The myth of paper folding

There is a myth that one sheet of paper can not be folded more than seven times so that the line of each subsequent fold was perpendicular to the line of the previous bend. However, this is not true.

There are no fundamental laws of physics that forbid folding a sheet of paper in this way for the eighth and subsequent times. However, this would require a lot of paper. The fact is that with each such folding of a sheet of paper, its thickness doubles. So if we take the initial thickness of a sheet of paper as 0.1 mm = 0.0001 meter (and this is perfectly realistic) then we can write the following formula for the thickness (H) of a folded sheet of paper after N folds:

H = 0.0001∙2N meters

Thus, for example, after 12 folds of this sheet we would get the height of the resulting paper stack equal to 41 centimeters (it is already clear that it is very difficult to bend a stack of paper 41 centimeters thick for the 13th time). But if we had managed to continue, after 15 folds the thickness of the pile would have been 3.28 meters, after 20 folds – 105 meters, and after 42 folds – 439,805 kilometers, which is more than the distance from the Earth to the Moon (which is approximately 384,400 kilometers). Thus, although no laws of physics forbid folding paper many times, it is clear that whoever wants to perform such an experiment will very quickly run out of paper and the technical ability to bend such thick stacks of paper without tearing it.

By the way, the famous TV show “Legends Breakers” had a similar experiment of repeatedly folding paper. In this experiment, a sheet of paper the size of a soccer field was used, and it was folded with heavy construction and road construction equipment. Each subsequent bend was made perpendicular to the previous one. According to the results of the experiment was able to fold the paper 11 times. Thus, the legend of the maximum possible seven folds of a sheet of paper was destroyed, not only theoretically, but also in practice.

But if you move away from the condition that the paper should be folded making every next bend perpendicular to the previous one, the world record for folding paper counts 12 folds. It was set by a group of American schoolchildren (see photo below). During the experiment was used a very long roll of very thin and flexible foil. In this case, by the way, the danger of tearing the paper is greatly reduced, but the problem with the rapidly increasing thickness of the pile, and, therefore, the availability of the proper amount of material and technical ability to bend such thick objects, remains.

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