How can folding a paper 42 times reach the moon?

In: Physics

When you fold a paper you double its thickness. If you do it 42 times you double it 42 times. That’s 2^42 which is over 4 trillion. The moon orbits Earth at about 400,000 kilometers or 4 trillion micrometers. So as long as the paper is thicker than a micrometer, it’ll theoretically reach the moon.

A piece of paper is notionally 0.004 inches thick. The moon is 238,000 miles away. That’s nearly four quadrillion sheets of paper stacked up to reach the moon. Surely just 42 folds isn’t that thick? But wait. Every time you fold a piece of paper, you double its thickness. So multiply two times two times two and so on forty-two times, or by exponent notation 2^42 . Turns out that really is a huge number, more than enough thicknesses to make it to the moon.

Another popular demonstration of the power of doubling: start with a penny. Double it every day. In a month you will be a millionaire. If you kept doubling it for 42 days you would own the whole world, I think, though I haven’t done the math. I leave it as an exercise for the student.

It’s because the thickness of the paper grows exponentially. Fold it once, and its thickness is 2. Fold it twice, and its thickness is 2^2, or 4, and at three times the thickness is 2^3, or 8. So if you fold it 42 times, the thickness is 2^42, which is 4,398,046,511,104.

It may take 42 folds to reach the moon, it is impossible however to fold a piece of paper more than 7 times

Is it the same if you cut it in half and stack it?

I thought it was the other way and they couldn’t do it..had been some time since I saw though..I do recall they ended up in an aircraft hangar due to the size of sheet they needed

think of folding it as an exponential equation. so look at it as every time you fold you double the previous height of the paper. its important to think theoretical here, cause in reality the strand that would reach the moon would be so thin it would be tough to see

Everytime you fold a paper it doubles in thickness.

Start with .1mm

Folds thickness

1 .2

2 .4

3 . 8

4 1.6

5 3.2

So you can see in 5 folds our paper has grown to 32x the thickness. Imagine 37 more folds.

In fact given that we start with 0.1mm our thickness follows a nice relation that is t = (2^x ) /10 where x is the number of folds.

For example X = 2, t = 0.4mm

So using 42 we get t = (2^42 ) / 10 mm = 439804651110.4 mm or

439804 km

The distance between the earth and moon is

384,400

So you can see on the 41st fold we would be at a thickness of ~200,000 km and with one more fold we would be past the moon.