根矩形1
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①本范例演示了根矩形与函数图像、切线、交点的几何关系;②涉及核心数学概念包括函数、切线、根、矩形、复数、解析几何;③构造要点:使用Point, Segment, Polygon, Line, Circle, Intersect, OrthogonalLine, CircleArc等命令绘制图形;④适合高中及以上数学学习者和教师用于函数图像分析、切线绘制及复数几何表示的教学与探索。
GeoGebra 命令及参数
Point(xAxis) → APoint(xAxis) → BPoint(xAxis) → DPoint(yAxis) → ESegment(O, P) → nPoint(xAxis) → CPoint(xAxis) → GPolygon(C, G, 4) → poly1, f, g, h, i, H, ISegment(C, H) → jLine(C, G) → kCircle(C, H) → cIntersect(c, k, 2) → JOrthogonalLine(J, k) → lLine(H, k) → mIntersect(l, m) → A_1Polygon(G, H, A_1, J) → q1, g_1, h_1, a_1, j_1Circle(C, A_1) → dIntersect(d, k, 2) → B_1Line(B_1, l) → pIntersect(m, p) → C_1Polygon(J, B_1, C_1, A_1) → q2, j_2, b_1, c_1, qCircle(C, C_1) → eIntersect(e, k, 2) → D_1Line(D_1, p) → rIntersect(m, r) → E_1Polygon(B_1, D_1, E_1, C_1) → q3, s, d_1, e_1, tCircle(C, E_1) → f_1Intersect(f_1, k, 2) → F_1Line(F_1, r) → aIntersect(m, a) → G_1Polygon(D_1, F_1, G_1, E_1) → q4, b, i_1, k_1, l_1Circle(C, G_1) → p_1Intersect(p_1, k, 2) → H_1Line(H_1, a) → m_1Intersect(m, m_1) → I_1Polygon(F_1, H_1, I_1, G_1) → q5, n_1, q_1, r_1, s_1Circle(C, I_1) → t_1Intersect(t_1, k, 2) → J_1Line(J_1, m_1) → f_2Intersect(m, f_2) → K_1Polygon(H_1, J_1, K_1, I_1) → q6, g_2, h_2, i_2, k_2Circle(C, K_1) → c_2Intersect(c_2, k, 2) → L_1Line(L_1, f_2) → l_2Intersect(m, l_2) → M_1Polygon(J_1, L_1, M_1, K_1) → q7, m_2, n_2, p_2, q_2Circle(C, M_1) → d_2Intersect(d_2, k, 2) → N_1Line(N_1, l_2) → r_2Intersect(m, r_2) → O_1Polygon(L_1, N_1, O_1, M_1) → q8, s_2, t_2, o_1, a_2CircleArc(C, J, H) → e_2CircleArc(C, B_1, A_1) → c_3CircleArc(C, D_1, C_1) → d_3CircleArc(C, F_1, E_1) → e_3CircleArc(C, J_1, I_1) → f_3CircleArc(C, H_1, G_1) → g_3CircleArc(C, L_1, K_1) → h_3CircleArc(C, N_1, M_1) → k_3Point(xAxis) → P_1Polygon(P_1, C, 4) → poly2, b_2, i_3, j_3, l_3, Q_1, R_1Polygon(G, C, 4) → poly3, m_3, n_3, p_3, q_3, S_1, T_1Polygon(C, P_1, 4) → poly4, r_3, s_3, t_3, a_3, U_1, V_1Segment(U_1, C) → b_3Line(U_1, T_1) → f_4Line(A_1, J) → g_4Line(C_1, B_1) → h_4Intersect(f_4, g_4) → W_1Circle(U_1, H) → c_4Intersect(c_4, f_4, 2) → Z_1Point(g_4) → A_2OrthogonalLine(Z_1, f_4) → i_4Intersect(i_4, e_1) → B_2Segment(Z_1, B_2) → j_4Circle(U_1, B_2) → d_4Intersect(d_4, f_4, 2) → C_2OrthogonalLine(C_2, f_4) → k_4Intersect(k_4, i_2) → D_2Segment(D_2, C_2) → l_4Circle(U_1, D_2) → e_4Intersect(e_4, f_4, 2) → E_2OrthogonalLine(E_2, f_4) → m_4Segment(E_2, N_1) → n_4Circle(S_1, E_1) → p_4Intersect(p_4, f_4, 2) → F_2Intersect(p_4, f_4, 2) → G_2Segment(G_2, L_1) → q_4
AI 绘图提示语参考
画一个函数图像,并在其上绘制多个矩形,每个矩形与函数图像相切,且其边平行于坐标轴。每个矩形的顶点都在函数图像上,且矩形的对角线与函数图像的切线垂直。用圆表示每个矩形的内切圆,并用线段连接矩形的顶点。展示函数图像、切线、矩形、圆和交点的几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。