Estimating Pi with Inscribed Polygons

Estimating Pi with Inscribed Polygons
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2013-07-19 22:15
This example approximates the value of pi by increasing the number of sides of inscribed polygons within a circle. Key mathematical concepts include polygons and the value of pi. GeoGebra commands used include Circle, Rotate, Distance, and Polygon. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, (360 / a)°, A) → B'
  3. Distance(B, A) → r
  4. Distance(B, B') → l
  5. Polygon(B, B', a) → poly1, b, m, j_5, k_5, l_5, m_5, n_5, p_5, q_5, r_5, s_5, t_5, n, a_6, b_6, c_6, d_6, e_6, f_6, g_6, h_6, i_6, j_6, q, k_6, l_6, m_6, n_6, p_6, q_6, r_6, s_6, t_6, a_7, s, b_7, c_7, d_7, e_7, f_7, g_7, h_7, i_7, j_7, k_7, t, l_7, m_7, n_7, p_7, q_7, r_7, s_7, t_7, a_8, b_8, a_1, c_8, d_8, e_8, f_8, g_8, h_8, i_8, j_8, k_8, l_8, b_1, m_8, n_8, p_8, q_8, r_8, s_8, t_8, a_9, b_9, c_9, c_1, d_9, e_9, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9, d_1, n_9, p_9, q_9, r_9, s_9, t_9, a_{10}, b_{10}, c_{10}, d_{10}, e_1, e_{10}, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}, b', f_1, p_{10}, C, D, E, F, G, H, I, J, K, g_1, L, M, N, O, P, R, S, T, U, V, h_1, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, i_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, j_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, k_1, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, l_1, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, m_1, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, n_1, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, p_1, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, e, q_1, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, r_1, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, B_5, s_1, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, t_1, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, a_2, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, b_2, I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, R_6, c_2, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, d_2, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_7, e_2, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, Z_7, f_2, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8, f, g_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2, g, r_2, s_2, t_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3, h, h_3, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3, i, s_3, t_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, j, i_4, j_4, k_4, l_4, m_4, n_4, p_4, q_4, r_4, s_4, k, t_4, a_5, b_5, c_5, d_5, e_5, f_5, g_5, h_5, i_5

AI Drawing Prompt Reference

Draw a circle, then inscribe a regular polygon inside it, gradually increasing the number of sides, and observe how the perimeter of the polygon approximates the circumference of the circle to estimate the value of pi (π).
The prompt above was compiled from the original drawing commands and is for reference only.