Francesca. Madonna 数学范例
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所属专题
geometriadinamica.es
①本范例演示了利用 GeoGebra 构建复杂的几何图形与函数图像,特别是涉及正交线、点、线段、旋转、镜像等操作;②核心数学概念包括正交中心、积分、函数图像绘制、平面图形构造;③作图要点:运用了 OrthogonalLine, Point, Segment, If, Dilate, Circle, Intersect, Polygon, Line, Midpoint, Rotate, Mirror 等命令与对象;④适合高中及以上数学学习者,用于理解几何变换与函数图像的交互。
GeoGebra 命令及参数
OrthogonalLine(B, xAxis) → aPoint(a) → CSegment(B, C) → bPoint(b) → L_2Point(b) → M_1If(pas > 1, 0, 100000) → t_2If(pas > 0, 0, 1000000000) → t_1OrthogonalLine(A, b) → eOrthogonalLine(A, e) → gOrthogonalLine(A, b) → dPoint(d) → DOrthogonalLine(D, e) → iDilate(D, 1.47, A) → ECircle(A, E) → fIntersect(f, g, 2) → FOrthogonalLine(F, g) → hIntersect(h, i) → GIf(pas > 2, 0, 1000000) → t_3If(pas > 3, 0, 100000) → t_4If(pas > 4, 0, 100000) → t_5If(pas > 5, 0, 100000) → t_6Segment(P_1, P_7) → cPolygon(A, F, G, D) → P, a_1, f_1, g_1, d_1OrthogonalLine(B_1, d_1) → jIntersect(f_1, j) → ISegment(B_1, I) → kOrthogonalLine(B_2, k) → lLine(L_2, l) → r_2Midpoint(D, A) → LIntersect(d_1, k) → HCircle(H, A) → pIntersect(p, k) → J,Circle(J, H) → qIntersect(f_1, k) → KIntersect(f_1, k) → MPoint(k) → NPoint(q) → OIntersect(l, k) → QCircle(Q, N) → rOrthogonalLine(B_3, k) → mIntersect(m, k) → RRotate(O, 59.99999999999999°, R) → SRotate(O, 29.999999999999996°, R) → TRotate(O, 90°, R) → UMirror(U, k) → VMirror(A, a_1) → A'Mirror(F, a_1) → F'Segment(A', F') → nMirror(S, k) → WMirror(T, k) → YMirror(T, m) → ZMirror(S, m) → C_1Mirror(O, m) → D_1Mirror(Z, k) → E_1Polygon(Y, T, U, Z, E_1, V) → Q_1, s, t, u, z, e_1, vMirror(C_1, k) → F_1Polygon(O, S, C_1, D_1, F_1, W) → R_1, o, s_{1}, c_1, d_2, f_2, wCircle(Y, T) → h_1Circle(T, Y) → k_1Point(k_1) → G_1Polygon(T, G_1, Y) → S_1, y_1, t_7, g_2OrthogonalLine(B_4, k) → b_1Point(b_1) → H_1OrthogonalLine(B_5, k) → i_1Point(i_1) → I_1Point(b_1) → J_1OrthogonalLine(J_1, b_1) → j_1OrthogonalLine(H_1, b_1) → l_1Point(l_1) → K_1Point(j_1) → L_1Polygon(H_1, J_1, L_1, K_1) → T_1, h_2, j_2, l_2, k_2OrthogonalLine(B_5, b) → m_1OrthogonalLine(B_5, b) → n_1OrthogonalLine(B_5, b) → p_1OrthogonalLine(B_5, b) → q_1Line(B_5, d_1) → r_1Point(m_1) → N_1OrthogonalLine(I_1, m_1) → s_1OrthogonalLine(N_1, m_1) → a_2Point(s_1) → O_1Point(a_2) → U_1Polygon(C_1, O_1, U_1, N_1) → V_1, c_2, o_1, u_1, n_2Line(B_6, b) → b_2Point(b_2) → W_1Point(b_2) → Y_1Point(b_2) → Z_1OrthogonalLine(W_1, b) → e_2OrthogonalLine(Z_1, b) → i_2OrthogonalLine(Y_1, b) → m_2Point(m_2) → C_2Point(m_2) → D_2Point(i_2) → E_2Point(e_2) → F_2Point(e_2) → G_2Polygon(Y_1, G_2, D_2, Z_1, F_2, C_2, W_1, E_2) → Q_2, y_2, g_3, d_3, z_1, f_3, c_3, w_1, e_3OrthogonalLine(M_1, b) → p_2Intersect(p_2, c) → H_2Point(k) → J_2Circle(Q, J_2) → q_2Point(k_2) → K_2Point(r_2) → I_2Point(q_2) → M_2Point(q_2) → N_2Point(q_2) → O_2Point(q_2) → R_2Point(q_2) → S_2Point(q_2) → T_2Point(k_2) → U_2Point(q_2) → V_2Point(q_2) → W_2Point(q_2) → Y_2Point(q_2) → Z_2Segment(I_2, S_2) → s_2Segment(I_2, R_2) → a_3Segment(I_2, O_2) → b_3Segment(I_2, N_2) → h_3Segment(I_2, V_2) → i_3Segment(I_2, Y_2) → j_3Segment(I_2, W_2) → k_3Segment(I_2, M_2) → l_3Segment(I_2, Z_2) → m_3Segment(I_2, T_2) → n_3
AI 绘图提示语参考
绘制一个复杂的几何图形,包含正交线、点、线段、旋转和反射等元素。首先通过点B和x轴构造正交线a,然后在a上取点C,连接BC得到线段b。接着在b上取点L2和M1,通过点A和线段b构造正交线e和d,再通过d取点D,构造一系列正交线和圆,最终形成一个四边形P,连接P的顶点形成多边形,并通过旋转和反射操作生成新的点和线段,最终得到完整的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。