A popular belief holds that it is impossible to fold a sheet of paper in half more than 7 times.
Suppose that you start with an standard A4 sheet of paper – about 300 mm long, and about 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.
In fact, if you had a sheet of paper, and folded it in half 50 times, how thick would it be? The answer is about 100 million kilometres, which is about two thirds of the distance between the Sun and the Earth.
In fact it is possible to fold paper 12 times you would need about 1.2 km of paper. A high school student called Britney Gallivan did it in 2002.
After some searching she found a roll of special toilet paper that would suit her needs – and that cost US $85. With her parents, she rolled out the jumbo toilet paper, marked the halfway point, and folded it the first time. It took a while, because it was a long way to the end of the paper. Then she folded the paper the second time, and then again and again.
After seven hours, she folded her paper for the 11th time into a skinny slab, about 80 cm wide and 40 cm high, and posed for photos. She then folded it another time to get that 12th fold. Read more here or here.