旋转与向量几何构造
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①本范例演示了利用旋转和向量构造多边形及其内切圆的几何过程;②涉及的核心数学概念包括旋转、向量运算、多边形构造、内切圆(或称内圆);③作图要点——从下方『构造摘要』提炼用到了Polygon(多边形)、Midpoint(中点)、Segment(线段)、Intersect(交点)、Circle(圆)、Point(点)等GeoGebra命令/对象;④适合高中数学教学或几何作图爱好者学习,有助于理解空间几何变换与图形性质。
GeoGebra 命令及参数
Polygon(E, F, G, H) → poly2, e, f, g, hPolygon(I, K, L, M_2) → poly3, ı, k, l, mMidpoint(A, D) → N_2Midpoint(B, C) → OMidpoint(D, C) → PMidpoint(A, B) → QMidpoint(E, F) → RMidpoint(G, H) → SMidpoint(E, H) → TMidpoint(F, G) → UMidpoint(K, L) → VMidpoint(I, M_2) → WMidpoint(M_2, L) → A_1Midpoint(I, K) → B_1Segment(N_2, O) → iSegment(Q, P) → jSegment(R, S) → nSegment(T, U) → pSegment(W, V) → qSegment(B_1, A_1) → rIntersect(i, j) → C_1Intersect(n, p) → D_1Intersect(q, r) → E_1Segment(K, L) → sSegment(C_1, D_1) → tSegment(E_1, D_1) → a_1Segment(E_1, C_1) → b_1Midpoint(C_1, D_1) → F_1Midpoint(C_1, E_1) → G_1Segment(D_1, G_1) → c_1Segment(F_1, E_1) → d_1Polygon(E_2, F_2, G_2, H_1) → poly2_1, e_1, f_1, g_1, h_1Midpoint(E_2, F_2) → R_1Midpoint(G_2, H_1) → S_1Midpoint(E_2, H_1) → T_1Midpoint(F_2, G_2) → U_1Segment(R_1, S_1) → n_1Segment(T_1, U_1) → p_1Intersect(n_1, p_1) → D_2Midpoint(C_1, E_1) → I_1Midpoint(D_2, D_1) → J_1Midpoint(D_1, E_1) → K_1Midpoint(C_1, D_2) → L_1Segment(I_1, J_1) → i_1Segment(L_1, K_1) → j_1Intersect(i_1, j_1) → MCircle(M, N) → k_1Point(k_1) → O_1Segment(O_1, A) → l_1Segment(O_1, D) → m_1Segment(O_1, B) → q_1Segment(O_1, C) → r_1Segment(O_1, I) → s_1Segment(O_1, M_2) → t_1Segment(O_1, K) → a_2Segment(O_1, L) → b_2Segment(O_1, H_1) → c_2Segment(O_1, E_2) → d_2Segment(O_1, F_2) → e_2Segment(O_1, G_2) → f_2Segment(O_1, H) → g_2Segment(O_1, E) → h_2Segment(O_1, F) → i_2Segment(O_1, G) → j_2Polygon(D, C, B, A) → poly1, d, c, b, a
AI 绘图提示语参考
画一个由多个多边形构成的图形,展示如何通过旋转和向量操作构建多边形及其内切圆。首先绘制几个多边形,然后找到各边的中点并连接,接着求出这些线段的交点,最后以这些交点为顶点构建新的多边形,并以内切圆展示其几何性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。