Q1.
How many times can you fold it over and over?
Answer
With ordinary paper, about 6 or 7 times — then it stops folding, whatever your strength.
The reason is that folding does two things at once, and they work against each other:
- the thickness doubles each time — after k folds it is 2k times the original;
- the length is halved each time — after k folds it is 1/2k of the original.
After 7 folds: thickness × 27 = 128 times
length ÷ 27 = 1/128 of the sheet
length ÷ 27 = 1/128 of the sheet
So a sheet that started 20 cm long and 0.01 cm thick is now about 0.16 cm long and 1.28 cm thick — a stubby block, taller than it is wide. There is no material left to bend round the fold.
Why it happens: Estu's "7 times" is not a rule about paper, it is a rule about doubling. Every fold multiplies the thickness by 2, and repeated multiplication grows far faster than our hands can keep up with. Roxie's idea is right in principle — thinner paper starts smaller, so it takes a few more folds to reach the same block. In 2002 a student folded a very long, very thin roll of paper 12 times.
Try This: Fold a newspaper sheet and a tissue and count. Then measure the folded stack with a ruler and check that the thickness really is doubling.