Parametric Star of David Construction
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This example demonstrates the geometric construction of the Star of David using parametric equations and transformations. It involves core concepts like equilateral triangles, dilation, and parametric curves. Key GeoGebra commands used include Polygon, Intersect, and Point. Suitable for high school and advanced mathematics learners exploring parametric curves and geometric constructions.
GeoGebra Commands & Parameters
Polygon(A, C, D) → t1, d, a, cPolygon(E, F, G) → t2, g, e, fIntersect(d, f) → HIntersect(c, g) → IPoint(e) → JPolygon(H, I, J) → t3, j, h, iIntersect(c, f) → KIntersect(d, e) → LIntersect(a, g) → MPolygon(K, L, M) → t4, m, k, lPolygon(E, A, G, C, F, D) → poly1, e_1, a_1, g_1, c_1, f_1, d_1Polygon(A, N, G, S, E, O, D, P, F, Q, C, R) → poly2, a_2, r, g_2, s, n, e_2, o, d_2, p, f_2, q, c_2Point(m) → TIntersect(h, l) → UIntersect(i, k) → VPolygon(T, U, V) → t5, v, t, uIntersect(j, l) → WIntersect(i, m) → ZIntersect(h, k) → A_1Polygon(W, Z, A_1) → t6, b, w, z_1Intersect(v, b) → B_1Intersect(t, z_1) → C_1Intersect(u, w) → D_1Polygon(B_1, C_1, D_1) → t7, h_1, b_1, i_1Intersect(u, b) → E_1Intersect(v, z_1) → F_1Intersect(t, w) → G_1Polygon(E_1, F_1, G_1) → t8, j_1, k_1, l_1Intersect(i_1, j_1) → H_1Intersect(h_1, k_1) → I_1Intersect(b_1, l_1) → J_1Polygon(H_1, I_1, J_1) → t9, m_1, n_1, p_1Intersect(h_1, j_1) → K_1Intersect(i_1, l_1) → L_1Intersect(b_1, k_1) → M_1Polygon(K_1, L_1, M_1) → t10, q_1, r_1, s_1Intersect(m_1, q_1) → N_1Intersect(n_1, s_1) → O_1Intersect(p_1, r_1) → P_1Polygon(N_1, O_1, P_1) → t11, t_1, h_2, o_1Intersect(p_1, q_1) → Q_1Intersect(m_1, s_1) → R_1Intersect(n_1, r_1) → S_1Polygon(Q_1, R_1, S_1) → t12, i_2, j_2, k_2Intersect(o_1, i_2) → T_1Intersect(t_1, j_2) → U_1Intersect(h_2, k_2) → V_1Polygon(T_1, U_1, V_1) → t13, v_1, l_2, u_1Intersect(t_1, i_2) → W_1Intersect(h_2, j_2) → Z_1Intersect(o_1, k_2) → A_2Polygon(W_1, Z_1, A_2) → t14, m_2, w_1, n_2Intersect(v_1, n_2) → B_2Intersect(l_2, m_2) → C_2Intersect(u_1, w_1) → D_2Polygon(B_2, C_2, D_2) → t15, p_2, b_2, q_2Intersect(l_2, w_1) → E_2Intersect(v_1, m_2) → F_2Intersect(u_1, n_2) → G_2Polygon(E_2, F_2, G_2) → t16, r_2, s_2, t_2Intersect(p_2, s_2) → H_2Intersect(b_2, r_2) → I_2Intersect(q_2, t_2) → J_2Polygon(H_2, I_2, J_2) → t17, f_3, g_3, h_3Intersect(q_2, s_2) → K_2Intersect(p_2, r_2) → L_2Intersect(b_2, t_2) → M_2Polygon(K_2, L_2, M_2) → t18, i_3, j_3, k_3Intersect(h_3, i_3) → N_2Intersect(f_3, j_3) → O_2Intersect(g_3, k_3) → P_2Polygon(N_2, O_2, P_2) → t19, l_3, m_3, o_2Intersect(g_3, j_3) → Q_2Intersect(f_3, i_3) → R_2Intersect(h_3, k_3) → S_2Polygon(Q_2, R_2, S_2) → t20, n_3, p_3, q_3Intersect(l_3, p_3) → T_2Intersect(m_3, n_3) → U_2Intersect(o_2, q_3) → V_2Polygon(T_2, U_2, V_2) → t21, v_2, r_3, u_2Intersect(o_2, p_3) → W_2Intersect(l_3, n_3) → Z_2Intersect(m_3, q_3) → A_3Polygon(W_2, Z_2, A_3) → t22, a_3, w_2, z_2Intersect(u_2, a_3) → B_3Intersect(v_2, w_2) → C_3Intersect(r_3, z_2) → D_3Polygon(B_3, C_3, D_3) → t23, d_3, b_3, c_3Intersect(u_2, z_2) → E_3Intersect(v_2, a_3) → F_3Intersect(r_3, w_2) → G_3Polygon(E_3, F_3, G_3) → t24, s_3, e_3, t_3
AI Drawing Prompt Reference
Draw a geometric construction of the Star of David, featuring two interwoven hexagons created through equilateral triangles, dilation, and parametric curves. Start by constructing two hexagons, then find their intersection points to form new triangles, progressively building the star pattern. The final image should highlight symmetry and geometric beauty, showcasing the application of parametric equations and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.