风筝形与维度
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①本范例演示风筝形的几何构造及其维度特性;②涉及核心数学概念包括多边形、角度、几何变换(旋转、镜像)、中位线等;③构造过程中运用了Polygon(多边形)、Segment(线段)、CircleArc(圆弧)、Rotate(旋转)、LineBisector(角平分线)、Intersect(交点)、Mirror(镜像)、OrthogonalLine(垂线)等GeoGebra命令;④适合高中数学几何学习,用于理解多边形性质及变换应用。
GeoGebra 命令及参数
Polygon(A, C, D, B) → vierhoek1, a, c, d, bSegment(B, E) → fCircleArc(B, DD, D) → ePolygon(A, C, E, B) → vierhoek2, a_1, c_1, e_1, b_1Polygon(B, E, D) → driehoek1, d_1, b_2, e_2Rotate(B, (((s - 1) * 180))°, d_1) → B'Rotate(E, (((s - 1) * 180))°, d_1) → E'Rotate(D, (((s - 1) * 180))°, d_1) → D'Polygon(B', E', D') → driehoek1', d', b', e'Polygon(DD, E, B) → driehoek2, b_3, dd, e_3LineBisector(DD, C) → gIntersect(g, a_1) → FIntersect(g, e_1) → GSegment(F, G) → hCircleArc(D, DD, C) → kPolygon(B, A, F, G) → vierhoek3, b_4, a_2, f_1, g_1Polygon(F, C, E, G) → vierhoek4, f_2, c_2, e_4, g_2Rotate(F, (((-(s - 3)) * 180))°, f_1) → F'Rotate(C, (((-(s - 3)) * 180))°, f_1) → C'Rotate(E, (((-(s - 3)) * 180))°, f_1) → E'_1Rotate(G, (((-(s - 3)) * 180))°, f_1) → G'Polygon(F', C', E'_1, G') → vierhoek4', f', c', e'_1, g'Mirror(E, f_1) → EEPolygon(DD, F, G, EE) → vierhoek5, dd_1, f_3, g_3, eeIntersect(b_3, h) → HPolygon(DD, H, G, B) → vierhoek6, dd_2, h_1, g_4, b_5Segment(DD, H) → iOrthogonalLine(DD, f_1) → jIntersect(j, f_1) → ISegment(DD, I) → lPolygon(B, DD, I, G) → vierhoek7, b_6, dd_3, i_1, g_5Intersect(b_6, dd_3) → JPolygon(J, A, F, I) → vierhoek8, j_1, a_3, f_4, i_2Rotate(J, (((s - 5) * 180))°, i_2) → J'Rotate(A, (((s - 5) * 180))°, i_2) → A'Rotate(F, (((s - 5) * 180))°, i_2) → F'_1Rotate(I, (((s - 5) * 180))°, i_2) → I'Polygon(J', A', F'_1, I') → vierhoek8', j', a', f'_1, i'Polygon(J, I, H) → driehoek3, h_2, j_2, i_3Polygon(DD, I, G, EE) → vierhoek9, dd_4, i_4, g_6, ee_1CircleArc(DD, A, EE) → pSegment(B, D) → mSegment(E, D) → nSegment(DD, C) → qIntersect(q, h) → LAngle(G, L, DD) → αIntersect(f_1, h_1) → MIntersect(i, f_1) → NSegment(N, O) → rSegment(F, C) → tSegment(E, C) → k_1Segment(A, DD) → l_1Segment(A, C) → m_1Segment(B, L) → n_1Segment(I, F) → p_1
AI 绘图提示语参考
绘制一个菱形风筝,包含四边形ABCD、四边形ABEF、三角形BDE、三角形BDE'、四边形BEGF、四边形BEGF'、四边形BDEG、四边形BDEG'、四边形BDEH、四边形BDEH'、四边形BDEI、四边形BDEI'、四边形BDEJ、四边形BDEJ'、四边形BDEK、四边形BDEK'。首先画出四边形ABCD,然后依次构造四边形ABEF、三角形BDE、四边形BEGF、四边形BEGF'、四边形BDEG、四边形BDEG'、四边形BDEH、四边形BDEH'、四边形BDEI、四边形BDEI'、四边形BDEJ、四边形BDEJ'、四边形BDEK、四边形BDEK'。
以上提示语为根据原始绘图命令整理而来,仅供参考。