Folding paper to the Moon

Take a sheet of paper, as big as you can find, and fold it in half. Again. And again. How many times can you go? Estu has heard a sheet can't be folded more than 7 times; Roxie wonders about thinner paper, a newspaper or a tissue. Try it and see.

Now suppose you could fold it as often as you liked. How thick would it be after 46 folds? Make a guess before you read on.

Say the sheet is 0.001 cm thick. Each fold doubles it:

Still almost nothing.

10 folds: 1.024 cm, just over a centimetre. 16 folds: 65.536 cm. 17 folds: about 131 cm, a little more than 4 feet. (The book writes ≈ for 'approximately equal to'.) Around 13 folds it's as thick as your hand, and around 19 as tall as a giraffe.

Now it runs away. After 26 folds the paper is about 670 m thick. The Burj Khalifa in Dubai, the tallest building in the world, is 830 m. One more fold and the paper is taller.

After 30 folds it is about 10.7 km: the height planes fly at, and nearly the 11 km depth of the Mariana Trench, the deepest point found in the oceans.

After 46 folds the thickness is more than 7,00,000 km. That's far enough to reach the Moon, from a sheet you could put in your pocket.

This is the power of multiplicative growth, also called exponential growth. And it works from anywhere in the table, not just the start: any 3 more folds multiply the thickness by 8 (2 × 2 × 2), and any 10 more folds multiply it by 1024. From fold 0 to 10, 10 to 20, 20 to 30 or 30 to 40, the thickness grows 1024 times each time.