对称之美

几何画板及绘图内容加载中，请稍等……

2020-12-07 18:36

多边形变换几何作图

这个范例展示了对称图形的美妙之处。它涉及的核心数学概念包括几何变换、对称性以及多边形。通过使用GeoGebra中的Point、Polygon、Centroid、Segment、Mirror等命令，可以构造出具有对称性的多边形。适合初中及以上学生或教师用于教学和学习几何变换和对称性。

GeoGebra 命令及参数

Point(Circle[A, a]) → B
Polygon(A, B, b) → poly1, g, D, E, F, G, H, h, i, j, k, l, m, n, C
Polygon(D, C, b) → poly2, f, J, K, L, I_1, U, p, q, r, s, t, n_2, p_1, I
Polygon(E, D, b) → poly3, c, N, O, P, J_1, V, d, e, f_1, g_1, h_1, p_2, q_1, M
Polygon(B, A, b) → poly6, b_1, B_1, C_1, D_1, M_1, Z, c_1, d_1, e_1, f_2, g_2, s_2, s_1, A_1
Polygon(C, B, b) → poly7, h_2, F_1, G_1, H_1, N_1, L_1, i_2, j_2, k_2, l_2, m_2, t_2, t_1, E_1
Polygon(F, E, b) → poly4, i_1, R, S, T, Q_1, S_1, j_1, k_1, l_1, m_1, n_1, c_2, e_2, Q
Polygon(G, F, b) → poly5, r_1, K_1, O_1, P_1, R_1, A_2, a_1, q_2, r_2, a_2, b_2, d_2, m_3, W
Polygon(H, G, b) → poly8, f_3, U_1, V_1, W_1, Z_1, B_2, g_3, h_3, i_3, j_3, k_3, l_3, n_3, T_1
Polygon(A, H, b) → poly9, p_3, D_2, E_2, F_2, G_2, H_2, q_3, r_3, s_3, t_3, a_3, b_3, c_3, C_2
Polygon(Q_1, W, F, S_1) → q1, d_3, w, f_4, e_3
Polygon(E, V, J_1, Q) → q2, e_4, v, g_4, q_4
Polygon(D, U, I_1, M) → q3, d_4, u, ı_1, m_4
Polygon(C, L_1, J, I) → q4, c_4, h_4, j_4, ı
Polygon(R_1, T_1, G, A_2) → q5, i_4, k_4, g_5, l_4
Polygon(H, C_2, Z_1, B_2) → q6, h_5, n_4, z_1, p_4
Polygon(A, A_1, B_1, H_2) → q7, a_4, r_4, s_4, t_4
Polygon(B, Z, M_1, E_1) → q8, b_4, z_2, f_5, i_5
Centroid(q1) → I_2
Centroid(q2) → J_2
Centroid(q3) → K_2
Centroid(q4) → L_2
Centroid(q5) → M_2
Centroid(q6) → N_2
Centroid(q7) → O_2
Centroid(q8) → P_2
Polygon(G, F, E, D, C, B, A, H) → poly10, g_6, f_6, e_5, d_5, c_5, b_5, a_5, h_6
Centroid(poly10) → Q_2
Polygon(M_2, I_2, J_2, K_2, L_2, P_2, O_2, N_2) → poly11, j_5, ı_2, k_5, l_5, m_5, n_5, o_2, p_5
Polygon(R_1, Q_1, J_1, I_1, J, M_1, B_1, Z_1) → poly12, q_5, r_5, s_5, t_5, j_6, i_6, k_6, l_6
Segment(S_2, R_2) → m_6
Mirror(T_2, m_6) → U_2
Segment(T_2, U_2) → n_6
Point(n_6) → V_2
Line(V_2, R_2) → p_6
Mirror(poly1, p_6) → poly1'
Mirror(poly2, p_6) → poly2'
Mirror(poly3, p_6) → poly3'
Mirror(poly6, p_6) → poly6'
Mirror(poly7, p_6) → poly7'
Mirror(poly4, p_6) → poly4'
Mirror(poly5, p_6) → poly5'
Mirror(poly8, p_6) → poly8'
Mirror(poly9, p_6) → poly9'
Mirror(Q_1, p_6) → W_2
Mirror(W, p_6) → W'
Mirror(F, p_6) → F'
Mirror(S_1, p_6) → Z_2
Polygon(W_2, W', F', Z_2) → q1', w_2, w', f', q_6
Mirror(E, p_6) → E'
Mirror(V, p_6) → V'
Mirror(J_1, p_6) → A_3
Mirror(Q, p_6) → Q'
Polygon(E', V', A_3, Q') → q2', e', v', r_6, q'
Mirror(D, p_6) → D'
Mirror(U, p_6) → U'
Mirror(I_1, p_6) → B_3
Mirror(M, p_6) → M'
Polygon(D', U', B_3, M') → q3', d', u', s_6, m'
Mirror(C, p_6) → C'
Mirror(L_1, p_6) → C_3
Mirror(J, p_6) → J'
Mirror(I, p_6) → I'
Polygon(C', C_3, J', I') → q4', c', t_6, j', ı'
Mirror(R_1, p_6) → D_3
Mirror(T_1, p_6) → E_3
Mirror(G, p_6) → G'
Mirror(A_2, p_6) → F_3
Polygon(D_3, E_3, G', F_3) → q5', a_6, b_6, g', c_6
Mirror(H, p_6) → H'
Mirror(C_2, p_6) → G_3
Mirror(Z_1, p_6) → H_3
Mirror(B_2, p_6) → I_3
Polygon(H', G_3, H_3, I_3) → q6', h', d_6, e_6, ı_3
Mirror(A, p_6) → A'
Mirror(A_1, p_6) → J_3
Mirror(B_1, p_6) → K_3
Mirror(H_2, p_6) → L_3
Polygon(A', J_3, K_3, L_3) → q7', a', f_7, g_7, h_7
Mirror(B, p_6) → B'
Mirror(Z, p_6) → Z'
Mirror(M_1, p_6) → M_3
Mirror(E_1, p_6) → N_3
Polygon(B', Z', M_3, N_3) → q8', b', z', i_7, j_7
Mirror(G, p_6) → G'_{1}
Mirror(F, p_6) → F'_{1}
Mirror(E, p_6) → E'_{1}
Mirror(D, p_6) → D'_{1}
Mirror(C, p_6) → C'_{1}
Mirror(B, p_6) → B'_{1}
Mirror(A, p_6) → A'_{1}
Mirror(H, p_6) → H'_{1}
Polygon(G'_{1}, F'_{1}, E'_{1}, D'_{1}, C'_{1}, B'_{1}, A'_{1}, H'_{1}) → poly10', g'_{1}, f'_{1}, e'_{1}, d'_{1}, c'_{1}, b'_{1}, a'_{1}, h'_{1}
Mirror(M_2, p_6) → O_3
Mirror(I_2, p_6) → P_3
Mirror(J_2, p_6) → Q_3
Mirror(K_2, p_6) → R_3
Mirror(L_2, p_6) → S_3
Mirror(P_2, p_6) → T_3
Mirror(O_2, p_6) → U_3
Mirror(N_2, p_6) → V_3
Polygon(O_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3) → poly11', o_3, k_7, l_7, m_7, n_7, p_7, u_3, v_3
Mirror(R_1, p_6) → W_3
Mirror(Q_1, p_6) → Z_3
Mirror(J_1, p_6) → A_4
Mirror(I_1, p_6) → B_4
Mirror(J, p_6) → J'_{1}
Mirror(M_1, p_6) → C_4
Mirror(B_1, p_6) → D_4
Mirror(Z_1, p_6) → E_4
Polygon(W_3, Z_3, A_4, B_4, J'_{1}, C_4, D_4, E_4) → poly12', w_3, z_3, q_7, r_7, j'_{1}, s_7, t_7, a_7
Mirror(Q_2, p_6) → F_4
Line(G_4, H_4) → b_7
Mirror(poly1, b_7) → poly1'_{1}
Mirror(poly2, b_7) → poly2'_{1}
Mirror(poly3, b_7) → poly3'_{1}
Mirror(poly6, b_7) → poly6'_{1}
Mirror(poly7, b_7) → poly7'_{1}
Mirror(poly4, b_7) → poly4'_{1}
Mirror(poly5, b_7) → poly5'_{1}
Mirror(poly8, b_7) → poly8'_{1}
Mirror(poly9, b_7) → poly9'_{1}
Mirror(Q_1, b_7) → I_4
Mirror(W, b_7) → W'_{1}
Mirror(F, b_7) → F'_{2}
Mirror(S_1, b_7) → J_4
Polygon(I_4, W'_{1}, F'_{2}, J_4) → q1'_{1}, ı_4, w'_{1}, f'_{2}, c_7
Mirror(E, b_7) → E'_{2}
Mirror(V, b_7) → V'_{1}
Mirror(J_1, b_7) → K_4
Mirror(Q, b_7) → Q'_{1}
Polygon(E'_{2}, V'_{1}, K_4, Q'_{1}) → q2'_{1}, e'_{2}, v'_{1}, d_7, q'_{1}
Mirror(D, b_7) → D'_{2}
Mirror(U, b_7) → U'_{1}
Mirror(I_1, b_7) → L_4
Mirror(M, b_7) → M'_{1}
Polygon(D'_{2}, U'_{1}, L_4, M'_{1}) → q3'_{1}, d'_{2}, u'_{1}, e_7, m'_{1}
Mirror(C, b_7) → C'_{2}
Mirror(L_1, b_7) → M_4
Mirror(J, b_7) → J'_{2}
Mirror(I, b_7) → I'_{1}
Polygon(C'_{2}, M_4, J'_{2}, I'_{1}) → q4'_{1}, c'_{2}, f_8, j'_{2}, ı'_{1}
Mirror(R_1, b_7) → N_4
Mirror(T_1, b_7) → O_4
Mirror(G, b_7) → G'_{2}
Mirror(A_2, b_7) → P_4
Polygon(N_4, O_4, G'_{2}, P_4) → q5'_{1}, g_8, o_4, g'_{2}, h_8
Mirror(H, b_7) → H'_{2}
Mirror(C_2, b_7) → Q_4
Mirror(Z_1, b_7) → R_4
Mirror(B_2, b_7) → S_4
Polygon(H'_{2}, Q_4, R_4, S_4) → q6'_{1}, h'_{2}, i_8, j_8, k_8
Mirror(A, b_7) → A'_{2}
Mirror(A_1, b_7) → T_4
Mirror(B_1, b_7) → U_4
Mirror(H_2, b_7) → V_4
Polygon(A'_{2}, T_4, U_4, V_4) → q7'_{1}, a'_{2}, l_8, u_4, v_4
Mirror(B, b_7) → B'_{2}
Mirror(Z, b_7) → Z'_{1}
Mirror(M_1, b_7) → W_4
Mirror(E_1, b_7) → Z_4
Polygon(B'_{2}, Z'_{1}, W_4, Z_4) → q8'_{1}, b'_{2}, z'_{1}, w_4, z_4
Mirror(G, b_7) → G'_{3}
Mirror(F, b_7) → F'_{3}
Mirror(E, b_7) → E'_{3}
Mirror(D, b_7) → D'_{3}
Mirror(C, b_7) → C'_{3}
Mirror(B, b_7) → B'_{3}
Mirror(A, b_7) → A'_{3}
Mirror(H, b_7) → H'_{3}
Polygon(G'_{3}, F'_{3}, E'_{3}, D'_{3}, C'_{3}, B'_{3}, A'_{3}, H'_{3}) → poly10'_{1}, g'_{3}, f'_{3}, e'_{3}, d'_{3}, c'_{3}, b'_{3}, a'_{3}, h'_{3}
Mirror(M_2, b_7) → A_5
Mirror(I_2, b_7) → B_5
Mirror(J_2, b_7) → C_5
Mirror(K_2, b_7) → D_5
Mirror(L_2, b_7) → E_5
Mirror(P_2, b_7) → F_5
Mirror(O_2, b_7) → G_5
Mirror(N_2, b_7) → H_5
Polygon(A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → poly11'_{1}, m_8, n_8, p_8, q_8, r_8, s_8, t_8, a_8
Mirror(R_1, b_7) → I_5
Mirror(Q_1, b_7) → J_5
Mirror(J_1, b_7) → K_5
Mirror(I_1, b_7) → L_5
Mirror(J, b_7) → J'_{3}
Mirror(M_1, b_7) → M_5
Mirror(B_1, b_7) → N_5
Mirror(Z_1, b_7) → O_5
Polygon(I_5, J_5, K_5, L_5, J'_{3}, M_5, N_5, O_5) → poly12'_{1}, ı_5, b_8, c_8, d_8, j'_{3}, e_8, f_9, o_5
Mirror(poly1', b_7) → poly1''
Mirror(poly2', b_7) → poly2''
Mirror(poly3', b_7) → poly3''
Mirror(poly6', b_7) → poly6''
Mirror(poly7', b_7) → poly7''
Mirror(poly4', b_7) → poly4''
Mirror(poly5', b_7) → poly5''
Mirror(poly8', b_7) → poly8''
Mirror(poly9', b_7) → poly9''
Mirror(W_2, b_7) → P_5
Mirror(W', b_7) → W''
Mirror(F', b_7) → F''
Mirror(Z_2, b_7) → Q_5
Polygon(P_5, W'', F'', Q_5) → q1'', g_9, w'', f'', h_9
Mirror(E', b_7) → E''
Mirror(V', b_7) → V''
Mirror(A_3, b_7) → R_5
Mirror(Q', b_7) → Q''
Polygon(E'', V'', R_5, Q'') → q2'', e'', v'', i_9, q''
Mirror(D', b_7) → D''
Mirror(U', b_7) → U''
Mirror(B_3, b_7) → S_5
Mirror(M', b_7) → M''
Polygon(D'', U'', S_5, M'') → q3'', d'', u'', j_9, m''
Mirror(C', b_7) → C''
Mirror(C_3, b_7) → T_5
Mirror(J', b_7) → J''
Mirror(I', b_7) → I''
Polygon(C'', T_5, J'', I'') → q4'', c'', k_9, j'', ı''
Mirror(D_3, b_7) → U_5
Mirror(E_3, b_7) → V_5
Mirror(G', b_7) → G''
Mirror(F_3, b_7) → W_5
Polygon(U_5, V_5, G'', W_5) → q5'', u_5, v_5, g'', w_5
Mirror(H', b_7) → H''
Mirror(G_3, b_7) → Z_5
Mirror(H_3, b_7) → A_6
Mirror(I_3, b_7) → B_6
Polygon(H'', Z_5, A_6, B_6) → q6'', h'', z_5, l_9, m_9
Mirror(A', b_7) → A''
Mirror(J_3, b_7) → C_6
Mirror(K_3, b_7) → D_6
Mirror(L_3, b_7) → E_6
Polygon(A'', C_6, D_6, E_6) → q7'', a'', n_9, p_9, q_9
Mirror(B', b_7) → B''
Mirror(Z', b_7) → Z''
Mirror(M_3, b_7) → F_6
Mirror(N_3, b_7) → G_6
Polygon(B'', Z'', F_6, G_6) → q8'', b'', z'', r_9, s_9
Mirror(G'_{1}, b_7) → H_6
Mirror(F'_{1}, b_7) → I_6
Mirror(E'_{1}, b_7) → J_6
Mirror(D'_{1}, b_7) → K_6
Mirror(C'_{1}, b_7) → L_6
Mirror(B'_{1}, b_7) → M_6
Mirror(A'_{1}, b_7) → N_6
Mirror(H'_{1}, b_7) → O_6
Polygon(H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6) → poly10'', t_9, ı_6, a_9, b_9, c_9, d_9, e_9, o_6
Mirror(O_3, b_7) → P_6
Mirror(P_3, b_7) → Q_6
Mirror(Q_3, b_7) → R_6
Mirror(R_3, b_7) → S_6
Mirror(S_3, b_7) → T_6
Mirror(T_3, b_7) → U_6
Mirror(U_3, b_7) → V_6
Mirror(V_3, b_7) → W_6
Polygon(P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6) → poly11'', f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, u_6, v_6, w_6
Mirror(W_3, b_7) → Z_6
Mirror(Z_3, b_7) → A_7
Mirror(A_4, b_7) → B_7
Mirror(B_4, b_7) → C_7
Mirror(J'_{1}, b_7) → D_7
Mirror(C_4, b_7) → E_7
Mirror(D_4, b_7) → F_7
Mirror(E_4, b_7) → G_7
Polygon(Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7) → poly12'', z_6, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}
Mirror(S_2, b_7) → H_7
Mirror(R_2, b_7) → I_7
Segment(H_7, I_7) → s_{10}
Mirror(T_2, b_7) → J_7
Mirror(U_2, b_7) → K_7
Segment(J_7, K_7) → t_{10}
Mirror(Q_2, b_7) → L_7
Mirror(V_2, b_7) → M_7
Mirror(F_4, b_7) → N_7

AI 绘图提示语参考

绘制一个对称的多边形图案，首先创建一个中心点，然后围绕该点绘制多个大小和形状相似的多边形，通过几何变换和镜像操作，使这些多边形呈现出完美的对称性，最终形成一个具有高度装饰性和艺术感的对称图形。

以上提示语为根据原始绘图命令整理而来，仅供参考。