PS 2标志
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该范例演示了一个等腰三角形和正方形组成的PS 2标志。涉及的核心数学概念包括等腰三角形和正方形的性质。作图要点包括使用向量、线段、镜像、中点等GeoGebra命令。适合初中及以上学生学习几何作图。
GeoGebra 命令及参数
Line(A, B) → sOrthogonalLine(A, s) → bVector(A, B) → uOrthogonalVector(u) → vOrthogonalLine(F, b) → fOrthogonalLine(A_1, b) → rOrthogonalLine(I_1, r) → f_1OrthogonalLine(O_1, s) → g_1LineBisector(A, B) → mIntersect(m, f) → EMirror(H, m) → H'OrthogonalLine(H', s) → kLine(H, I) → jLine(D_1, j) → qIntersect(f_1, q) → J_1Line(J_1, E_1) → m_1Intersect(g_1, q) → Q_1Line(Q_1, m_1) → i_2Line(C_1, j) → n_2Intersect(n_2, i_2) → W_1Midpoint(Q_1, W_1) → U_1OrthogonalLine(U_1, i_2) → m_2Line(M, j) → g_3Intersect(m_2, g_3) → V_1Line(V_1, m_1) → h_3OrthogonalLine(P_1, s) → j_1Intersect(j_1, h_3) → R_1Line(R_1, i_2) → j_2Midpoint(E_1, B_1) → F_1Intersect(i_2, k) → S_1Line(F_1, q) → tIntersect(t, j_1) → G_1OrthogonalLine(B, u, xOyPlane) → gIntersect(g, r) → CPolygon(A_1, C, B, A) → q1, a_1, c, b_1, a_2LineBisector(A_1, A) → hMirror(f, h) → f'OrthogonalLine(D, s) → iIntersect(k, f') → KLine(K, j) → lMirror(k, m) → k'Intersect(k', l) → LLine(M, m) → nLine(N, h) → pIntersect(p, n) → OIntersect(n, h) → PSemicircle(N, O) → dIntersect(n, l) → RPolygon(K, L, H, I) → q2, k_1, l_1, h_1, i_1Polygon(L, R, O, N) → q3, l_2, r_1, o_1, n_1OrthogonalLine(H_1, r) → ePolygon(E_1, F_1, G_1) → t1, p_1, e_1, q_1Intersect(h_3, k) → WPolygon(D_1, W, R_1) → t2, s_1, d_1, k_2Polygon(G_1, J_1, Q_1, S_1, F_1) → poly1, t_1, c_1, f_2, g_2, h_2CurveCartesian(((1 - t)^(5) * R) + (((5 * t) * (1 - t)^(4)) * T_1) + (((10 * (1 - t)^(3)) * t^(2)) * S) + (((10 * (1 - t)^(2)) * t^(3)) * U) + (((5 * (1 - t)) * t^(4)) * V) + (t^(5) * Q), t, 0, 1) → aSemicircle(V_1, U_1) → c_2Polygon(R_1, V_1, U_1, Q_1) → q4, p_2, v_1, u_1, q_2Polygon(R_1, V_1, C_1, D_1) → q5, r_2, s_2, t_2, b_2Polygon(J_1, Q_1, U_1) → t3, d_2, e_2, f_3CurveCartesian(((1 - t)^(5) * J_1) + (((5 * t) * (1 - t)^(4)) * Z_1) + (((10 * (1 - t)^(3)) * t^(2)) * K_1) + (((10 * (1 - t)^(2)) * t^(3)) * L_1) + (((5 * (1 - t)) * t^(4)) * M_1) + (t^(5) * C_1), t, 0, 1) → wLine(H, m_1) → i_3Intersect(k', q) → N_1Line(N_1, i_3) → j_3Intersect(t, l_1) → A_2Intersect(t, i_3) → B_2Intersect(t, j_3) → C_2Line(A_2, i_3) → k_3Line(D_2, i_3) → l_3Intersect(q, i_3) → E_2Intersect(t, l_3) → F_2Polygon(H, N_1, E_2) → t4, m_3, h_4, n_3Polygon(B_2, C_2, N_1, E_2) → q6, p_3, q_3, r_3, s_3Polygon(F_2, A_2, D_2) → t5, t_3, a_3, b_3Segment(O, Q) → c_3OrthogonalLine(B_2, i_3) → d_3Intersect(d_3, l_3) → I_2Intersect(d_3, j_3) → M_2Polygon(F_2, I_2, M_2, C_2) → q7, f_4, g_4, i_4, j_4CurveCartesian(((1 - t)^(5) * A_2) + (((5 * t) * (1 - t)^(4)) * N_2) + (((10 * (1 - t)^(3)) * t^(2)) * H_2) + (((10 * (1 - t)^(2)) * t^(3)) * L_2) + (((5 * (1 - t)) * t^(4)) * J_2) + (t^(5) * B_2), t, 0, 1) → w_1Segment(F_2, C_2) → k_4CurveCartesian(((1 - t)^(3) * I_2) + (((3 * (1 - t)^(2)) * t) * Q_2) + (((3 * (1 - t)) * t^(2)) * K_2) + (t^(3) * M_2), t, 0, 1) → o_2Segment(N, O) → e_3
AI 绘图提示语参考
绘制一个由等腰三角形和正方形组成的PS 2标志。首先画出等腰三角形的底边AB,然后通过A点和B点画出底边的垂直平分线m。接着画出正方形的底边BC,通过B点画出垂直于底边的线u,再画出u的垂线v。利用这些线构造等腰三角形的高线和底边的垂直平分线,逐步完成等腰三角形和正方形的构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。