Folding circles is about decompressing spherical information. 2-D information is folded into the creased lines and 3-D information is in the spatial configuring of the circle. This is not possible with the drawing of the circle. It is only possible when working with the circle disc in space, the only possible compressed form of spherical order. A paper circle can model everything that can be modeled by all polygons and polyhedra; it also models things that are not possible with any other shape or form.
I just finished posting an instructable for a FedEx Tyvek Wallet. Simple, compact, holds change, and it works. Free, takes 10mins, a few cuts, and 1 staple. Enjoy!