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Rolling regular n-gons on catenary “roads”

Here's an interesting exploration, illustration courtesy of Mathematica:

There's a nice animated illustration at Mathematica.

A particularly interesting case of a roulette is a regular n-gon rolling on a "road" composed of a sequence of truncated catenaries, as illustrated above. This motion is smooth in the sense that the geometric centroid follows a straight line, although in the case of the rolling equilateral triangle, a physical model would be impossible to construct because the vertices of the triangles would get "stuck" in the ruts (Wagon 2000).

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  1. Hi
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    Nadia Lopez & Jose Eduardo Parraguez

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