20 1 1 year, teachers and students of St. Mark's Middle School in Texas, USA, folded a piece of toilet paper with a length of 13,000 feet (nearly 4 kilometers) in half13 times. In order to complete the experiment, they put the toilet paper in the corridor of MIT more than 200 meters and folded it collectively for more than 4 hours. After folding 13 times, the toilet paper reached 8 192 layers.

According to the thickness and width of the paper, after a certain number of folds, the thickness of the paper will exceed the width. After that, you can't continue to fold, and you will reach the limit.

Every time it is folded in half, the thickness of the paper will double, so a piece of paper with a thickness of t is folded n times, and the thickness is 2nt. At the same time, every two folds will halve the width. So after N folds, the width will be reduced from the original W to (1/2) (n/2) W. When the total thickness of the paper is equal to its width, it can't be folded any more.

Extended data

Theoretical origami:

Fold it with a piece of paper with a thickness of 0.1mm. Folding 1 time is two layers of paper, folding twice is 2 2 = 4 layers of paper, folding once is 2 3 = 8 layers of paper ... folding 42 times is 2 42 = 439804651165438.

The distance between the moon and the earth is 389,802 kilometers, so theoretically a piece of paper can be folded 42 times to reach the moon.

Baidu encyclopedia-origami mathematics