Dividing line segment in given ratio with an instrument.
Source:
February 12, 2011
rationumber theoryrelatively primegeometry proposedgeometry
Problem Statement
Pete has an instrument which can locate the midpoint of a line segment, and also the point which divides the line segment into two segments whose lengths are in a ratio of , where is any positive integer. Pete claims that with this instrument, he can locate the point which divides a line segment into two segments whose lengths are at any given rational ratio. Is Pete right?