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Hi. My name's Simon and I'm the National Numeracy Ambassador.
What's your favourite number? Everyone should
have a favourite number. Is it five? Is it three?
Is it seven? Is it 2,713? It's up to you.
My favourite number is a very special number.
It's a number you can't get from counting. It's very special.
So special in actual fact, it doesn't look like
a regular number. Here's my favour number.
It doesn't look like a number. In actual fact, it's a
special number called "pi". That's what this symbol
represents, and I love pi. So where does this
number come from, pi? Well I'll show you.
It actually comes from circles, and circles are really cool.
Now how can you understand the circle?
Well, it turns out pi is the secret to understanding
how circles work, and here's how it goes.
What you do is you draw a line across the middle of
a circle so that you cut it exactly in half.
Now that line is called the diameter. Now once
you've got the diameter, what you can do is you
can grab the circle part - and another word for
that name there is a circumference - and you can
stretch it out so it becomes a straight line. Then
you count how many times the diameter goes into
the circumference, and it happens to go once,
twice, three times and a bit, and that's what pi
is, three and a bit. But what is it exactly? Well
I can tell you it's somewhere between 3.1 and 3.2,
but to say what it is exactly, well for the moment
we just have to use this symbol pi. But it's
actually very useful okay? It's actually pretty
close to 3.14. So with this number, when you want
to measure the circumference or the outside of a
circle, all you need is the diameter - so here's
the circumference equals this number pi times the
diameter. Now this works for any circle. Let me give you
an example. There's a circle right here,
on top of my head. So this is roughly circular. So if
I get a ruler and try and measure the diameter of my
head and slide across, what I find is that it's 20cm. So now
to know the circumference of my head, all I need to do is to
times 20 x pi, which is roughly 3.14. So let's do that.
20 x 3.14 - now 20 is 2 x 10, so 2 x 3.14 is 6.28,
and 6.28 x 10 is 62.8. So without having to
measure the actual circumference of my head, all I
had to do was measure the diameter and with pi, I
know that the circumference is equal to 62.8. Now,
I actually said before this number - this number pi,
is not just 3.14. The reason why we use the
symbol is because it's actually longer than 3.14.
Here are the first 10 digits of pi. 3.1415926535.
But you know what? It's even bigger than that. Here's the
first 100 digits. 3.1415926535 8979323846 2643383279
5028841971 6939937510 5820974944 5923078164 0628620899
8628034825 3421170679. Now that's a pretty big number, but
still that's not all of pi. It actually goes all
the way to 10,000,000,000,050 digits as of October
the 22nd, 2011. Because they're always discovering
new digits every day. In actual fact, the total
number of digits of pi, how big that huge decimal
number is, is infinite. So how can you actually
measure the circumference of a circle if this
number, this weird number pi, never stops? How
are you supposed to actually multiply by that
number if it never ends? Well that's an
interesting question, because you know what? pi
is only for a perfect circle, but in our world
circles aren't perfect. They're nearly perfect,
but usually just circular. Let me give you an
example. Say you were asked to make a circle that
had a diameter of 30cm, and say this circle
was a pizza. So this pizza here is not
actually that circular. In actual fact, the less
circular a pizza is the more expensive it is.
I actually don't understand how that works, but
something I've just discovered. So what we see
here is that this is circular with a diameter of
30 centimetres, but in actual fact we can see
that, well the circle of this pizza can be
anywhere between 27 and 33 centimetres in
diameter. So there seems to be a bit of give
there. Now what does this mean? Well, this means if
we actually take the circumference of the pizza
and we stretch that out, and then if we took the
original diameter - even though it's not perfect -
if we count the number of times the diameter goes
into this circumference we'll get 1, 2, 3 spot on.
So pi - for pizzas - happens to be three, and what that means is
is allowing pi to be three is enough when making a
pizza. Even making a cake, if you want to put a ribbon around
a cake, you just take the diameter, times it by three.
It's roughly going to be enough, because you're not making a
perfect circle. But you know what? We actually
need more perfect circles in different scenarios.
When you're building like a truck or a plane or
something that requires very precise components, a
ball bearing needs to be very precise in circular dimensions.
So the diameter here for example, with this one here
- I've made it quite big - is 30mm, and it needs to spin
around. But see if it was the shape of a
pizza, I really wouldn't want to get in a plane with a
ball bearing shaped like that would you? So what we see is
that the precision of somewhere between 27mm and 33mm
in diameter in this case, is not enough. We have
to have a much more precise circle. So we need
this circle to be between 29.9 and 30.1, and what that means
is this circle here to spin freely - if we actually take
the circumference now and we get the diameter, we find that
the diameter of that circle is 30.0 and the circumference
is 94.5. So if we divide the diameter into the circumference
we'll find that it goes once, twice, three times .13.
Now that's not pi. Three - well it's almost pi,
but in actual fact that number doesn't belong to
pi. We've only got 3.1. So we've got an extra
digit of pi to give us perfect ball bearings, or
near perfect. So how many digits of pi would you
need to make the most perfect circle in the
universe? Well what we're talking about is size
and thinness, okay? So if we take it to the
logical extreme - well for example, even though
things are very thin and very, very precise (even the
edge of a ball bearing) perhaps that's perfect
but it's not, because even on a knife edge, if we
actually blew up the edge of a knife edge, you can
see here that's not perfect. In actual fact it
looks like a mountain range. So in actual fact,
things, even though they look perfect, they're
not. So how perfect can we get? Well let's take a circle
around the entire universe, which happens to be
880,000,000,000,000,000,000,000, 000 metres across,
and if we made it the thickness of an atom, which is
1 รท 240,000,000,000, how many digits of pi would we need?
We would need 39. 39 digits of pi would be required to make
the most precise and the largest circle possible.
But of course we need more digits of pi because 136 00:09:35,867 there could be bigger circles out there. We just don't know.