extreme and mean ratio
中外比较 comparison between China and abroad
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几何学有两大珍宝,其一是毕达哥拉斯定理,另一个是分一线段为中外比。
Geometry has two great treasures, one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio .
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分已知线段为两部分,使其中一部分是全线段与另一部分的比例中项的数学问题。作法很简单,设已知线段为AB,作BD⊥AB使BD=AB/2,连接AD,以D为心,BD为半径作弧交AD于E,再以A为心,AE为半径作弧交AB于C,则C就是所求的分点。AC=(√5-1)/2AB 记 G=(√5-1)/2=0.6180339…
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