立方体分割演示
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①本范例演示立方体的分割构造与几何关系;②涉及积分定义、自然数、几何构造、线性规划优化、最大公约数与最小公倍数等核心概念;③构造过程中运用了Intersect(相交)、Point(点)、Polygon(多边形)、Pyramid(金字塔)、Mirror(镜像)、Plane(平面)、IntersectPath(路径相交)、Midpoint(中点)等GeoGebra命令与对象;④适合高中及以上学生及数学爱好者学习立体几何、微积分与优化方法。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → APoint(xAxis) → BPolygon(A, B, 4) → pol1, f, g, h, i, C, DPolygon(A, B, 4) → pol2, j, k, l, m, E, FPyramid(pol2, f / 2) → a_{3}, G, faceABG, faceBEG, faceEFG, faceAFG, arestaAG, arestaBG, arestaEG, arestaFGMirror(a_{3}, faceBEG) → a'Mirror(a_{3}, G) → a'_{1}Plane(G, A, B) → pIntersectPath(p, a'_{1}) → pol3, H, I, J, n, q, rPolygon(H, E, J) → t2, j_2, h_2, ePolygon(J, E, F) → t3, f_1, j_3, e_1Polygon(J, F, A) → t4, a_1, j_4, f_2Polygon(J, A, B) → t5, b, j_5, a_2Polygon(H, B, E) → t6, e_2, h_3, b_1Polygon(H, J, B) → t7, b_2, h_4, j_6Polygon(P_7, P_5, P_6) → t1, p_6, p_7, p_5Polygon(P_3, P_6, P_5, P_4) → q1, p_3, s, t, p_4Polygon(P_7, P_4, P_5) → t8, c, d, g_1Polygon(P_2, P_4, P_3) → t9, h_1, p_2, i_1Polygon(P_2, P_7, P_4) → t10, j_1, k_1, l_1Polygon(P_3, P_2, P_7) → t11, m_1, n_1, p_1Polygon(P_3, P_7, P_6) → t12, q_1, r_1, s_1Midpoint(R_4, R_1) → KPolygon(R_4, R_3, R_2, R_5) → q2, r_4, r_3, r_2, r_5Polygon(R_5, R_2, R_1) → t13, t_1, c_1, d_1Polygon(K, R_5, R_4) → t14, g_2, k_2, i_2Polygon(K, R_3, R_4) → t15, l_2, k_3, m_2Polygon(R_1, K, R_5) → t16, n_2, q_2, k_4Polygon(K, R_1, R_2) → t17, s_2, k_5, t_2Polygon(K, R_3, R_2) → t18, c_2, k_6, d_2Midpoint(S_5, S_2) → LPolygon(S_3, L, S_4) → t19, s_4, s_3, l_3Polygon(S_3, S_5, S_1) → t20, f_3, g_3, s_5Polygon(S_3, L, S_5) → t21, i_3, m_3, l_4Polygon(S_3, S_4, S_2, S_1) → q3, n_3, q_3, t_3, b_3Polygon(S_2, L, S_1) → t22, c_3, d_3, l_5Polygon(S_1, L, S_5) → t23, e_3, f_4, l_6Polygon(S_4, S_2, L) → t24, l_7, g_4, i_4
AI 绘图提示语参考
在三维空间中先给定一条水平与一条竖直基准轴并取它们的交点,然后以该交点为顶点构造两组等深的四边形底面(每组由同一对轴上的点与其衍生点组成)。将其中一组底面沿其中心高度拉起形成金字塔,并以该金字塔的特定棱与其对应面作为镜像平面,在另一面上得到镜像顶点及其投影线。再经过镜像顶点与镜像线,确定若干截面三角/四边形面片,并用多组多边形把这些面片组合成完整的分割立方体外观,最后在若干条边上取中点,将中点作为新顶点继续连接形成内部分割的面。
以上提示语为根据原始绘图命令整理而来,仅供参考。