{71}, N_{71}, O_{71}, n_{19}, P_{71}, Q_{71}, R_{71}, S_{71}, T_{71}, U_{71}, F_{73}, G_{73}, H_{73}, I_{73}, q_{19}, J_{73}, K_{73}, L_{73}, M_{73}, N_{73}, O_{73}, P_{73}, Q_{73}, R_{73}, S_{73}, t_{19}, T_{73}, U_{73}, V_{73}, W_{73}, Z_{73}, A_{74}, B_{74}, C_{74}, D_{74}, E_{74}, a_{20}, F_{74}, G_{74}, H_{74}, I_{74}, J_{74}, K_{74}, L_{74}, M_{74}, U_{76}, V_{76}, e_{20}, W_{76}, Z_{76}, A_{77}, B_{77}, C_{77}, D_{77}, E_{77}, F_{77}, G_{77}, H_{77}, e_2, f_{20}, I_{77}, J_{77}, K_{77}, L_{77}, M_{77}, N_{77}, O_{77}, P_{77}, Q_{77}, R_{77}, g_{20}, S_{77}, T_{77}, U_{77}, V_{77}, W_{77}, Z_{77}, A_{78}, B_{78}, C_{78}, D_{78}, n_{20}, E_{78}, F_{78}, G_{78}, H_{78}, I_{78}, J_{78}, K_{78}, L_{78}, M_{78}, N_{78}, p_{20}, O_{78}, P_{78}, Q_{78}, R_{78}, S_{78}, T_{78}, U_{78}, V_{78}, W_{78}, Z_{78}, q_{20}, A_{79}, B_{79}, C_{79}, T_{79}, U_{79}, V_{79}, W_{79}, Z_{79}, A_{80}, B_{80}, r_{20}, C_{80}, D_{80}, E_{80}, F_{80}, G_{80}, H_{80}, I_{80}, J_{80}, K_{80}, M_{80}, s_{20}, U_{80}, V_{80}, W_{80}, Z_{80}, A_{81}, B_{81}, C_{81}, A_{82}, B_{82}, C_{82}, t_{20}, D_{82}, E_{82}, F_{82}, G_{82}, H_{82}, I_{82}, J_{82}, K_{82}, L_{82}, M_{82}, f_{21}, N_{82}, O_{82}, P_{82}, Q_{82}, R_{82}, S_{82}, T_{82}, U_{82}, I_{83}, J_{83}, g_{21}, K_{83}, L_{83}, M_{83}, N_{83}, O_{83}, P_{83}, Q_{83}, R_{83}, S_{83}, b_1, g_2, h_{21}, i_{21}, j_{21}, p_{21}, q_{21}, r_{21}, s_{21}, b_{22}, c_{22}, e_{22}, i_2, j_{22}, k_{22}, l_{22}, m_{22}, a_{23}, b_{23}, c_{23}, d_{23}, e_{23}, f_{23}, k_2, i_{23}, j_{23}, l_{23}, p_{23}, q_{23}, c_{24}, d_{24}, e_{24}, f_{24}, g_{24}, m_2, k_{24}, l_{24}, m_{24}, p_{24}, s_{24}, t_{24}, f_{25}, g_{25}, h_{25}, i_{25}, p_2, j_{25}, n_{25}, p_{25}, q_{25}, t_{25}, a_{26}, e_{26}, f_{26}, g_{26}, p_{26}, r_2, q_{26}, r_{26}, s_{26}, t_{26}, a_{27}, b_{27}, t_{27}, a_{28}, b_{28}, c_{28}, t_2, d_{28}, e_{28}, f_{28}, g_{28}, h_{28}, i_{28}, j_{28}, k_{28}, l_{28}, m_{28}, b_3, n_{28}, p_{28}, a_{29}, b_{29}, c_{29}, d_{29}, f_{29}, m_{29}, n_{29}, p_{29}, d_3, q_{29}, r_{29}, s_{29}, i_{30}, j_{30}, k_{30}, l_{30}, m_{30}, n_{30}, p_{30}, f_3, q_{30}, r_{30}, b_{31}, c_{31}, d_{31}, j_{31}, k_{31}, l_{31}, m_{31}, n_{31}, c_1, h_3, s_{31}, t_{31}, a_{32}, d_{32}, e_{32}, g_{32}, j_{32}, k_{32}, m_{32}, p_{32}, j_3, r_{32}, t_{32}, c_{33}, d_{33}, f_{33}, h_{33}, j_{33}, l_{33}, n_{33}, q_{33}, l_3, a_{34}, b_{34}, c_{34}, e_{34}, g_{34}, i_{34}, k_{34}, m_{34}, p_{34}, s_{34}, n_3, t_{34}, c_{35}, d_{35}, g_{35}, h_{35}, j_{35}, l_{35}, p_{35}, q_{35}, t_{35}, q_3, a_{36}, c_{36}, e_{36}, g_{36}, j_{36}, k_{36}, p_{36}, q_{36}, r_{36}, t_{36}, s_3, c_{37}, d_{37}, g_{37}, h_{37}, k_{37}, l_{37}, r_{37}, s_{37}, t_{37}, a_{38}, a_4, d_{38}, f_{38}, i_{38}, j_{38}, l_{38}, n_{38}, r_{38}, s_{38}, c_{39}, d_{39}, c_4, e_{39}, j_{39}, k_{39}, l_{39}, m_{39}, t_{39}, a_{40}, b_{40}, c_{40}, d_{40}, e_4, k_{40}, l_{40}, m_{40}, n_{40}, p_{40}, q_{40}, e_{41}, f_{41}, g_{41}, h_{41}, g_4, i_{41}, j_{41}, k_{41}, p_{41}, q_{41}, r_{41}, e_{42}, f_{42}, g_{42}, h_{42}, d_1, i_4, i_{42}, j_{42}, q_{42}, r_{42}, s_{42}, t_{42}, a_{43}, f_{43}, g_{43}, h_{43}, k_4, i_{43}, n_{43}, p_{43}, q_{43}, r_{43}, b_{44}, c_{44}, d_{44}, j_{44}, k_{44}, m_4, l_{44}, m_{44}, n_{44}, h_{45}, i_{45}, j_{45}, k_{45}, l_{45}, m_{45}, n_{45}, p_4, p_{45}, q_{45}, r_{45}, s_{45}, t_{45}, c_{47}, d_{47}, e_{47}, f_{47}, g_{47}, r_4, h_{47}, i_{47}, j_{47}, k_{47}, l_{47}, m_{47}, n_{47}, p_{47}, q_{47}, r_{47}, t_4, s_{47}, t_{47}, a_{48}, b_{48}, c_{48}, d_{48}, r_{48}, s_{48}, t_{48}, a_{49}, b_5, b_{49}, c_{49}, d_{49}, e_{49}, f_{49}, g_{49}, h_{49}, i_{49}, k_{49}, t_{49}, d_5, a_{50}, b_{50}, c_{50}, d_{50}, e_{50}, f_{50}, p_{50}, q_{50}, r_{50}, s_{50}, f_5, t_{50}, a_{51}, b_{51}, c_{51}, s_{51}, t_{51}, a_{52}, b_{52}, c_{52}, d_{52}, h_5, e_{52}, f_{52}, g_{52}, h_{52}, i_{52}, j_{52}, k_{52}, l_{52}, j_{53}, k_{53}, e_1, j_5, l_{53}, m_{53}, n_{53}, p_{53}, q_{53}, r_{53}, s_{53}, t_{53}, a_{54}, b_{54}, l_5, c_{54}, d_{54}, e_{54}, f_{54}, q_{55}, r_{55}, s_{55}, t_{55}, a_{56}, b_{56}, n_5, c_{56}, d_{56}, e_{56}, f_{56}, g_{56}, h_{56}, i_{56}, j_{56}, k_{56}, l_{56}, q_5, m_{56}, n_{56}, p_{56}, q_{56}, r_{56}, s_{56}, t_{56}, a_{57}, b_{57}, c_{57}, s_5, d_{57}, e_{57}, b_{58}, c_{58}, d_{58}, e_{58}, f_{58}, g_{58}, h_{58}, i_{58}, a_6, j_{58}, k_{58}, l_{58}, m_{58}, n_{58}, p_{58}, q_{58}, a_{59}, b_{59}, c_{59}, c_6, f_{59}, g_{59}, l_{59}, m_{59}, n_{59}, p_{59}, d_{60}, e_{60}, f_{60}, g_{60}, e_6, h_{60}, i_{60}, j_{60}, r_{60}, s_{60}, t_{60}, a_{61}, b_{61}, c_{61}, h_{61}, g_6, i_{61}, j_{61}, k_{61}, r_{61}, s_{61}, t_{61}, a_{62}, b_{62}, p_{62}, q_{62}, i_6, r_{62}, s_{62}, t_{62}, a_{63}, b_{63}, c_{63}, d_{63}, e_{63}, f_{63}, g_{63}, f_1, k_6, h_{64}, i_{64}, j_{64}, k_{64}, l_{64}, m_{64}, n_{64}, p_{64}, q_{64}, r_{64}, m_6, s_{64}, t_{64}, a_{65}, b_{65}, c_{65}, d_{65}, e_{65}, f_{65}, g_{65}, n_{66}, p_6, p_{66}, q_{66}, r_{66}, s_{66}, t_{66}, a_{67}, b_{67}, c_{67}, d_{67}, e_{67}, a_7, f_{67}, g_{67}, h_{67}, i_{67}, j_{67}, k_{67}, l_{67}, m_{67}, n_{67}, p_{67}, b_7, q_{67}, r_{67}, s_{67}, t_{67}, k_{69}, l_{69}, m_{69}, n_{69}, p_{69}, q_{69}, c_7, r_{69}, s_{69}, t_{69}, a_{70}, b_{70}, c_{70}, d_{70}, e_{70}, f_{70}, g_{70}, d_7, h_{70}, i_{70}, j_{70}, k_{70}, l_{70}, m_{70}, n_{70}, p_{70}, q_{70}, r_{70}, n_7, s_{70}, t_{70}, a_{71}, j_{73}, k_{73}, l_{73}, m_{73}, n_{73}, p_{73}, q_{73}, p_7, r_{73}, s_{73}, t_{73}, a_{74}, b_{74}, c_{74}, d_{74}, e_{74}, f_{74}, g_{74}, q_7, h_{74}, i_{74}, j_{74}, k_{74}, l_{74}, m_{74}, n_{74}, p_{74}, q_{74}, r_{74}, g_1, r_7, s_{74}, t_{74}, a_{75}, b_{75}, c_{75}, d_{75}, e_{75}, f_{75}, g_{75}, h_{75}, s_7, i_{75}, j_{75}, k_{75}, l_{75}, m_{75}, n_{75}, p_{75}, q_{75}, r_{75}, i_{77}, t_7, j_{77}, k_{77}, l_{77}, m_{77}, n_{77}, p_{77}, q_{77}, r_{77}, s_{77}, t_{77}, a_8, a_{78}, b_{78}, c_{78}, d_{78}, e_{78}, f_{78}, g_{78}, h_{78}, i_{78}, j_{78}, b_8, k_{78}, l_{78}, m_{78}, n_{78}, p_{78}, q_{78}, r_{78}, s_{78}, b_{79}, c_{79}, c_8, q_{79}, r_{79}, s_{79}, t_{79}, a_{80}, b_{80}, c_{80}, d_{80}, e_{80}, f_{80}, k_8, g_{80}, h_{80}, b_{81}, c_{81}, d_{81}, e_{81}, f_{81}, g_{81}, h_{81}, i_{81}, l_8, j_{81}, k_{81}, l_{81}, m_{81}, s_{82}, t_{82}, a_{83}, b_{83}, c_{83}, d_{83}, m_8, e_{83}, f_{83}, g_{83}, h_{83}, i_{83}, j_{83}, k_{83}, l_{83}, m_{83}, n_{83}, n_8, p_{83}, q_{83}, r_{83}, s_{83}, t_{83}, a_{84}, b_{84}, p_{84}, q_{84}, r_{84}, h_1, p_8, s_{84}, t_{84}, a_{85}, b_{85}, c_{85}, d_{85}, e_{85}, f_{85}, g_{85}, t_{87}, q_8, a_{88}, b_{88}, c_{88}, d_{88}, e_{88}, f_{88}, g_{88}, h_{88}, i_{88}, j_{88}, r_8, k_{88}, l_{88}, m_{88}, n_{88}, p_{88}, q_{88}, r_{88}, s_{88}, t_{88}, a_{89}, b_9, b_{89}, c_{89}, d_{89}, e_{89}, f_{89}, g_{89}, h_{89}, i_{89}, j_{89}, k_{89}, c_9, l_{89}, m_{89}, n_{89}, p_{89}, q_{89}, r_{89}, s_{89}, t_{89}, a_{90}, b_{90}, d_9, c_{90}, d_{90}, e_{90}, f_{90}, g_{90}, h_{90}, i_{90}, j_{90}, e_{92}, f_{92}, h_9, g_{92}, h_{92}, i_{92}, j_{92}, k_{92}, l_{92}, m_{92}, n_{92}, p_{92}, q_{92}, i_9, r_{92}, s_{92}, t_{92}, a_{93}, b_{93}, c_{93}, d_{93}, e_{93}, f_{93}, g_{93}, j_9, h_{93}, i_{93}, j_{93}, k_{93}, l_{93}, m_{93}, n_{93}, p_{93}, q_{93}, r_{93}, q_9, q_{96}, r_{96}, s_{96}, t_{96}, a_{97}, b_{97}, c_{97}, d_{97}, e_{97}, f_{97}, i_1, r_9, g_{97}, h_{97}, i_{97}, j_{97}, k_{97}, l_{97}, m_{97}, n_{97}, p_{97}, q_{97}, s_9, r_{97}, s_{97}, t_{97}, a_{98}, b_{98}, c_{98}, d_{98}, e_{98}, f_{98}, g_{98}, t_9, h_{98}, i_{98}, j_{98}, k_{98}, l_{98}, m_{98}, n_{98}, p_{98}, q_{98}, r_{98}, a_{10}, s_{98}, t_{98}, a_{99}, b_{99}, c_{99}, d_{99}, e_{99}, f_{99}, g_{99}, h_{99}, c_{10}, i_{99}, j_{99}, k_{99}, l_{99}, m_{99}, k_{100}, l_{100}, m_{100}, n_{100}, p_{100}, e_{10}, q_{100}, r_{100}, s_{100}, t_{100}, a_{101}, b_{101}, c_{101}, d_{101}, e_{101}, f_{101}, g_{10}, g_{101}, i_{101}, r_{101}, s_{101}, t_{101}, a_{102}, b_{102}, c_{102}, d_{102}, g_{103}, i_{10}, h_{103}, i_{103}, j_{103}, k_{103}, l_{103}, m_{103}, n_{103}, p_{103}, q_{103}, r_{103}, k_{10}, s_{103}, t_{103}, a_{104}, b_{104}, c_{104}, d_{104}, e_{104}, f_{104}, g_{104}, h_{104}, m_{10}, a_{105}, b_{105}, c_{105}, d_{105}, e_{105}, f_{105}, g_{105}, h_{105}, i_{105}, j_{105}