Folding Regular Polygons and how it leads to a Theorem about Numbers

In our paper we showed how to fold a regular $7$-gon - and much else besides!  We showed which convex polygons could be folded by a period-$2$ folding procedure these turned out to be those polygons whose number of sides,  $s$, had the form $$s=\frac{2^{m+n}-1}{2^n-1} $$