Folding

As a kid I remember learning that paper couldn't be folded more than 7 times without using a tool to compress the paper. This fact figured in an Encyclopedia Brown story, where one of E. Brown's friends had a collection of toilet paper, and the local bully claimed to have folded the paper 8 times to fit it somewhere, but E. Brown demonstrated that it was impossible.

Naturally I tried myself to fold a sheet of paper and was foiled around 6 or 7 folds, because the wad was too small to bend. Intuitively though, I thought that there must be a way, if only the paper were bigger.

Then I saw on TV (some science show) where the host ridiculed his assistant who claimed to have folded a newspaper sheet 8 times. The last fold was pretty bad but given how small the wad was, it wasn't surprising. I was young so I considered the question solved, because, if a bigger sheet would help, wouldn't they try it on TV?

Today I was thinking about the problem again, because I bought some furniture and it came in a box, which I was folding down to recycle. Folding cardboard is hard but it got me thinking that even with its high thickness I can still fold it, so why not a thick wad of folded paper? I wondered if I could dust off my physics knowledge to determine how big a sheet of paper would need to be for you to fold it. The hard part of folding is that a single sheet folded 5 times is 32 sheets thick... but if you had a sheet that was much longer it wouldn't matter if it was thicker. I could work out the formula by calculating the force needed... ugh. Why not Google it?

Not surprisingly, someone has already solved this problem. Britney Gallivan has devised the equation determining how long a sheet must be if you want to keep folding it in half, depending on how many folds you want and how thick the sheet is. She devised two equations, one for folding in alternate directions (length-wise, width-wise) and one for folding always in the same direction. She proved her theory by folding a sheet of toilet paper 12 times. The sheet was 4000 feet long and it took her 7 hours to complete, but it's a clear win for Britney and all those who doubted the folding limit. I guess they'll need to reprint the Encyclopedia Brown story....