Octagons - Obtuse
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This example demonstrates the construction of Islamic geometric patterns using octagons. It involves the symmetry and obtuse angle properties of octagons. Using GeoGebra commands such as Intersect, ConstructionStep, and Point, complex geometric patterns can be constructed. Suitable for middle school and above students to learn geometric construction and symmetry.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → AConstructionStep() → stapPoint(xAxis) → BPolygon(A, B, 8) → veelhoek1, f, D, E, F, G, H, g, h, i, j, k, l, m, CPolygon(D, C, 8) → veelhoek2, n, J, K, L, M, N, p, q, r, s, t, a, b, IPolygon(L, K, 8) → veelhoek3, c, P, Q, R, S, T, d, e, f_1, g_1, h_1, i_1, j_1, OPolygon(R, Q, 8) → veelhoek4, k_1, V, W, Z, A_1, B_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, UPolygon(B, A, 8) → veelhoek5, t_1, D_1, E_1, F_1, G_1, H_1, a_1, b_1, c_1, d_1, e_1, f_2, g_2, C_1Polygon(J, I, 8) → veelhoek6, h_2, J_1, K_1, L_1, M_1, N_1, i_2, j_2, k_2, l_2, m_2, n_2, p_2, I_1Polygon(P, O, 8) → veelhoek7, q_2, P_1, Q_1, R_1, S_1, T_1, r_2, s_2, t_2, a_2, b_2, c_2, d_2, O_1Polygon(V, U, 8) → veelhoek8, e_2, V_1, W_1, Z_1, A_2, B_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, U_1Polygon(F, E, 8) → veelhoek9, m_3, D_2, E_2, F_2, G_2, H_2, n_3, p_3, q_3, r_3, s_3, t_3, a_3, C_2Polygon(N, M, 8) → veelhoek10, b_3, J_2, K_2, L_2, M_2, N_2, c_3, d_3, e_3, f_4, g_4, h_4, i_4, I_2Polygon(T, S, 8) → veelhoek11, j_4, P_2, Q_2, R_2, S_2, T_2, k_4, l_4, m_4, n_4, p_4, q_4, r_4, O_2Polygon(B_1, A_1, 8) → veelhoek12, s_4, V_2, W_2, Z_2, A_3, B_3, t_4, a_4, b_4, c_4, d_4, e_4, f_5, U_2Midpoint(f) → C_3Midpoint(g) → D_3Midpoint(h) → E_3Midpoint(i) → F_3Midpoint(j) → G_3Midpoint(k) → H_3Midpoint(l) → I_3Midpoint(m) → J_3Segment(C_3, D_3) → g_5Segment(D_3, E_3) → h_5Segment(E_3, F_3) → i_5Segment(F_3, G_3) → j_5Segment(G_3, H_3) → k_5Segment(H_3, I_3) → l_5Segment(I_3, J_3) → m_5Segment(J_3, C_3) → n_5Centroid(veelhoek1) → K_3Mirror(CL, C_3) → CRIntersect(vgl1, n_5) → L_3Intersect(vgl1, k_5) → M_3Intersect(vgl2, j_5) → N_3Intersect(vgl2, g_5) → O_3Segment(M_3, CL) → p_5Segment(N_3, O_3) → q_5Rotate(M_3, 90°, K_3) → P_3Rotate(CL, 90°, K_3) → CL'Segment(P_3, CL') → r_5Rotate(N_3, 90°, K_3) → Q_3Rotate(O_3, 90°, K_3) → R_3Segment(Q_3, R_3) → s_5Rotate(M_3, 45°, K_3) → S_3Rotate(CL, 45°, K_3) → CL'_1Segment(S_3, CL'_1) → t_5Rotate(N_3, 45°, K_3) → T_3Rotate(O_3, 45°, K_3) → U_3Segment(T_3, U_3) → a_5Rotate(M_3, (-(45°)), K_3) → V_3Rotate(CL, (-(45°)), K_3) → CL'_2Segment(V_3, CL'_2) → b_5Rotate(N_3, (-(45°)), K_3) → W_3Rotate(O_3, (-(45°)), K_3) → Z_3Segment(W_3, Z_3) → c_5Intersect(a_5, b_5) → A_4Intersect(s_5, b_5) → B_4Intersect(p_5, veelhoek1) → C_4Intersect(p_5, s_5) → D_4Intersect(p_5, b_5) → E_4Intersect(t_5, b_5) → F_4Intersect(p_5, t_5) → G_4Intersect(p_5, r_5) → H_4Intersect(r_5, t_5) → I_4Intersect(t_5, c_5) → J_4Intersect(r_5, c_5) → K_4Intersect(q_5, r_5) → L_4Intersect(q_5, c_5) → M_4Intersect(a_5, c_5) → N_4Intersect(q_5, a_5) → O_4Intersect(q_5, s_5) → P_4Intersect(s_5, a_5) → Q_4PolyLine(G_3, M_3, O_4, N_3, G_3, E_4, F_4, G_4, L_3, C_3, O_3, M_4, N_4) → d_5Intersect(h_5, r_5) → R_4PolyLine(I_3, P_3, B_4, Q_3, I_3, I_4, J_4, K_4, R_4, E_3, R_3, Q_4, A_4) → e_5Intersect(g_5, t_5) → S_4PolyLine(H_3, S_3, Q_4, T_3, H_3, G_4, H_4, I_4, S_4, D_3, U_3, O_4, P_4) → f_6Intersect(m_5, b_5) → T_4PolyLine(F_3, V_3, M_4, W_3, F_3, B_4, D_4, E_4, T_4, J_3, Z_3, K_4, L_4) → g_6Vector(A, I) → horVector(A, F) → vertSequence(Translate[Sequence[Translate[l1, Vector[(nn * hor)]], nn, 0, 3], Vector[(mm * vert)]], mm, -1, 1) → l2Polygon(N_1, O, K, J) → vierhoek1, h_6, o, k_6, j_6Sequence(Translate[Sequence[Polygon[Translate[N_1, Vector[(nn * hor)]], Translate[O, Vector[(nn * hor)]], Translate[K, Vector[(nn * hor)]], Translate[J, Vector[(nn * hor)]]], nn, -1, 1], Vector[(mm * vert)]], mm, 0, 1) → l3