根矩形4-8
几何画板及绘图内容加载中,请稍等……
①本范例演示根矩形4-8的几何构造与性质;②涉及核心数学概念包括矩形、根号运算、对称性、线段运算、百分比计算;③作图要点:使用Point, Segment, Polygon, Line, Circle, Intersect, OrthogonalLine, CircleArc, Rotate, Angle等GeoGebra命令进行点线面构造与变换;④适合高中数学教学,用于理解几何变换与代数运算的结合应用。
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_3Polygon(C, G, 8) → poly2, b_2, Q_1, R_1, S_1, T_1, U_1, i_3, j_3, l_3, m_3, n_3, p_3, q_3, P_1Rotate(H, (-(135°)), I) → H'Angle(H', I, H) → βRotate(H, 135°, I) → H'_1Angle(H, I, H'_1) → γRotate(H, (-(67.5°)), I) → H'_2Angle(H'_2, I, H) → αLine(I, H'_2) → r_3Intersect(r_3, f) → V_1Rotate(I_1, 67.5°, M_1) → Z_1Angle(I_1, M_1, Z_1) → εLine(M_1, Z_1) → s_3Intersect(s_3, n_1) → A_2Segment(V_1, I) → t_3Segment(A_2, M_1) → a_3Polygon(I, V_1, 8) → poly3, b_3, C_2, D_2, E_2, F_2, G_2, f_4, g_4, h_4, i_4, j_4, k_4, l_4, B_2Segment(G_2, E_2) → m_4Polygon(E_2, G_2, 4) → poly4, n_4, p_4, q_4, r_4, W_1, H_2Segment(I, F_2) → s_4Polygon(F_2, I, 4) → poly5, t_4, a_4, b_4, c_4, I_2, J_2Point(xAxis) → K_2Point(xAxis) → L_2Polygon(K_2, L_2, 8) → poly6, d_4, N_2, O_2, P_2, Q_2, R_2, e_4, f_5, g_5, h_5, i_5, j_5, k_5, M_2Segment(P_2, K_2) → l_5Segment(R_2, M_2) → m_5Intersect(l_5, m_5) → S_2Segment(S_2, R_2) → n_5Point(xAxis) → T_2Line(T_2, K_2) → p_5OrthogonalLine(T_2, p_5) → q_5Intersect(q_5, n_5) → U_2Polygon(U_2, S_2, 4) → poly7, r_5, s_5, t_5, a_5, V_2, W_2Segment(S_2, W_2) → b_5CircleArc(S_2, W_2, R_2) → c_5Rotate(U_2, 45°, S_2) → Z_2CircleArc(S_2, U_2, Z_2) → d_5Segment(Z_2, S_2) → e_5
AI 绘图提示语参考
画一个由四个矩形组成的图形,每个矩形都通过正方形根、对称性、线段操作和百分比计算构造。首先在x轴上创建四个点,然后连接这些点形成矩形。接着,通过旋转、绘制圆和正交线等操作,在每个矩形内部构造新的几何形状,最终形成复杂的几何图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。