Box Q1 几何作图
几何画板及绘图内容加载中,请稍等……
①本范例演示如何通过 GeoGebra 构造一个包含内切圆的矩形,并展示其相关几何性质;②涉及的核心数学概念包括内切圆、函数图像、向量、旋转、多边形构造等;③作图要点:使用 Circle, Vector, Translate, Intersect, Rotate, Polygon, Segment, OrthogonalLine, newbox, Point, blackbox, Length 等命令和对象进行构造;④适合高中数学教学,用于讲解几何作图和内切圆相关性质。
GeoGebra 命令及参数
Circle(Origin, len - (2 * h)) → cVector((width - (2 * h), 0)) → uTranslate(A, u) → A'Intersect(c, xAxis) → B, CRotate(C, α) → C'Vector(C') → vTranslate(A, v) → A'_1Translate(A', v) → A''Polygon(A, A'_1, A'', A') → poly1, a, a'_1, a'', a'Vector((0, h)) → wTranslate(A, w) → A'_2Translate(A', w) → A''_1Translate(A'_1, w) → DTranslate(A'', w) → A'''Segment(A'_2, A) → bSegment(A''_1, A') → dSegment(D, A'_1) → eSegment(A''', A'') → fPolygon(A'_2, A''_1, A', A) → poly2, a'_2, a''_1, a'_3, a_1Polygon(D, A''', A'', A'_1) → poly3, d_1, a''', a''_2, a'_4Polygon(A''_1, A''', A'', A') → poly4, a''_3, a'''_1, a''_4, a'_5Polygon(D, A'_2, A, A'_1) → poly5, d_2, a'_6, a_2, a'_7Rotate(E, α) → E'Vector(E') → gSegment(W_1, A_2) → c_7Segment(A_2, Z_1) → d_7Segment(Z_1, V_1) → e_7Segment(V_1, W_1) → f_7Segment(Paper, U_1) → g_7Segment(U_1, S_1) → h_7Segment(S_1, T_1) → i_7Segment(T_1, Paper) → j_7OrthogonalLine(Z_1, g_7) → m_7OrthogonalLine(Z_1, h_7) → n_7OrthogonalLine(A_2, h_7) → a_8OrthogonalLine(W_1, i_7) → b_8Intersect(j_7, a_8) → B_2Intersect(i_7, b_8) → C_2Intersect(m_7, i_7) → D_2Intersect(h_7, a_8) → E_2Intersect(n_7, h_7) → F_2Intersect(m_7, g_7) → G_2Intersect(g_7, b_8) → H_2Intersect(n_7, j_7) → I_2Polygon(B_2, W_1, 4) → poly26, c_8, d_8, e_8, f_8, J_2, K_2Polygon(Paper, H_2, 4) → poly27, g_8, h_8, i_8, j_8, L_2, M_2Polygon(G_2, U_1, 4) → poly28, k_8, l_8, m_8, n_8, N_2, O_2Polygon(A_2, E_2, 4) → poly29, p_8, q_8, r_8, s_8, P_2, Q_2Polygon(V_1, Z_1, A_2, W_1) → poly31, v_1, z_1, a_9, w_1newbox(α, E, G) → n, p, c_1, e_1, f_1, g_1, h_1, i_1, j_1, k_1, J, q, H, poly6, poly7, r, s, t, b_1Intersect(r, i_1) → KIntersect(r, i_1) → LIntersect(r, e_1) → MPolygon(J, M, H, G) → poly8, j_2, m_1, h_2, g_2Polygon(B_2, W_1, V_1, I_2) → poly9, b_2, w_2, v_2, i_2Polygon(W_1, A_2, D_2, C_2) → poly10, w_3, a_3, d_3, c_2Point(w_3) → NPolygon(N, Z_1, F_2, E_2) → poly11, n_1, z_2, f_2, e_2Point(n_1) → OPoint(w_2) → PPolygon(H_2, G_2, O, P) → poly12, h_3, g_3, o, p_1blackbox(α, E, Q) → poly13, poly14, r_1, s_1, t_1, k_2, l_2, m_2, n_2, p_2, q_2, r_2, poly15, s_2, t_2, i, j, k, l, m, l_1, q_1blackbox(α, E, R) → poly16, poly17, l_3, m_3, n_3, p_3, q_3, r_3, s_3, t_3, a_4, b_4, poly18, c_4, d_4, b_3, c_3, e_3, f_3, i_3, j_3, k_3Vector(S, T) → u_1Point(xAxis) → UOrthogonalLine(U, xAxis) → e_4Point(xAxis) → VOrthogonalLine(V, xAxis) → f_4Segment(U, V) → g_4Length(g_4) → o_1Translate(W, u_1) → W'Translate(W', u_1) → W''Vector(W', W'') → u_2
AI 绘图提示语参考
画一个矩形,使其内切一个圆。首先绘制圆的圆心和半径,然后创建矩形的边,通过旋转和向量平移确定矩形的顶点。接着用线段连接顶点形成矩形和圆。最后,展示圆心到矩形边的垂线,以及由这些垂线构成的内部多边形,突出几何性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。