JAMES GRIME: We love pi, of course.
Everyone loves pi.
But one of my favorite pi facts is--
and I think it's fun.
You only need 39 digits of pi to be able to measure the
circumference of the observable universe within the
width of one hydrogen atom.
And that's all you need.
Shall we write out the 39 digits?
So the 39 digits of pi.
It's 3 point--
now, 3 counts as one of the digits.
So it's now 38 decimal places.
Let's do the 38 decimal places--
1 4 1 6 5 9 7 9 3 2 7 4 2 0.
-He didn't memorize that, everyone.
There you go.
Show them what you did, just in case.
JAMES GRIME: Wolfram Alpha app, never leave
home without it.
-You're not a pi memorizer, James.
JAMES GRIME: No, I'm not.
And that's another thing altogether, people that
memorize this pi figure to a massive amount of digits.
But people who calculate it using computers, have
calculated it to, currently, 10 trillion digits of pi.
-Go on then.
Let's do it.
JAMES GRIME: OK.
So that would be all you need.
And that's overkill as it is.
Because that's all you need to measure the circumference of
the observable universe.
So the observable universe is the distance that light has
traveled since the big bang.
And if you say travelled in a big sphere, in a big bubble,
then if you measured the distance around it, we'd have
the circumference of the universe.
And we would need pi to work out that circumference.
And we could be as accurate as a hydrogen atom, if we used
just 39 digits of pi.
We don't need to use the whole thing, of course, which goes
on forever.
So in fact, and in practical day-to-day use in engineering
and real life, you would only need a handful of digits of pi
to have an accuracy that would be suitable for anything that
you need to do.
So Wolfram Alpha told me that the diameter of the universe
was 8.8 times 10 to the 26 meters.
So that's the diameter of the observable universe.
If you want to work out the circumference, then
we times it by pi.
So the circumference would be pi times the diameter.
What's the difference when I take away my truncated pi?
What I mean is, what if I took away my pi with 39 digits--
I've called it pi 39--
and did the same thing times my d?
So that's the real circumference of the universe,
take away my approximation.
What's the difference?
If I do that, what I got was actually around about 2.5
times 10 to the minus 12 meters.
So that's how accurate.
That's the difference between my approximation
and the real value.
That's how accurate it is.
And a hydrogen atom that Wolfram Alpha told me had a
diameter of about 2.5 times 10 to minus 11 meters.
So in fact, this is more accurate.
This is more accurate than a hydrogen atom.
So why do we calculate pi to 10 trillion digits?
These days, it's a way to test our computers, our
supercomputers and our algorithms.
It's a way to test them to see how good they are.
That's why computer scientists are interested in
this sort of thing.
Mathematicians have tried to do this for thousands of years
out of curiosity.
So it started with Archimedes.
He tried to get an accurate idea of pi about 250 BC.
He didn't have decimals in those days.
He had to use fractions.
But he tried to work it out.
Then in the 17th century, there was a Dutch
mathematician called-- now I'll probably Anglicize his
Dutch name.
And I apologize.
He was called Ludolph van Ceulen.
And his life's work was working out the digits of pi.
And by the end of his life, he had worked out
35 digits of pi.
And they're on his tombstone, which is kind of cool.
It's kind of neat.
We skip on to the 19th century.
There was a guy who had about 707 digits of pi.
This was the authoritative example of pi for over 100
years, until 1945.
And they found a mistake.
I know, shock.
They found a mistake.
And the last 180 digits were wrong.
Because somewhere along in his calculations, somewhere around
the 500th decimal point, he had made a mistake.
And from that point on, everything else was wrong.
What a disaster.
Fortunately, we were able to use computers by this point.
So in 1949, ENIAC, the American computer, was able to
calculate pi to 2000 digits.
So suddenly, it just exploded after that.
Once we've got computers, it just exploded.
We had more and more digits of pi.
And now, we've got 10 trillion digits of pi.