逼近圆的面积

逼近圆的面积
几何画板及绘图内容加载中,请稍等……
2016-03-21 06:46
本范例通过内接和外切正多边形逼近单位圆的面积,演示了极限的概念。使用了多边形、切线、直线、交点、面积等命令。适合高中数学教学,帮助学生理解圆的面积计算及极限思想。

GeoGebra 命令及参数

  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