A segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .
Given :
given a segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .
You are asked to construct P such that :
PB / AP = AP / AB
This ratio is the reciprocal of the Golden Ratio.
( AP )^2 = PB * AB
( AP )^2 = PB * ( AP + BP )
( AP )^2 = PB ( AP ) + ( BP )^2
Divide by PB^2 on both sides
ф^2 = ф + 1
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