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M is the golden section of line AB, am > BM
∵ m is the golden section of line AB, and am > BM,
∴AM²=AB*BM,
∴AM²+AB*AM=AB*BM+AB*AM
That is am (am + AB) = AB (BM + AM)
AM(AM+AB)=AB²
∴(AM+AB)/AB=AB/AM
It is known that M is the golden section point of line segment AB, and am > BM. (1) write the proportion formula among line segments AB, am and BM; (2) if AB = 12cm, find the ratio of AM and BM
Golden section: the ratio of the long segment to the whole segment is equal to the ratio of the short segment to the long segment. Golden section: 0.618! Because am > BM, BM: am = am: ab = 0.618:1. Because AB is 12, am = 12x0.618 = 12 - (12x0.312). BM = 12x0.312 = 12 - (12x0.618)
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