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Putnam 1995 B2

Source:

July 1, 2014
Putnamconicsellipsetrigonometryintegrationcalculusfunction

Problem Statement

An ellipse, whose semi-axes have length aa and bb, rolls without slipping on the curve y=csin⁡(xa)y=c\sin{\left(\frac{x}{a}\right)}. How are a,b,ca,b,c related, given that the ellipse completes one revolution when it traverses one period of the curve?
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