Can I reach the moon with a bit of paper?

Question

If I was to fold my (particularly big) sheet of paper in half, then it doubles it's height. If I fold it in half again, it is now four times it's original height. How many times must I fold it to make it reach the moon?

Answer 1

22 folds is higher than the Empire State Building
27 folds is higher than Mount Everest
42 folds will take you beyond the Moon
51 folds will take you further than the Sun
53 folds will go beyond Jupiter
56 folds will stretch beyond Pluto
69 folds will more than reach the nearest star
70 folds will overshoot the nearest extra-solar planet

Assuming ordinary everyday 70 gsm office photocopying paper, 500 sheets (one ream) of which is 2 inches thick.

This is not an exercise in paper-folding but in using your imagination and appreciating how rapidly doubling up can get you to any named target.

The physical difficulty of folding a piece of paper is irrelevant, If this creates a mental block, think of it as tearing or guillotining the paper and placing the two piles on top of one another.

No actual going to the moon or making a paper ladder is involved. It is a conceptual problem.

DIFFICULT TO BELIEVE BUT TRUE!

Most people do not believe these answers as they are counter-intuitive, so I will talk you through it in easy stages. The point to grasp is that every ten folds means just over a thousand times increase in the height of the resulting pile of paper.

As I suggest above, a ream of ordinary 70 gsm photocopy paper is 500 sheets and about 2 inches thick,

So let us say that after 10 folds of our theoretically infinitely large (i.e. as large as we need it to be) piece of paper we have 1,024 thicknesses (2^10) and that that is 4 inches thick (a third of a foot).

After 20 folds we have 2^20 thicknesses = 4096 inches = 341 feet 4 inches.

The Empire State Building is 1,250 feet tall, so after 22 folds of the paper it has grown taller than the height of a 102-floors-tall skyscraper,

There are 5280 feet in a mile,

After 30 folds we have 2^30 thicknesses = 349,184 feet 4 inches = 116,395 yards = 66.13 miles. i.e. it was over a mile high after 24 folds and more than 2 miles high after 25 folds

Mount Everest is only 5 miles high so the pile of paper was taller than Mount Everest after 27 folds.

The moon is 238,000 miles away on average (let us not worry about apogee and perigee).

After 40 folds we have 2^40 thicknesses = 1,024 x 66.13 miles = 67,720 miles i.e. more than a quarter of the way to the moon.

So clearly 42 folds more than suffices to take us to the moon. How about the Sun?

The Sun is on average 93,000,000 miles away (let us not worry about perihelion and aphelion)

After 50 folds we have 2^50 thicknesses = 1,024 x 67,720 miles = 69,345,477 miles

So after 50 folds, we would then be most of the way to the sun. 51 folds more than suffices to get there. So how about Jupiter?

There are on average 486,587,517 miles to Jupiter. So another couple of folds should do the trick. 53 folds = 8 x 69,345,477 miles = 554,762,813 miles i.e. 53 folds more than suffices to get to Jupiter, And 56 is ample for the short hop to Pluto.

And the nearest star? (Proxima Centauri.)

1 light year = 5.879 ×10^12 miles
4.2 light years = 24.69 ×10^12 miles

After 60 folds we have 2^60 thicknesses = 1,024 x 69,345,477 miles = 71,009,769,448 miles

After 70 folds we have 2^70 thicknesses = 1,024 x 71,009,769,448 miles = 72,714,002,890,752 miles (72 x 10^12 miles)

So clearly 69 folds gets us to Proxima Centauri and half way back again! 70 would take us to Sirius (8.6 light years away) and half way back again. Or, more interestingly, it would easily take us to Epsilon Eridani b, the nearest known extra-solar planet (10.5 light years away),

I will leave you to work out how many folds you would need to get to the nearest galaxy! :-)

Answer 2

You can't fold a piece of paper more than 7 times no matter how big or small it is (or is it 9) and no chance of reaching the moon unless it's your own moon your on about!!

Answer 3

Depends on the thickness of your paper.
Let's say it is 0.1 mm thick (which is 10^(-3) m).

For every fold you multiply with 2 - so n folds is multiply with 2^n.

As the distance earth-moon is about 700.000 km (= 7*10^5 m), you need to find the first number n, such that 10^(-3) * 2^n is bigger than 7*10^5, in other words:
2^n > 7*10^8
To find that n, you take the 2-log of 7*10^8 (take your calculator), giving you: 30.

Answer: 30 times.

You can check this, by calculating that 0.1 mm times 2^29 and 2^30.

(Note: to calculate the 2-log, you can calculate the 10-log ("log") and divide it by the 10-log of 2).

Answer 4

This brings to mind a peculiar phenomenon
that I once read.No piece of paper can be folded more than 6 times regardless.

Answer 5

You can't reach the moon because it is theoretically impossible. You can't fold a piece enough no matter how big it is to reach the moon.

Answer 6

It won't be possible. You couldn't fold it enough times even if the paper was big enough in the first place

Answer 7

What? Huh? And it's 42 times, with a 0.1 mm sheet of paper.

There's enough DNA inside you to go several light years.

4 billion base pairs times 100 trillion cells equals alot.

Answer 8

It would be physically impossible. The folds would get too big, and you wouldn't be able to fold it anymore.

Answer 9

Raygun your life must be filled with excitement. Paper folding, is that the latest therapy. I hear ink blobs can be fun.

Answer 10

if you unfolded a piece of paper once call a cheque with 1 billion pounds written on it (of course you would need the money to back this cheque in your bank) to lets say... the russian space industry. i'm sure they will land you on the moon and throw in a free cup of tea aswell.