立方体四分之一重叠演示
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①本范例演示立方体四分之一部分的重叠与几何关系;②涉及核心数学概念包括立体几何、线性规划、多边形构造、向量运算及二次方程;③构造要点:使用Intersect(交集)、Point(点)、Polygon(多边形)、Midpoint(中点)、Segment(线段)、Rotate(旋转)、Circle(圆)、Vector(向量)、Translate(平移)、Prism(棱柱)等命令;④适合高中及以上学生及数学爱好者用于理解空间几何与优化问题。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → APoint(xAxis) → BPolygon(A, B, 4) → poly1, f, g, h, i, C, DMidpoint(i) → EMidpoint(h) → FMidpoint(f) → HMidpoint(F, H) → IMidpoint(E, I) → LMidpoint(F, I) → JMidpoint(D, I) → B_1Midpoint(B_1, L) → N_1Midpoint(N_1, B_1) → A_1Midpoint(L, N_1) → TPolygon(T, A_1, 4) → poly5, p_1, q_1, r_1, s_1, C_1, F_1Midpoint(I, C) → D_1Midpoint(J, D_1) → P_1Midpoint(J, P_1) → MMidpoint(P_1, D_1) → OPolygon(M, O, 4) → poly4, m, n, p, q, R, SSegment(F, H) → jMidpoint(F, J) → NRotate(E, (-(90°)), I) → E'Rotate(B_1, (-(90°)), I) → Z_1Rotate(L, (-(90°)), I) → L'Rotate(D, (-(90°)), I) → D'Rotate(D', (-(90°)), I) → D''Rotate(E', (-(180°)), I) → E''_1Rotate(D', (-(180°)), I) → D''_1Polygon(E, L, R, S, M, J, F, D, T, F_1, C_1, A_1, B_1, I, D_1, O) → poly2, l, l_1, m_1, n_1, t_1, a_1, b_1, d_1, s, t, e, f_1, h_1, i_1, j_1, k_1Circle(I, r) → c_1Segment(I, Z_1) → g_1Intersect(c_1, i_1, 1) → GIntersect(c_1, j_1, 1) → KVector(I, G) → uVector(I, K) → vRotate(E, 90°, I) → E'_1Rotate(L, 90°, I) → L'_1Rotate(T, 90°, I) → T'Rotate(F_1, 90°, I) → PRotate(C_1, 90°, I) → QRotate(A_1, 90°, I) → URotate(B_1, 90°, I) → VRotate(I, 90°, I) → I'Rotate(D_1, 90°, I) → WRotate(O, 90°, I) → O'Rotate(R, 90°, I) → R'Rotate(S, 90°, I) → S'Rotate(M, 90°, I) → M'Rotate(J, 90°, I) → J'Rotate(F, 90°, I) → F'Rotate(D, 90°, I) → D'_1Polygon(E'_1, L'_1, R', S', M', J', F', D'_1, T', P, Q, U, V, I', W, O') → poly2', e'_1, o', r', s', m', j', f', d'_1, l'_1, t', p_2, q_2, u_1, v_1, i', wRotate(E, 180°, I) → E'_2Rotate(L, 180°, I) → L'_2Rotate(T, 180°, I) → T'_1Rotate(F_1, 180°, I) → ZRotate(C_1, 180°, I) → E_1Rotate(A_1, 180°, I) → G_1Rotate(B_1, 180°, I) → H_1Rotate(I, 180°, I) → I'_1Rotate(D_1, 180°, I) → I_1Rotate(O, 180°, I) → O'_1Rotate(R, 180°, I) → R'_1Rotate(S, 180°, I) → S'_1Rotate(M, 180°, I) → M'_1Rotate(J, 180°, I) → J'_1Rotate(F, 180°, I) → F'_1Rotate(D, 180°, I) → D'_2Polygon(E'_2, L'_2, R'_1, S'_1, M'_1, J'_1, F'_1, D'_2, T'_1, Z, E_1, G_1, H_1, I'_1, I_1, O'_1) → poly2'_1, e'_2, o'_1, r'_1, s'_1, m'_1, j'_1, f'_1, d'_2, l'_2, t'_1, z_1, e_1, g_2, h_2, i'_1, i_2Rotate(E'_1, 180°, I) → J_1Rotate(L'_1, 180°, I) → K_1Rotate(T', 180°, I) → T''Rotate(P, 180°, I) → P'Rotate(Q, 180°, I) → Q'Rotate(U, 180°, I) → U'Rotate(V, 180°, I) → V'Rotate(I', 180°, I) → I''Rotate(W, 180°, I) → W'Rotate(O', 180°, I) → O''Rotate(R', 180°, I) → R''Rotate(S', 180°, I) → S''Rotate(M', 180°, I) → M''Rotate(J', 180°, I) → J''Rotate(F', 180°, I) → F''Rotate(D'_1, 180°, I) → L_1Polygon(J_1, K_1, R'', S'', M'', J'', F'', L_1, T'', P', Q', U', V', I'', W', O'') → poly2'', j_2, o'', r'', s'', m'', j'', f'', l_2, k_2, t'', p', q', u', v', i'', w'Translate(J_1, v) → M_1Translate(K_1, v) → O_1Translate(T'', v) → T'''Translate(P', v) → P''Translate(Q', v) → Q''Translate(U', v) → U''Translate(V', v) → V''Translate(I'', v) → I'''Translate(W', v) → W''Translate(O'', v) → O'''Translate(R'', v) → R'''Translate(S'', v) → S'''Translate(M'', v) → M'''Translate(J'', v) → J'''Translate(F'', v) → F'''Translate(L_1, v) → Q_1Polygon(M_1, O_1, R''', S''', M''', J''', F''', Q_1, T''', P'', Q'', U'', V'', I''', W'', O''') → poly2''', m_2, o''', r''', s''', m''', j''', f''', q_3, o_1, t''', p'', q'', u'', v'', i''', w''Translate(E'_2, u) → R_1Translate(L'_2, u) → S_1Translate(T'_1, u) → T_1Translate(Z, u) → Z'Translate(E_1, u) → U_1Translate(G_1, u) → V_1Translate(H_1, u) → W_1Translate(I'_1, u) → A_2Translate(I_1, u) → B_2Translate(O'_1, u) → C_2Translate(R'_1, u) → D_2Translate(S'_1, u) → E_2Translate(M'_1, u) → F_2Translate(J'_1, u) → G_2Translate(F'_1, u) → H_2Translate(D'_2, u) → I_2Translate(E'_2, Vector[(-u)]) → J_2Translate(L'_2, Vector[(-u)]) → K_2Translate(T'_1, Vector[(-u)]) → L_2Translate(Z, Vector[(-u)]) → Z'_1Translate(E_1, Vector[(-u)]) → M_2Translate(G_1, Vector[(-u)]) → N_2Translate(H_1, Vector[(-u)]) → O_2Translate(I'_1, Vector[(-u)]) → P_2Translate(I_1, Vector[(-u)]) → Q_2Translate(O'_1, Vector[(-u)]) → R_2Translate(R'_1, Vector[(-u)]) → S_2Translate(S'_1, Vector[(-u)]) → T_2Translate(M'_1, Vector[(-u)]) → U_2Translate(J'_1, Vector[(-u)]) → V_2Translate(F'_1, Vector[(-u)]) → W_2Translate(D'_2, Vector[(-u)]) → Z_2Polygon(J_2, K_2, S_2, T_2, U_2, V_2, W_2, Z_2, L_2, Z'_1, M_2, N_2, O_2, P_2, Q_2, R_2) → poly3, j_3, r_2, s_2, t_2, u_2, v_2, w_2, z_2, k_3, l_3, z'_1, m_3, n_2, o_2, p_3, q_4Translate(E'_1, Vector[(-v)]) → A_3Translate(L'_1, Vector[(-v)]) → B_3Translate(T', Vector[(-v)]) → T''_1Translate(P, Vector[(-v)]) → P'_1Translate(Q, Vector[(-v)]) → Q'_1Translate(U, Vector[(-v)]) → U'_1Translate(V, Vector[(-v)]) → V'_1Translate(I', Vector[(-v)]) → I''_1Translate(W, Vector[(-v)]) → W'_1Translate(O', Vector[(-v)]) → O''_1Translate(R', Vector[(-v)]) → R''_1Translate(S', Vector[(-v)]) → S''_1Translate(M', Vector[(-v)]) → M''_1Translate(J', Vector[(-v)]) → J''_1Translate(F', Vector[(-v)]) → F''_1Translate(D'_1, Vector[(-v)]) → C_3Polygon(A_3, B_3, R''_1, S''_1, M''_1, J''_1, F''_1, C_3, T''_1, P'_1, Q'_1, U'_1, V'_1, I''_1, W'_1, O''_1) → poly2''_1, a_3, o''_1, r''_1, s''_1, m''_1, j''_1, f''_1, c_3, b_3, t''_1, p'_1, q'_1, u'_1, v'_1, i''_1, w'_1Translate(E, u) → E'_3Translate(L, u) → L'_3Translate(T, u) → T'_2Translate(F_1, u) → D_3Translate(C_1, u) → E_3Translate(A_1, u) → F_3Translate(B_1, u) → G_3Translate(I, u) → I'_2Translate(D_1, u) → H_3Translate(O, u) → O'_2Translate(R, u) → R'_2Translate(S, u) → S'_2Translate(M, u) → M'_2Translate(J, u) → J'_2Translate(F, u) → F'_2Translate(D, u) → D'_3Polygon(E'_3, L'_3, R'_2, S'_2, M'_2, J'_2, F'_2, D'_3, T'_2, D_3, E_3, F_3, G_3, I'_2, H_3, O'_2) → poly2'_2, e'_3, o'_2, r'_2, s'_2, m'_2, j'_2, f'_2, d'_3, l'_3, t'_2, d_3, e_3, f_3, g_3, i'_2, h_3Prism(poly2''', 8) → a, I_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, face1, face3, face4, J_3, face5, face6, face7, face8, face9, face10, face11, face12, face13, face14, K_3, face15, face16, face2, face17, edge1, edge2, edge3, edge4, edge5, edge6, L_3, edge7, edge8, edge9, edge10, edge11, edge12, edge13, edge14, edge15, edge16, M_3, edge17, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, N_3, edge28, edge29, edge30, edge31, edge32, edge18, O_3, P_3, Q_3Prism(poly3, 8) → b, A_4, J_4, K_4, L_4, M_4, N_4, O_4, P_4, face18, face20, face21, B_4, face22, face23, face24, face25, face26, face27, face28, face29, face30, face31, C_4, face32, face33, face19, face34, edge33, edge34, edge35, edge36, edge37, edge38, D_4, edge39, edge40, edge41, edge42, edge43, edge44, edge45, edge46, edge47, edge48, E_4, edge49, edge51, edge52, edge53, edge54, edge55, edge56, edge57, edge58, edge59, F_4, edge60, edge61, edge62, edge63, edge64, edge50, G_4, H_4, I_4Prism(poly2''_1, 8) → c, Q_4, B_5, C_5, D_5, E_5, F_5, G_5, H_5, face35, face37, face38, R_4, face39, face40, face41, face42, face43, face44, face45, face46, face47, face48, S_4, face49, face50, face36, face51, edge65, edge66, edge67, edge68, edge69, edge70, T_4, edge71, edge72, edge73, edge74, edge75, edge76, edge77, edge78, edge79, edge80, U_4, edge81, edge83, edge84, edge85, edge86, edge87, edge88, edge89, edge90, edge91, V_4, edge92, edge93, edge94, edge95, edge96, edge82, W_4, Z_4, A_5Prism(poly2'_2, 8) → d, I_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, face52, face54, face55, J_5, face56, face57, face58, face59, face60, face61, face62, face63, face64, face65, K_5, face66, face67, face53, face68, edge97, edge98, edge99, edge100, edge101, edge102, L_5, edge103, edge104, edge105, edge106, edge107, edge108, edge109, edge110, edge111, edge112, M_5, edge113, edge115, edge116, edge117, edge118, edge119, edge120, edge121, edge122, edge123, N_5, edge124, edge125, edge126, edge127, edge128, edge114, O_5, P_5, Q_5
AI 绘图提示语参考
绘制一个立方体的四分之一部分重叠示例。首先在x轴和y轴的交点创建点A,然后在x轴上创建点B。以A、B为顶点构造一个四边形,接着找到四边形的中点E、F、H、I,并依次构造其他关键点和四边形。通过旋转和中点构造,最终形成一个复杂的重叠图形,包括多个四边形和圆。
以上提示语为根据原始绘图命令整理而来,仅供参考。