圆内正多边形
几何画板及绘图内容加载中,请稍等……
①本范例演示了如何在圆内绘制正多边形,并分析其中心角、内角、外角与等腰三角形底角之间的关系;②涉及核心数学概念包括圆、多边形、角度关系、几何作图等;③构造过程中运用了Circle(圆)、Rotate(旋转)、Polygon(多边形)、Angle(角度)等GeoGebra命令;④适合高中阶段学生用于理解正多边形性质及几何变换,也可用于数学教学演示。
GeoGebra 命令及参数
Intersect(yAxis, xAxis) → ACircle(A, radius) → cRotate(B, a, A) → B'Polygon(B, B', n) → poly1, b, l, k_5, l_5, m_5, n_5, p_5, q_5, r_5, s_5, t_5, a_6, m, b_6, c_6, d_6, e_6, f_6, g_6, h_6, i_6, j_6, k_6, p, l_6, m_6, n_6, p_6, q_6, r_6, s_6, t_6, a_7, b_7, q, c_7, d_7, e_7, f_7, g_7, h_7, i_7, j_7, k_7, l_7, r, m_7, n_7, p_7, q_7, r_7, s_7, t_7, a_8, b_8, c_8, s, d_8, e_8, f_8, g_8, h_8, i_8, j_8, k_8, l_8, m_8, t, n_8, p_8, q_8, r_8, s_8, t_8, a_9, b_9, c_9, d_9, a_1, e_9, f_9, g_9, h_9, i_9, j_9, k_9, l_9, m_9, n_9, b_1, p_9, q_9, r_9, s_9, t_9, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, c_1, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, d, d_1, q_{10}, r_{10}, s_{10}, t_{10}, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, e_1, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, f_1, r_{11}, s_{11}, t_{11}, a_{12}, b_{12}, c_{12}, d_{12}, e_{12}, f_{12}, g_{12}, g_1, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, h_1, s_{12}, t_{12}, a_{13}, b_{13}, c_{13}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, i_1, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, j_1, t_{13}, a_{14}, b_{14}, c_{14}, d_{14}, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, k_1, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, l_1, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, m_1, k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, e, n_1, b_{16}, C, D, E, F, G, H, I, J, K, q_1, L, M, N, O, P, Q, R, S, T, U, r_1, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, H_1, a_2, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, b_2, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, c_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, d_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, e_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, f_2, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, g_2, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, f, h_2, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, i_2, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Z_4, A_5, B_5, j_2, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, k_2, M_5, N_5, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, l_2, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, F_6, G_6, H_6, m_2, I_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, R_6, n_2, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, B_7, C_7, D_7, p_2, E_7, F_7, G_7, H_7, I_7, J_7, K_7, L_7, M_7, N_7, q_2, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, Z_7, r_2, A_8, B_8, C_8, D_8, E_8, F_8, G_8, H_8, I_8, J_8, g, s_2, K_8, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, t_2, U_8, V_8, W_8, Z_8, A_9, B_9, C_9, D_9, E_9, F_9, a_3, G_9, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, b_3, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, c_3, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, d_3, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, e_3, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, f_3, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, g_3, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, h_3, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}, M_{12}, h, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, r_3, s_3, i, t_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, h_4, i_4, j, j_4, k_4, l_4, m_4, n_4, p_4, q_4, r_4, s_4, t_4, k, a_5, b_5, c_5, d_5, e_5, f_5, g_5, h_5, i_5, j_5Area(c) → oOrthogonalLine(A, b) → p_1Intersect(p_1, b) → G_1Segment(A, G_1) → ApothemSegment(A, B) → RadiusOfCircleAngle(G_1, B, A) → βSegment(A, B') → s_1Segment(G_1, B) → t_1Segment(A, C) → d_{16}Angle(B', A, C) → θCircle(B, 3) → e_{16}Intersect(e_{16}, RadiusOfCircle, 1) → O_{12}Ray(B, B') → c_{16}Point(d) → N_{12}Point(c_{16}) → P_{12}Angle(P_{12}, B', N_{12}) → γAngle(C, B', B) → δRay(B, B') → f_{16}LaTeX(δ, true, true) → text6LaTeX(θ, true, true) → text7LaTeX(γ, true, true) → text10LaTeX(β, true, true) → text11