How Folding Paper Can Get You to the Moon

Can folding a piece of paper 45 times get you to the moon? By seeing what happens when folding just one piece of paper, we see the unbelievable potential of exponential growth. This lesson will leave you wanting to grab a piece of paper to see how many times you can fold it!

Lesson by Adrian Paenza, animation by TED-Ed.

How many times can you
fold a piece of paper?

Assume that one had a piece
of paper that was very fine,

like the kind they typically
use to print the Bible.

In reality, it seems like a piece of silk.

To qualify these ideas,

let's say you have a paper

that's one-thousandth
of a centimeter in thickness.

That is 10 to the power
of minus three centimeters,

which equals .001 centimeters.

Let's also assume that you have
a big piece of paper,

like a page out of the newspaper.

Now we begin to fold it in half.

How many times do you think
it could be folded like that?

And another question:

If you could fold the paper over and over,
as many times as you wish,

say 30 times,

what would you imagine
the thickness of the paper would be then?

Before you move on,

I encourage you to actually think
about a possible answer to this question.

OK.

After we have folded the paper once,

it is now two thousandths
of a centimeter in thickness.

If we fold it in half once again,

the paper will become
four thousandths of a centimeter.

With every fold we make,
the paper doubles in thickness.

And if we continue to fold
it again and again,

always in half, we would confront
the following situation

after 10 folds.

Two to the power of 10,

meaning that you multiply
two by itself 10 times,

is one thousand and
24 thousandths of a centimeter,

which is a little bit over one centimeter.

Assume we continue folding
the paper in half.

What will happen then?

If we fold it 17 times,

we'll get a thickness
of two to the power of 17,

which is 131 centimeters,

and that equals just over four feet.

If we were able to fold it 25 times,

then we would get two to the power of 25,

which is 33,554 centimeters,

just over 1,100 feet.

That would make it almost
as tall as the Empire State Building.

It's worthwhile to stop here
and reflect for a moment.

Folding a paper in half, even a paper
as fine as that of the Bible,

25 times would give us a paper
almost a quarter of a mile.

What do we learn?

This type of growth
is called exponential growth,

and as you see, just by folding a paper

we can go very far, but very fast too.

Summarizing, if we fold a paper 25 times,

the thickness is almost
a quarter of a mile.

30 times, the thickness reaches 6.5 miles,

which is about the average
height that planes fly.

40 times, the thickness
is nearly 7,000 miles,

or the average GPS satellite's orbit.

48 times, the thickness
is way over one million miles.

Now, if you think that the distance
between the Earth and the Moon

is less than 250,000 miles,

then starting with a piece of Bible paper

and folding it 45 times,
we get to the Moon.

And if we double it one more time,

we get back to Earth.