Have you heard the old adage that it’s impossible to fold a single piece of paper moret han 7 times.  Not so!

Britney Gallivan (of Pomona, California) worked out that the minimum length of paper to get n folds – all in the same direction – is:

where t = thickness of the paper.

She assumes that a paper can be defined as being successfuly folded if there is some distance where all the folded layers are parallel to each other (otherwise you just have a ball, not really a fold). This leaves some amount of paper that is consumed in the turning at the folds. In the limit, if the distance of paralell-ness approaches zero, you have the minimum length of paper required, in whch case it is all consumed in the folds. She calculats that length by modeling the paper as folding in a perfect semicircle, and the length of the semicircle for any fold is equal to , where k is the number of the layer of that fold from the center. For example, in the first fold the length of the fold is  – which is the length of a semi-circle of radius t. If you have two layers and you fold it the inner layer will be of length  and the second layer will be of length , and so on. Her formula is a way of adding up the number and lengths of all the folds.