R

r

n = 5 (slider from 3 to 18, step 1)
text2: "La razón entre las áreas de los polígonos es la misma, 
por semejanza, que la razón entre las áreas 
de los círculos inscrito y circunscrito al interpoli.

Razón = (π r²)/(π R²) = (r/R)² = 

= cos² α = cos² (180°/n) = " + (cos(180 ° / n)^(2))
K = (13.470100149182748, 14.483217548347058)
L = (16.537253355367223, 22.44003528612997)
p = Circle(K, L)
M = Point(p)
M' = Rotate(M, 360 ° / n, K)
poly1, c, e, f, A = Polygon(M, M', 3)
poly2, i, m', k, l, E, F = Polygon(M, M', 4)
poly6, e_1, f_1, g_1, u, i_1, j_1, T, U, A_1, B_1 = Polygon(M, M', 6)
poly7, l_1, m_1, n_1, p_1, q_1, r_1, s_1, E_1, F_1, G_1, H_1, I_1 = Polygon(M, M', 7)
poly8, b_2, c_2, d_2, e_2, f_2, o_1, h_2, i_2, L_1, M_1, N_1, O_1, P_1, Q_1 = Polygon(M, M', 8)
poly9, k_2, l_2, m_2, u_1, v_1, w_1, z_1, s_2, t_2, T_1, U_1, V_1, W_1, Z_1, A_2, B_2 = Polygon(M, M', 9)
poly10, q_2, r_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h_3, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2 = Polygon(M, M', 10)
poly11, k_3, l_3, o_2, n_3, p_3, q_3, r_3, s_3, u_2, v_2, w_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2 = Polygon(M, M', 11)
poly12, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, i_4, j_4, k_4, l_4, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3 = Polygon(M, M', 12)
poly13, p_4, q_4, r_4, o_3, t_4, a_5, b_5, c_5, d_5, u_3, v_3, w_3, z_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3 = Polygon(M, M', 13)
poly14, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5, p_5, q_5, r_5, s_5, t_5, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4 = Polygon(M, M', 14)
poly15, c_6, d_6, e_6, f_6, g_6, h_6, u_4, v_4, w_4, z_4, m_6, n_6, p_6, q_6, r_6, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5 = Polygon(M, M', 15)
poly16, k_6, l_6, s_6, t_6, a_7, b_7, c_7, d_7, e_7, o_5, g_7, h_7, i_7, j_7, k_7, u_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5 = Polygon(M, M', 16)
poly17, m_7, n_7, z_5, q_7, r_7, s_7, t_7, a_8, b_8, c_8, d_8, e_8, f_8, g_8, h_8, i_8, j_8, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6 = Polygon(M, M', 17)
poly18, l_8, m_8, n_8, p_8, q_8, r_8, u_6, v_6, w_6, z_6, c_9, d_9, e_9, f_9, g_9, h_9, i_9, j_9, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7 = Polygon(M, M', 18)
poly3, q, s, t, a_1, b_1, I, J, N = Polygon(M, M', 5)
C = Midpoint(c)
D = Midpoint(e)
poly21, d, g, h, G = Polygon(C, D, 3)
S = Midpoint(m')
poly22, d_1, e_1, h_1, k_1, C_1, D_1 = Polygon(C, S, 4)
R_1 = Midpoint(s)
poly23, g_2, j_2, n_2, p_2, i_3, S_1, C_2, D_2 = Polygon(C, R_1, 5)
Z_2 = Midpoint(f_1)
poly24, t_3, z_2, n_4, s_4, e_5, a_6, A_3, L_3, M_3, A_4 = Polygon(C, Z_2, 6)
P_4 = Midpoint(m_1)
poly25, i_6, j_6, f_7, l_7, v_5, w_5, o_6, F_5, G_5, V_5, W_5, O_6 = Polygon(C, P_4, 7)
J_7 = Midpoint(c_2)
poly26, s_8, t_8, p_9, b_{10}, z_8, d_{11}, e_{11}, f_{11}, D_8, E_8, Z_8, A_9, B_9, C_9 = Polygon(C, J_7, 8)
F_9 = Midpoint(l_2)
poly27, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, G_9, H_9, I_9, J_9, K_9, L_9, M_9 = Polygon(C, F_9, 9)
P_9 = Midpoint(r_2)
poly28, t_{11}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, u_9, v_9, w_9, z_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9 = Polygon(C, P_9, 10)
C_{10} = Midpoint(l_3)
poly29, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, s_{12}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10} = Polygon(C, C_{10}, 11)
O_{10} = Midpoint(b_4)
poly30, b_{13}, o_{10}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, u_{10}, v_{10}, w_{10}, z_{10}, m_{13}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11} = Polygon(C, O_{10}, 12)
D_{11} = Midpoint(q_4)
poly31, j_{13}, k_{13}, l_{13}, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}, a_{14}, b_{14}, c_{14}, d_{14}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11} = Polygon(C, D_{11}, 13)
R_{11} = Midpoint(g_5)
poly32, g_{14}, h_{14}, i_{14}, j_{14}, u_{11}, v_{11}, w_{11}, z_{11}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, a_{15}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12} = Polygon(C, R_{11}, 14)
I_{12} = Midpoint(d_6)
poly33, m_{14}, n_{14}, b_{15}, c_{15}, d_{15}, e_{15}, f_{15}, o_{12}, h_{15}, i_{15}, j_{15}, k_{15}, l_{15}, u_{12}, v_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12} = Polygon(C, I_{12}, 15)
A_{13} = Midpoint(l_6)
poly34, n_{15}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, b_{16}, c_{16}, d_{16}, e_{16}, f_{16}, g_{16}, h_{16}, i_{16}, o_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, L_{13}, M_{13}, N_{13}, O_{13} = Polygon(C, A_{13}, 16)
R_{13} = Midpoint(n_7)
poly35, l_{16}, m_{16}, n_{16}, p_{16}, u_{13}, v_{13}, w_{13}, z_{13}, a_{17}, b_{17}, c_{17}, d_{17}, e_{17}, f_{17}, g_{17}, h_{17}, i_{17}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14} = Polygon(C, R_{13}, 17)
L_{14} = Midpoint(m_8)
poly36, s_{16}, t_{16}, j_{17}, k_{17}, o_{14}, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}, u_{14}, v_{14}, w_{14}, z_{14}, c_{18}, d_{18}, e_{18}, f_{18}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15} = Polygon(C, L_{14}, 18)
r_9 = Segment(C, K)
a = Segment(K, M')
b = OrthogonalLine(C, a)
P = Intersect(a, b)
r = Segment(K, P)
O = Midpoint(r)
H = Midpoint(r_9)
α = Angle(C, K, P)
c_1 = Circle(K, C)
t_1 = Circle(K, P)