正多边形:当边数趋于无穷时会发生什么?

正多边形:当边数趋于无穷时会发生什么?
几何画板及绘图内容加载中,请稍等……
2023-01-26 19:56
①本范例演示当正多边形的边数N趋于无穷时,其形状如何逼近圆;②涉及的核心数学概念包括极限、正多边形、圆、几何变换;③作图要点——使用了Point(点)、Circle(圆)、Sequence(数列)、Polygon(多边形)等GeoGebra命令/对象来动态生成和展示正多边形及其极限形态;④适合高中及以上数学学习者,用于理解极限在几何中的应用及正多边形与圆的关系。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Point(Ray[(0, 0), (1, 0)]) → B
  3. Circle(A, B) → c
  4. Sequence(Rotate[B, (2 * ((pi * i)) / n), A], i, 1, n, 1) → l1
  5. Polygon(B, Element[l1, 1], n) → poly1, f, h_1, q_{11}, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{12}, j_1, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, i_{14}, l_1, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, n_1, a_{14}, b_{14}, c_{14}, d_{14}, e_{14}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, q_1, k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{15}, s_1, i_{16}, j_{16}, k_{16}, l_{16}, m_{16}, n_{16}, p_{16}, r_{17}, s_{17}, t_{17}, a_1, a_{17}, b_{17}, c_{17}, d_{17}, e_{17}, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, c_1, k_{18}, l_{18}, m_{18}, n_{18}, p_{18}, q_{18}, r_{18}, q_{20}, r_{20}, s_{20}, e_1, t_{20}, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, f_{21}, g_{21}, h_{21}, i_{21}, g_2, j_{21}, k_{21}, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, r_{21}, s_{21}, t_{21}, g, i_2, a_{21}, b_{21}, c_{21}, d_{21}, e_{21}, f_{22}, g_{22}, h_{22}, i_{22}, j_{22}, k_2, k_{22}, l_{22}, m_{22}, i_{24}, j_{24}, k_{24}, l_{24}, m_{24}, n_{24}, p_{24}, m_2, q_{24}, r_{24}, s_{24}, t_{24}, a_{24}, b_{24}, c_{24}, d_{24}, e_{24}, f_{25}, p_2, g_{25}, h_{25}, i_{25}, j_{25}, k_{25}, l_{25}, m_{25}, n_{25}, p_{25}, q_{25}, r_2, r_{25}, s_{25}, t_{25}, a_{25}, b_{25}, c_{25}, n_{27}, p_{27}, q_{27}, r_{27}, t_2, s_{27}, t_{27}, a_{27}, b_{27}, c_{27}, d_{27}, e_{27}, f_{28}, g_{28}, h_{28}, b_2, i_{28}, j_{28}, k_{28}, l_{28}, m_{28}, n_{28}, p_{28}, q_{28}, r_{28}, s_{28}, d_2, t_{28}, a_{28}, b_{28}, c_{28}, d_{28}, p_{29}, q_{29}, r_{29}, s_{29}, t_{29}, f_3, a_{29}, b_{29}, c_{29}, d_{29}, e_{29}, c_{30}, d_{30}, e_{30}, f_{31}, g_{31}, h_3, h_{31}, i_{31}, j_{31}, k_{31}, l_{31}, m_{31}, n_{31}, p_{31}, q_{31}, r_{31}, h, j_3, s_{31}, C, D, H, N, O, P, Q, R, T, l_3, V, Z, B_1, D_1, F_1, H_1, J_1, L_1, N_1, P_1, n_3, R_1, T_1, V_1, Z_1, B_2, D_2, F_2, H_2, J_2, L_2, q_3, N_2, P_2, S_2, T_2, W_2, Z_2, F_3, G_3, H_3, I_3, t_3, J_3, Q_3, R_3, S_3, T_3, U_3, V_3, F_4, G_4, H_4, a_3, I_4, J_4, K_4, L_4, U_4, V_4, W_4, Z_4, A_5, B_5, d_3, C_5, D_5, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, e_3, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, k_4, I_7, J_7, K_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7, l_4, S_7, T_7, U_7, V_7, W_7, Z_7, V_8, W_8, Z_8, A_9, i, m_4, B_9, C_9, D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, n_4, L_9, M_9, N_9, O_9, P_9, Q_9, R_9, B_{11}, C_{11}, D_{11}, p_4, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, c_4, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, d_4, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, P_{12}, Q_{12}, e_4, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, f_5, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}, g_5, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, h_5, H_{16}, I_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, q_5, R_{16}, S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}, B_{17}, C_{17}, q, r_5, D_{17}, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}, J_{17}, K_{17}, L_{17}, M_{17}, s_5, N_{17}, Z_{18}, A_{19}, B_{19}, C_{19}, D_{19}, E_{19}, F_{19}, G_{19}, H_{19}, t_5, I_{19}, J_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}, P_{19}, Q_{19}, R_{19}, a_5, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, B_{20}, C_{20}, D_{20}, b_5, E_{20}, F_{20}, G_{20}, H_{20}, N_{21}, O_{21}, P_{21}, Q_{21}, R_{21}, S_{21}, c_5, T_{21}, U_{21}, V_{21}, W_{21}, Z_{21}, A_{22}, B_{22}, C_{22}, D_{22}, E_{22}, l_6, F_{22}, G_{22}, H_{22}, I_{22}, J_{22}, K_{22}, L_{22}, M_{22}, N_{22}, O_{22}, m_6, P_{22}, Q_{22}, R_{22}, E_{23}, F_{23}, G_{23}, H_{23}, I_{23}, J_{23}, K_{23}, n_6, L_{23}, M_{23}, N_{23}, G_{24}, H_{24}, I_{24}, J_{24}, K_{24}, L_{24}, M_{24}, p_6, N_{24}, O_{24}, P_{24}, Q_{24}, R_{24}, S_{24}, T_{24}, U_{24}, V_{24}, d, q_6, r_6, s_6, t_6, t_7, a_7, b_7, c_7, d_7, e_7, e, f_8, g_8, h_8, i_8, j_8, k_8, l_8, m_8, n_8, p_8, f_1, q_8, r_8, p_9, q_9, r_9, s_9, t_9, a_9, b_9, c_9, g_1, d_9, e_9, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, n_{11}, p_{11}

AI 绘图提示语参考

一个图形由一个圆和一系列点构成。这些点构成一个正多边形,随着边数增加,多边形逐渐逼近圆。图形以圆心为基准,圆上分布着这些点。N可以很大,使得多边形看起来像圆。
以上提示语为根据原始绘图命令整理而来,仅供参考。