Today I was sent the old adage about not being able to fold any piece of paper in half more than seven (7) times; to which I immediately responded with this article from the SD archives. However, I got to thinking that there must be some kind of formula to figure out how many times you can fold a piece of paper in half given its three(3) dimentions. Any ideas?
I always heard it as 9.
The thickness doubles each time a sheet is folded in half, so powers of two works as a formula.
2 4 8 16 32 64 128 256 512 1024 2048 4096…
For a sheet of paper 1/1000" thick folding it 9 times would result in a piece 512/1000, or half an inch, thick.
The other (x,y) dimensions of the sheet, if folding to retain squareness, decreases by a factor of two for every two folds. Sooner or later the sheets x,y dimensions will be less than the thickness of the wad of paper-at which point it becomes impossible to fold without tearing. In practice, tearing probably happens well before this point.