It'stops being possible to fold something when it is higher than it is wide, simply because there is not enough material to close the fold. Ignoring the amount that is lost on the corners, you can think of the increase in height per decrease in width as a doubling in height for every fold, resulting in a pile that is now half as wide but twice as thick. Of course there are corners to include too, but this will do for now. If you know what the amount of paper is that you would need to start with to leave you with a m metre wide pile after n folds, and you know what the height of the pile after n-folds is, then you can calculate whether or not it will be possible to fold it again (is it'still wide enough to be able to close the fold one more time, or is there no longer enough material)

In the formula, L is the minimum length of material that is needed to enable that number of folds with that thickness of material... any shorter and it will not have enough material to close the fold - it will not be wide enough to close over the height of the pile. The formula looks the way it does because folding the material involves "loosing" some in the corners (which are assumed circular). Actually I am surprised that this paper-folding thing was touted as an impossibility, because it truely is dependent on the material used, though the fact you can not keep folding indefinitely is obviously true.

Hope that helps

In 2001, Gallivan determined equations that characterize the limit on the number times we can fold a sheet of paper of a given size. For the case of folding in a single direction of a paper with thickness t, we can estimate the initial minimal length L of a paper that is required in order to achieve n folds: L = <(PI*t)/6>*(2^n+4) * (2^n-1). We may study the behavior of (2n+4) × (2n-1). Starting with n=0, we have 0, 1, 4, 14, 50, 186, 714, 2794, 11050, 43946, 175274, 700074…, This means that for the 11th folding of the paper in half, 700,074 times as much material has been lost to folding, at the curved edges along the fold, as was lost on the first fold.