分数比较 by Eva Lai
几何画板及绘图内容加载中,请稍等……
①本范例演示如何通过可视化方法比较不同分数的大小关系;②涉及的核心数学概念包括分数比较、最小公倍数(LCM)、向量与几何变换;③作图要点——从下方『构造摘要』提炼用到了 LCM, Segment, OrthogonalLine, Vector, Translate, Polygon, Sequence 等GeoGebra命令与对象;④适合初中及以上学生学习分数比较方法,也可用于数学教学演示。
GeoGebra 命令及参数
LCM(d1, d2) → cdSegment(A, B) → cOrthogonalLine(A, c) → dVector(A, C) → uTranslate(B, u) → B'Vector(A, D) → vTranslate(B, v) → B'_1Translate(C, v) → C'Translate(B', v) → B''Segment(A, C) → eSegment(C, B') → fSegment(B', B) → gSegment(D, C') → jSegment(C', B'') → kSegment(B'', B'_1) → lSegment(B'_1, D) → mPolygon(A, C, (x(C) + ((a * w)) / d1, y(C)), (x(A) + ((a * w)) / d1, y(A))) → poly1, q, r, f_1, g_1Polygon(D, C', (x(C') + (b * w / d2), y(C')), (x(D) + (b * w / d2), y(D))) → poly2, d_1, c', s, tVector(A, (x(A) + (a * w / d1), y(A))) → arrow1Vector(D, (x(D) + (b * w / d2), y(D))) → arrow2Sequence(Segment[(x(A) + (w * i / cd), y(C)), (x(A) + (w * i / cd), y(A))], i, 1, cd - 1, 1) → cdlist1Sequence(Segment[(x(A) + (w * i / d1), y(C)), (x(A) + (w * i / d1), y(A))], i, 1, d1 - 1, 1) → list1Sequence(Segment[(x(A) + (w * i / d2), y(C')), (x(A) + (w * i / d2), y(D))], i, 1, d2 - 1, 1) → list2Sequence(Segment[(x(A) + (w * i / cd), y(C')), (x(A) + (w * i / cd), y(D))], i, 1, cd - 1, 1) → cdlist2Vector(H, I) → hSequence(Segment[(x(A) + (w * i / cd), y(H)), (x(A) + (w * i / cd), y(H + 0.5))], i, 0, cd, 1) → numlineSegment(arrowend2, (x(arrowend2), y(arrowend2) - 0.5)) → arrowl2Segment(arrowend1, (x(arrowend1), y(arrowend1) - 0.5)) → arrowl1Vector(H, K) → i
AI 绘图提示语参考
画两个分数的比较图形,使用分母的最小公倍数作为共同分母,通过线段、垂直线、向量和平移构造等分点,绘制两个分数的等分线段,用多边形表示分数区域,并添加箭头和数字线标注。
以上提示语为根据原始绘图命令整理而来,仅供参考。