Approximating the Area of a Unit Circle

Approximating the Area of a Unit Circle
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2016-03-21 06:46
This example demonstrates the concept of limits by approximating the area of a unit circle using inscribed and circumscribed regular polygons. It utilizes commands such as Polygon, Tangent, Line, Intersect, and Area. Suitable for high school mathematics education, aiding students in understanding the calculation of circle area and the concept of limits.

GeoGebra Commands & Parameters

  1. Polygon(B, C, n) → poly1, a, k, n_{10}, p_{10}, s_{10}, a_{11}, D, E, F, G, H, I, l, J, K, L, M, N, O, P, Q, R, S, m, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, p, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, q, P_1, Q_1, K_3, M_3, O_3, Q_3, S_3, U_3, W_3, A_4, r, C_4, E_4, G_4, I_4, K_4, M_4, O_4, Q_4, S_4, U_4, s, W_4, A_5, C_5, E_5, G_5, I_5, K_5, M_5, O_5, Q_5, t, S_5, T_5, W_5, A_6, C_6, E_6, G_6, I_6, K_6, M_6, a_1, N_6, Q_6, S_6, U_6, W_6, A_7, C_7, E_7, G_7, I_7, b_1, K_7, M_7, O_7, Q_7, S_7, U_7, W_7, A_8, C_8, D_8, b, c_1, E_8, I_8, J_8, M_8, O_8, d_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, d, m_1, n_1, p_1, q_1, r_1, s_1, t_1, a_2, b_2, c_2, e, d_2, j_4, l_4, n_4, q_4, s_4, a_5, c_5, e_5, g_5, f, i_5, k_5, m_5, p_5, r_5, t_5, b_6, d_6, f_6, h_6, g, j_6, l_6, n_6, q_6, s_6, a_7, c_7, e_7, g_7, i_7, h, j_7, m_7, p_7, r_7, t_7, b_8, d_8, f_8, h_8, i_8, i, l_8, n_8, q_8, s_8, a_9, c_9, e_9, g_9, i_9, k_9, j, m_9, p_9, r_9, t_9, b_{10}, d_{10}, f_{10}, h_{10}, i_{10}, j_{10}
  2. Tangent(R_1, c) → e_2,
  3. Line(A, C) → f_2
  4. Line(A, B) → g_2
  5. Intersect(g_2, e_2) → S_1
  6. Intersect(f_2, e_2) → T_1
  7. Polygon(S_1, T_1, n) → poly2, h_2, r_2, q_{10}, r_{10}, t_{10}, b_{11}, U_1, V_1, W_1, Z_1, A_2, B_2, s_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, t_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, a_3, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, b_3, I_3, J_3, L_3, N_3, P_3, R_3, T_3, V_3, Z_3, B_4, c_3, D_4, F_4, H_4, J_4, L_4, N_4, P_4, R_4, T_4, V_4, d_3, Z_4, B_5, D_5, F_5, H_5, J_5, L_5, N_5, P_5, R_5, e_3, U_5, V_5, Z_5, B_6, D_6, F_6, H_6, J_6, L_6, O_6, f_3, P_6, R_6, T_6, V_6, Z_6, B_7, D_7, F_7, H_7, J_7, g_3, L_7, N_7, P_7, R_7, T_7, V_7, Z_7, B_8, F_8, G_8, i_2, h_3, H_8, K_8, L_8, N_8, P_8, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3, j_2, s_3, t_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, k_2, i_4, k_4, m_4, p_4, r_4, t_4, b_5, d_5, f_5, h_5, l_2, j_5, l_5, n_5, q_5, s_5, a_6, c_6, e_6, g_6, i_6, m_2, k_6, m_6, p_6, r_6, t_6, b_7, d_7, f_7, h_7, k_7, n_2, l_7, n_7, q_7, s_7, a_8, c_8, e_8, g_8, j_8, k_8, p_2, m_8, p_8, r_8, t_8, b_9, d_9, f_9, h_9, j_9, l_9, q_2, n_9, q_9, s_9, a_{10}, c_{10}, e_{10}, g_{10}, k_{10}, l_{10}, m_{10}
  8. Area(poly1) → Inscr
  9. Area(poly2) → Circum
  10. LaTeX(Inscr, true, true) → Inscribed
  11. LaTeX(Circum, true, true) → text2