Symmetry in Beauty

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2020-12-07 18:36

This example demonstrates the beauty of symmetric shapes. It involves key mathematical concepts such as geometric transformations and symmetry. Using GeoGebra commands like Point, Polygon, Centroid, Segment, Mirror, etc., symmetric polygons can be constructed. Suitable for middle school and above students or teachers for teaching and learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

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 Drawing Prompt Reference

Draw a symmetric polygon pattern by creating a central point and then drawing multiple similar polygons around it. Use geometric transformations and mirror operations to achieve perfect symmetry, resulting in a highly decorative and artistic symmetric figure.

The prompt above was compiled from the original drawing commands and is for reference only.