棱柱几何演示
几何画板及绘图内容加载中,请稍等……
①本范例演示棱柱的几何构造与性质;②涉及核心概念包括立体几何、多边形、向量、三维空间中的点线面关系;③作图要点运用了PointIn, Polygon, OrthogonalLine, Point, OrthogonalPlane, Vector, Translate, Segment, Plane, Intersect等GeoGebra命令与对象;④适合高中及以上学生及数学爱好者用于立体几何学习和探索。
GeoGebra 命令及参数
PointIn(a) → APointIn(a) → BPointIn(a) → CPointIn(a) → DPointIn(a) → EPointIn(a) → FPointIn(a) → GPolygon(A, B, C, D, E, F, G) → poly1, a_1, b, c, d, e, f, gOrthogonalLine(H, a) → hPoint(h) → IPolygon(J, K, N, M) → poly2, j, k, n, mOrthogonalPlane(I, h) → iVector(H, I) → uTranslate(poly2, u) → poly2'Translate(poly1, u) → poly1'OrthogonalLine(A, a) → lOrthogonalLine(B, a) → pOrthogonalLine(C, a) → qOrthogonalLine(D, a) → rOrthogonalLine(E, a) → sOrthogonalLine(F, a) → tOrthogonalLine(G, a) → b_1OrthogonalLine(K, a) → c_1OrthogonalLine(N, a) → d_1OrthogonalLine(M, a) → e_1OrthogonalLine(J, a) → f_1Segment(I, H) → g_1Point(g_1) → OPlane(O, a) → oIntersect(l, i) → PIntersect(b_1, i) → QIntersect(p, i) → RIntersect(q, i) → SIntersect(r, i) → TIntersect(t, i) → UIntersect(s, i) → VIntersect(c_1, i) → WIntersect(f_1, i) → ZIntersect(d_1, i) → A_1Intersect(e_1, i) → B_1Intersect(d_1, o) → C_1Intersect(e_1, o) → D_1Intersect(c_1, o) → E_1Intersect(f_1, o) → F_1Intersect(s, o) → G_1Intersect(l, o) → H_1Intersect(p, o) → I_1Intersect(q, o) → J_1Intersect(r, o) → K_1Intersect(t, o) → L_1Intersect(b_1, o) → M_1Polygon(I_1, J_1, K_1, G_1, L_1, M_1, H_1) → poly3, i_1, j_1, k_1, g_2, l_1, m_1, h_1Polygon(F_1, E_1, C_1, D_1) → poly4, f_2, e_2, c_2, d_2Segment(W, K) → n_1Segment(A_1, N) → p_1Segment(B_1, M) → q_1Segment(Z, J) → r_1Segment(R, B) → s_1Segment(S, C) → t_1Segment(T, D) → a_2Segment(V, E) → b_2Segment(P, A) → h_2Segment(Q, G) → i_2Segment(U, F) → j_2
AI 绘图提示语参考
绘制一个棱柱,首先在平面上创建七个点A、B、C、D、E、F、G,然后用这七个点构成一个底面多边形。接着在底面多边形所在的平面上创建一条线h,并在线上创建一个点I,用点I和线h创建一个垂直于底面的平面i。将多边形沿向量u平移,得到另一个平行的多边形。然后创建从每个点到线h的垂线,以及从每个点到平面i的垂线,最后找到这些垂线的交点,形成棱柱的侧面。
以上提示语为根据原始绘图命令整理而来,仅供参考。