六点シュタイナー点构造
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①本范例演示六点シュタイナー点的构造方法与性质;②涉及核心数学概念包括旋转、台形、统计、多边形、坐标几何;③作图要点:使用Polygon、Circle、Segment、Distance、Rotate、Angle、Intersect等GeoGebra命令构造基础图形并计算交点;④适合高中及以上数学学习者,用于理解特殊点构造与几何变换。
GeoGebra 命令及参数
Polygon(C, B, 3) → poly1, f, g, h, FCircle(B, C, F) → cPolygon(F, A, 3) → poly2, i, j, k, GCircle(G, F, A) → dPolygon(G, E, 3) → poly3, l, m, n, HCircle(G, E, H) → eSegment(H, D) → pDistance(A, B) → ABDistance(B, C) → BCDistance(C, D) → CDDistance(D, E) → DESegment(A, B) → j_1Segment(B, C) → k_1Segment(D, E) → m_1Segment(A, E) → i_1Rotate(B, (-(60°)), A) → B'Angle(B', A, B) → αRotate(A, (-(60°)), E) → A'Angle(A', E, A) → εRotate(B', (-(60°)), E) → B''Angle(B'', E, B') → ζSegment(D, L) → t_1Polygon(H, D, 3) → poly4, q_1, r_1, s_1, MCircle(H, D, M) → c_1Segment(L, M) → a_1Intersect(c_1, a_1, 2) → ISegment(H, I) → qIntersect(e, q, 2) → JSegment(G, J) → rIntersect(d, r, 2) → KSegment(F, K) → sIntersect(c, s) → N, OSegment(C, O) → tSegment(B, O) → aSegment(O, K) → bSegment(K, A) → f_1Segment(K, J) → g_1Segment(J, E) → h_1Segment(J, I) → b_1Segment(I, L) → d_1Segment(D, I) → e_1Distance(L, M) → vDistance(C, O) → CODistance(B, O) → BODistance(O, K) → OKDistance(A, K) → AKDistance(K, J) → KJDistance(E, J) → EJRotate(A', (-(60°)), D) → A''Angle(A'', D, A') → βRotate(B'', (-(60°)), D) → B'''Angle(B''', D, B'') → γRotate(E, (-(60°)), D) → E'Angle(E', D, E) → δSegment(M, B''') → l_1Segment(B''', A'') → n_1Segment(A'', E') → p_1Segment(E', D) → f_2Segment(G, B') → g_2Segment(B', A) → h_2Segment(H, B'') → i_2Segment(B'', A') → j_2Segment(A', E) → k_2
AI 绘图提示语参考
画一个包含六个点的Steiner点几何构造图。首先绘制三个点构成的三角形,然后以这些点为圆心画圆,再以圆与圆的交点为顶点构建新的三角形。接着,通过旋转和连接线段,形成多个相交的几何图形,最终确定Steiner点的位置。展示旋转、梯形、多边形和坐标几何的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。