To achieve this: http://en.wikipedia.org/wiki/Square_wheel, what should $L$ be?
rolling wheel problem
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$\begingroup$
calculus
differential-geometry
plane-curves
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0If the road the square wheel is rolling on is made up of catenary pieces, then the center traces a straight line. On the other hand, how would a square wheel roll on a single catenary? – 2011-09-07
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0@J.M.: it rolls along the bottom of a single catenary. i.e. It starts from when the up-right corner of the wheel touches the catenary, rolls along it, and ends when the up-left corner touches the catenary. – 2011-09-07
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2In any event, have you seen [this](http://www.maa.org/pubs/sampMMA.pdf), [this](http://dx.doi.org/10.1119/1.17401), and [this](http://dx.doi.org/10.1119/1.17675)? – 2011-09-07
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2Now the question is less clear. $L$ is supposedly what? – 2011-09-07