正多边形的内角与外角

正多边形的内角与外角
几何画板及绘图内容加载中,请稍等……
2018-10-06 22:47
①本范例演示正多边形的内角与外角计算与可视化;②涉及核心数学概念包括多边形、角度计算、几何作图;③构造要点:使用Polygon, Ray, Point, Angle等GeoGebra命令创建多边形及角度;④适合高中数学教学与几何学习。

GeoGebra 命令及参数

  1. Polygon(A, B, n) → poly1, f, q, k_5, l_5, m_5, n_5, p_5, q_5, r_5, s_5, t_5, a_5, r, b_5, c_5, d_5, e_5, f_6, g_6, h_6, i_6, j_6, k_6, s, l_6, m_6, n_6, p_6, q_6, r_6, s_6, t_6, a_6, b_6, t, c_6, d_6, e_6, f_7, g_7, h_7, i_7, j_7, k_7, l_7, a, m_7, n_7, p_7, q_7, r_7, s_7, t_7, a_7, b_7, c_7, b, d_7, e_7, f_8, g_8, h_8, i_8, j_8, k_8, l_8, m_8, c, n_8, p_8, q_8, r_8, s_8, t_8, a_8, b_8, c_8, d_8, d, e_8, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9, n_9, e, p_9, q_9, r_9, s_9, t_9, a_9, b_9, c_9, d_9, e_9, f_1, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, g, g_1, q_{10}, r_{10}, s_{10}, t_{10}, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, f_{11}, h_1, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, i_1, r_{11}, s_{11}, t_{11}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{12}, g_{12}, j_1, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, k_1, s_{12}, t_{12}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, f_{13}, g_{13}, h_{13}, l_1, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, m_1, t_{13}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{14}, g_{14}, h_{14}, i_{14}, n_1, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, p_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}, h, r_1, b_{15}, d_{15}, e_{15}, f_{16}, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, l_{16}, s_1, m_{16}, n_{16}, p_{16}, q_{16}, r_{16}, s_{16}, t_{16}, a_{16}, b_{16}, c_{16}, t_1, d_{16}, e_{16}, f_{17}, g_{17}, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, m_{17}, a_1, n_{17}, p_{17}, q_{17}, r_{17}, s_{17}, t_{17}, a_{17}, b_{17}, c_{17}, d_{17}, b_1, e_{17}, f_{18}, g_{18}, h_{18}, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, n_{18}, c_1, p_{18}, q_{18}, r_{18}, s_{18}, t_{18}, a_{18}, b_{18}, c_{18}, d_{18}, e_{18}, d_1, f_{19}, g_{19}, h_{19}, i_{19}, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}, p_{19}, e_1, q_{19}, r_{19}, s_{19}, t_{19}, a_{19}, b_{19}, c_{19}, d_{19}, e_{19}, f_{20}, f_2, g_{20}, h_{20}, i_{20}, j_{20}, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, q_{20}, g_2, r_{20}, s_{20}, t_{20}, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, f_{21}, g_{21}, i, h_2, h_{21}, i_{21}, j_{21}, k_{21}, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, r_{21}, i_2, s_{21}, t_{21}, a_{21}, b_{21}, c_{21}, d_{21}, e_{21}, f_{22}, g_{22}, h_{22}, j_2, i_{22}, j_{22}, k_{22}, l_{22}, m_{22}, n_{22}, p_{22}, q_{22}, r_{22}, s_{22}, k_2, t_{22}, a_{22}, b_{22}, c_{22}, d_{22}, e_{22}, f_{23}, g_{23}, h_{23}, i_{23}, l_2, j_{23}, k_{23}, l_{23}, m_{23}, n_{23}, p_{23}, q_{23}, r_{23}, s_{23}, t_{23}, m_2, a_{23}, b_{23}, c_{23}, d_{23}, e_{23}, f_{24}, g_{24}, h_{24}, i_{24}, j_{24}, n_2, k_{24}, l_{24}, m_{24}, n_{24}, p_{24}, q_{24}, r_{24}, s_{24}, t_{24}, a_{24}, p_2, b_{24}, c_{24}, d_{24}, e_{24}, f_{25}, g_{25}, h_{25}, i_{25}, j_{25}, k_{25}, q_2, l_{25}, m_{25}, n_{25}, p_{25}, q_{25}, r_{25}, s_{25}, t_{25}, a_{25}, b_{25}, r_2, c_{25}, d_{25}, e_{25}, f_{26}, g_{26}, h_{26}, i_{26}, j_{26}, k_{26}, l_{26}, j, s_2, m_{26}, C, D, E, F, G, H, I, J, K, t_2, L, M, N, O, P, Q, R, S, T, U, a_2, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, b_2, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, c_2, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, d_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, e_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, f_3, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, g_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, h_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, k, i_3, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, j_3, P_4, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, k_3, B_5, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, l_3, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, m_3, V_5, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, n_3, H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, p_3, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, q_3, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, r_3, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, s_3, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8, l, t_3, J_8, K_8, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, a_3, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9, D_9, E_9, b_3, F_9, G_9, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, c_3, P_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, d_3, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, e_3, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, f_4, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, g_4, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, h_4, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, i_4, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}, N_{12}, m, j_4, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, k_4, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, l_4, K_{13}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, m_4, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, n_4, G_{14}, H_{14}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, p_4, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, q_4, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, r_4, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, U_{15}, V_{15}, s_4, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, t_4, I_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}, P_{16}, Q_{16}, R_{16}, p, a_4, S_{16}, T_{16}, U_{16}, V_{16}, W_{16}, Z_{16}, A_{17}, B_{17}, C_{17}, D_{17}, b_4, E_{17}, F_{17}, G_{17}, H_{17}, I_{17}, J_{17}, K_{17}, L_{17}, M_{17}, N_{17}, c_4, O_{17}, P_{17}, Q_{17}, R_{17}, S_{17}, T_{17}, U_{17}, V_{17}, W_{17}, Z_{17}, d_4, A_{18}, B_{18}, C_{18}, D_{18}, E_{18}, F_{18}, G_{18}, H_{18}, I_{18}, J_{18}, e_4, K_{18}, L_{18}, M_{18}, N_{18}, O_{18}, P_{18}, Q_{18}, R_{18}, S_{18}, T_{18}, f_5, U_{18}, V_{18}, W_{18}, Z_{18}, A_{19}, B_{19}, C_{19}, D_{19}, E_{19}, F_{19}, g_5, G_{19}, H_{19}, I_{19}, J_{19}, K_{19}, L_{19}, M_{19}, N_{19}, O_{19}, P_{19}, h_5, Q_{19}, R_{19}, S_{19}, T_{19}, U_{19}, V_{19}, W_{19}, Z_{19}, A_{20}, B_{20}, i_5, C_{20}, D_{20}, E_{20}, F_{20}, G_{20}, H_{20}, I_{20}, J_{20}, K_{20}, L_{20}, j_5, M_{20}, N_{20}, O_{20}, P_{20}, Q_{20}, R_{20}, S_{20}, T_{20}, U_{20}
  2. Ray(A, B) → c_{15}
  3. Point(c_{15}) → M_{12}
  4. Angle(M_{12}, B, C) → α
  5. Angle(C, B, A) → β

AI 绘图提示语参考

绘制一个正多边形,在其中一个顶点处作一条射线,射线经过相邻顶点并向外延伸;在射线上取一点,标出该点、顶点与相邻顶点构成的外角,同时标出两条相邻边在该顶点形成的内角。多边形边数可由参数控制,展示内外角的几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。