Folding paper, again
I was looking at the earlier topic about folding paper, and I found something interesting.
I think 7 times is the max for any size paper
Just a guess
I've seen a large sheet of paper folded 11 times... so no.
we have to stop folding, when both our dimensions of the piece we hold are less than the twice the height of the folded thing - there won't be enough paper to wrap around the edge. So our width not only halves, but there's some more gone around the edge. Unfortunately, the simple model developed that way - ie, from X, Y, Z go to X/2 - Z, Y, 2Z, doesn't really preserve volume, so it seems quite unrealistic. Nevertheless, it's amusing to play with - if we only fold along one side, thus having 1D paper, maximum folds is something like 1/2 * log2 ( 3X/2Z +1 ), where X and Z are the original dimensions. So in the case of X = 0.1m, Z = 0.0001m, this comes to around 5... Then we try folding both ways, alternating, and we get 2/3 * log2 ( 7X/2Z +1 ), which arrives at the 7 mentioned. There might be some +/- 1, so if you're really strong, you might get 8 from the equation. First time in my experience where physical strength can give you a different solution of a maths problem.
Fog Creek Home