How do we keep finding extra digits of pi?

07 February 2017

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Pi

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Question

Hannah - How do we keep finding extra digits of pi?

Answer

Chris Smith put this question to mathmetician Timothy Revell...

Tim - That’s a really good question. So what is pi, let’s start with that? You grab your favourite circle and we call the distance around the outside the circumference. And we call the width, making sure you go through the middle the diameter. If you divide the circumference by the diameter, then you end up with pi, which is just this number 3.14159ish.

But the thing is, I don’t think we take the time to realise just how crazy pi really is. If you take a circle that is the size of a pin prick, or that you take a circle that is the size of the moon and you divide its circumference by its diameter, you get the same number.

This is like some sort of universal conspiracy. This is why mathematicians study this so much. This is why we want to know pi so precisely. Because it’s a conspiracy, how does this happen?

Chris - Why should we be surprised though Tim that that’s the case because a circle, if you make it bigger, then all those things increase in proportion? That’s exactly what pi is so why is that a surprise?

Tim - Well, for me it’s a surprise. Why should there be a particular relation between the way a circle looks round the outside versus going straight through the middle? These seem to me to be rather different things but, obviously, the right answer is they’re not different things because pi is what links them.

Over the years there’s been lots of attempts to try and work our pi to the most number of digits, but the truth is pi is actually a rather tricky beast. You’re never going to work out all the digits of pi because it’s what’s called an irrational number. What this means is that if you write it out after the decimal point you are never going to stop. There are an infinite number of digits after that decimal point.

Over the years there’s been lots of different ways to try and calculate pi beyond just measuring it - various formulas and things, and the current world record is 22 trillion digits which was calculated by a guy called Peter Trueb in 2016, in November.

Chris - Why?

Tim - That’s a good question why? At the moment it just seems to be to show off how good is your algorithm and your computer.

Chris - I was going to say how good is your computer because that’s a lot of memory you’re going to need to handle all of that?

Time - And a lot of time that it takes to actually compute these things. You need a big computer and you need to leave it for a long period of time. In terms of how useful is that? It’s not very useful. NASA, they only use 15 digits of pi, and if you wanted to measure the whole universe down to a precision of a single atom you would only need 40 digits of pi. So to get to 22 trillion is a lot.

Chris - So when we have this question from Hannah which is: how do we keep finding extra digits? Because it’s an irrational number, if you just keep cranking the handle, you will keep churning out numbers as long as you keep turning the handle. It will never end.

Tim - Yeah. We know ways of getting closer and closer to this idea of what is pi? This sort of number but writing down those digits will take an awfully long time so it’s about finding the time and the energy and the people to want to do it.  So we will be able to do that for the rest of humanity.

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