黄金矩形 by Jonathan Garfield
几何画板及绘图内容加载中,请稍等……
这个范例展示了黄金矩形的构造。黄金矩形是一种特殊的矩形,其长宽比为黄金比例。本例涉及的核心数学概念包括比例与相似。通过使用GeoGebra命令如Polygon, Midpoint, Circle等,可以动态地构造黄金矩形。适合初中及以上学生学习比例与黄金分割的概念。
GeoGebra 命令及参数
Polygon(A, B, 4) → poly1, a, b, c, d, C, DMidpoint(A, B) → ECircle(E, C) → eRay(A, B) → fIntersect(e, f, 1) → FRay(D, C) → gOrthogonalLine(F, f) → hIntersect(h, g) → GSegment(C, G) → iSegment(G, F) → jSegment(F, B) → kPolygon(G, C, 4) → poly2, l, m, n, p, H, IPolygon(F, I, 4) → poly3, q, r, s, t, J, KPolygon(B, K, 4) → poly4, a_1, b_1, c_1, d_1, L, MPolygon(H, M, 4) → poly5, e_1, f_1, g_1, h_1, N, OPolygon(J, O, 4) → poly6, i_1, j_1, k_1, l_1, P, QPolygon(L, Q, 4) → poly7, m_1, n_1, p_1, q_1, R, SPolygon(N, S, 4) → poly8, r_1, s_1, t_1, a_2, T, UPolygon(P, U, 4) → poly9, b_2, c_2, d_2, e_2, V, WPolygon(R, W, 4) → poly10, f_2, g_2, h_2, i_2, Z, A_1Polygon(T, A_1, 4) → poly11, j_2, k_2, l_2, m_2, B_1, C_1Polygon(V, C_1, 4) → poly12, n_2, p_2, q_2, r_2, D_1, E_1Polygon(Z, E_1, 4) → poly13, s_2, t_2, a_3, b_3, F_1, G_1Polygon(B_1, G_1, 4) → poly14, c_3, d_3, e_3, f_3, H_1, I_1Polygon(D_1, I_1, 4) → poly15, g_3, h_3, i_3, j_3, J_1, K_1Polygon(F_1, K_1, 4) → poly16, k_3, l_3, m_3, n_3, L_1, M_1Polygon(H_1, M_1, 4) → poly17, p_3, q_3, r_3, s_3, N_1, O_1CircleArc(N_1, O_1, M_1) → t_3CircleArc(L_1, M_1, K_1) → c_4CircleArc(J_1, K_1, I_1) → d_4CircleArc(H_1, I_1, G_1) → e_4CircleArc(F_1, G_1, E_1) → f_4CircleArc(D_1, E_1, C_1) → g_4CircleArc(B_1, C_1, A_1) → h_4CircleArc(Z, A_1, W) → k_4CircleArc(V, W, U) → p_4CircleArc(T, U, S) → q_4CircleArc(R, S, Q) → r_4CircleArc(P, Q, O) → s_4CircleArc(N, O, M) → t_4CircleArc(L, M, K) → c_5CircleArc(J, K, I) → d_5CircleArc(H, I, C) → e_5CircleArc(B, C, A) → f_5
AI 绘图提示语参考
绘制一个黄金矩形,首先创建一个矩形ABCD,然后找到AB的中点E,以E为圆心,C为半径画圆,交AB延长线于F,再作FC的垂线交DC延长线于G,连接CG、GF、FB,形成新的矩形CGFB,重复此过程,每次以新矩形的对角线为直径画圆,交相邻边的延长线于新点,连接这些点形成新的矩形,直到图形变得足够小为止。
以上提示语为根据原始绘图命令整理而来,仅供参考。