Maths: Fold a Paper 103 Times and You’ll Exceed the Thickness of the Universe

Folding paper in half over and over again seems pretty easy. Currently, the record is just 12 times. What did you think? Britney Gallivan is the current record holder.

This actually concerns the exponential growth of the thickness of a sheet of paper when it’s folded in half. Each time you fold a paper, its thickness doubles and it requires more and more energy to fold. Dr. Karl Kruszelnicki has done some awesome maths over at ABC Science Online with a standard A4 sheet of paper, measuring about 300 mm long and 0.05 mm thick:

“The first time you fold it in half, it becomes 150 mm long and 0.1 mm thick. The second fold takes it to 75 mm long and 0.2 mm thick. By the 8th fold (if you can get there), you have a blob of paper 1.25 mm long, but 12.8 mm thick. It’s now thicker than it is long, and, if you’re trying to bend it, seems to have the structural integrity of steel.”

If you have enough energy and a paper long enough, you can fold a 0.099 mm-thick paper 103 times to get its thickness to exceed the thickness of the known universe!

Here is some maths by Jesus Diaz at Gizmodo:

“Folding the paper in half a third time will get you about the thickness of a nail.
10 folds and the paper will be about the width of a hand.
23 folds will get you to one kilometer.
30 folds will get you to space. Your paper will be now 100km high.
Keep folding it. 42 folds will get you to the Moon.
Now fast forward to 81 folds and your paper will be 127,786 light-years, almost as thick as the Andromeda Galaxy.
And finally, at 103 folds, you will get outside of the observable Universe, which is estimated at 93 billion light-years in diameters.”

Via Gizmodo, ABC Science Online


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