A high-school student has defied the received wisdom that it is impossible to fold a paper more than eight times by folding one twelve times:
For extra credit in a math class Britney was given the challenge to fold anything in half 12 times. After extensive experimentation, she folded a sheet of gold foil 12 times, breaking the record. This was using alternate directions of folding. But, the challenge was then redefined to fold a piece of paper. She studied the problem and was the first person to realize the basic cause for the limits. She then derived the folding limit equation for any given dimension. Limiting equations were derived for the case of folding in alternate directions and for the case of folding in a single direction using a long strip of paper. The merits of both folding approaches are discussed, but for high numbers of folds, single direction folding requires less paper.
(Thanks, Alex!)
Update: Ari sez, "I really enjoyed the story about the student who figured out how to fold a piece of paper more than eight times — but it's too bad that the proof is only available by mail order! I've posted an independent derivation of her equation here."
