And I think we should stop using pi and start using tau.

MATT PARKER: And I'm Matt Parker.

And I think Steve said something ridiculous.

I think pi is fantastic.

It's wonderful.

And even if this was an equal race, we would've been using

both of them.

Or even if tau had been established first, I'm still

pretty pro-pi.

STEVE MOULD: Wow, that's quite a claim.

MATT PARKER: Yes, there's [INAUDIBLE].

STEVE MOULD: So let's talk about this.

So pi is the circle constant.

It's the constant that defines a circle.

And the argument is--

MATT PARKER: We're agreed so far.

[RINGING]

STEVE MOULD: Let's think of a reasonable definition of what

a circle is.

The classic is all points equidistant

from a single point.

That distance is the radius.

And if you're ever doing maths using circles, you talk about

the radius.

All your equations about circles talk about the radius.

Unless you're an engineer, you use diameter.

But as a mathematician, you use the radius.

The circle constant should surely be defined in terms of

the radius.

[RINGING]

STEVE MOULD: But it isn't pi--

is the circumference divided by the

diameter, which is crazy.

So the circle constant should be the circumference divided

by the radius.

When you do that, you get 2 times pi.

[RINGING]

STEVE MOULD: And so we're not saying let's redefine pi and

call it 6.28.

But instead--

MATT PARKER: Wow.

STEVE MOULD: --we're saying--

[RINGING]

STEVE MOULD: Shut up.

Instead, we're saying that's going to be confusing, so

let's invent a new constant.

And we'll call it tau.

MATT PARKER: To be honest, one of the points was quite nice,

which is that if you're an engineer, you use pi.

And in fact, historically, we've used pi because when you

measure a circle, the only direct measurement you can

make is of the diameter.

[RINGING]

MATT PARKER: And so that's why historically we've done that.

And to this day in precision engineering we do that.

And yes, you can do some very nice maths with

the radius in a circle.

But the only thing you can directly

measure is the diameter.

So that's why we've used pi.

People say, oh, but we have to put 2 pi into lots of

equations, and then blah, blah, blah.

It's always 2 pi.

Why don't we just use tau instead?

There are as many fantastic equations out there which use

just the single pi.

And there's no reason to bring in 2 pi.

[RINGING]

MATT PARKER: And so I see Steve is holding a pen.

But I have brought my own.

STEVE MOULD: [CHUCKLING].

MATT PARKER: So everyone's classic is the e to the i pi

job, where e to the i pi plus 1 equals 0.

[RINGING]

MATT PARKER: And that is using a solitary pi

out the front there.

And if you want to go wild, things like

the area of a torus--

this is a nice one-- that equals pi squared--

[RINGING]

MATT PARKER: --outside the major radius squared minus the

minor radius squared.

So I'm still doing things in terms of

radiuses or radii or whatever.

But the pi squared-- that's lovely.

What-- you want 4?

I mean, how you are going to--

STEVE MOULD: Yeah, I want--

MATT PARKER: Tau squared on 4?

STEVE MOULD: What-- yeah, absolutely-- tau squared on 4.

And I'll explain why.

And this is important.

OK, let's just say that Matt has cherry-picked a couple of

nice equations there.

Two things I'd say-- let's look at, for example, the area

of a circle.

So we're looking at the area pi r squared.

MATT PARKER: That's just lovely.

Look at that.

[RINGING]

STEVE MOULD: Yeah, OK-- but here's the problem.

Here's the problem.

If we reframe that in tau, that would

be tau by 2 r squared.

And you think, OK, that's less beautiful.

But this tells us something important.

[RINGING]

STEVE MOULD: This tells us something.

This is information that you're obscuring by using pi.

Because you can derive the area--

MATT PARKER: By simplifying your--

[RINGING]

STEVE MOULD: No, listen.

You can derive the area of a circle by integrating.

[RINGING]

STEVE MOULD: So you say, OK, here's our full circle.

Let's look at the area of this little strip where the width

of it is delta r.

And this is r going up.

And so this is full r or whatever.

So you integrate.

The area of this is pi r dr.

MATT PARKER: Tau.

STEVE MOULD: No, but--

sorry, tau, yeah, actually.

[RINGING]

MATT PARKER: See, pi's just easier to use.

STEVE MOULD: Shut up.

And then you end up with 1/2 tau r squared.

[RINGING]

STEVE MOULD: And so that 1/2 tells you something.

It tells you you've done an integration to get there.

[RINGING]

STEVE MOULD: And an equation like this obscures it.

Similarly, with this, if you had tau squared over 4, that

would tell you something.

This equation here-- let's just reframe that.

e to the i tau minus 1 equals 0.

[RINGING]

STEVE MOULD: And the great thing is that is a full

circle, right?

If you want to go through half a circle, then it's e to the i

tau over 2.

If you want to go a quarter of a circle, it's e to

the i tau by 4.

[RINGING]

STEVE MOULD: The pi is confusing.

It's especially confusing for children when

they're learning as well.

A full circle is 2 pi?

OK, so that half a circle is pi.

A quarter of a circle is pi by 2.

So there's always this factor of 2--

[RINGING]

STEVE MOULD: --that you've got to keep in your mind when

you're doing calculations.

And actually, if you're a seasoned mathematician, you're

probably always thinking in terms of 2 pi, anyway.

[RINGING]

STEVE MOULD: And so let's just stop thinking in terms of 2 pi

and start thinking in terms of tau.

MATT PARKER: This is the hypocrisies of tau.

You want halves here.

You don't want halves over there.

[RINGING]

STEVE MOULD: I want halves here because the half tells

you something.

[RINGING]

MATT PARKER: This works out just as nicely.

Because if you want to integrate, and you've got your

2 pi r dr, then you get a wonderful

thing you can simplify.

Because you end up with this-- r squared--

STEVE MOULD: Yeah, so in this particular case--

MATT PARKER: --and you end up with a--

[RINGING]

STEVE MOULD: So in this particular case--

MATT PARKER: --2 pi and the 1/2 simplifies.

[RINGING]

STEVE MOULD: Yeah, yeah.

MATT PARKER: Pi r-- that's just--

there's nowhere else in maths where you say, you know what?

Let's not simplify it.

Let's leave it in a more complicated form because it--

STEVE MOULD: No, but in fact, this is the one case where you

think, actually it's useful to have a 2 there because we can

cancel later.

Most other cases you don't get to do that cancel because

you're not dividing by 2 later on.

[RINGING]

STEVE MOULD: In most cases, you end up with an equation

that's got 2 pi in it.

BRADY HARAN: A lot of smart people, who I know you

respect-- and I know you respect the guy

sitting next to you--

STEVE MOULD: [CHUCKLING].

BRADY HARAN: --make the case--

STEVE MOULD: That's correct.

MATT PARKER: Professionally.

BRADY HARAN: A lot of smart people make the case for tau.

MATT PARKER: Yeah.

BRADY HARAN: How do you explain their reasoning?

How do you--

I mean, you don't think Steve's an idiot.

But he has this feeling about tau that you disagree with.

What's different about his thinking to yours?

MATT PARKER: You know what?

A lot of people do have very good arguments for tau.

And a lot of people have very good arguments for pi.

And there is a wonderful thing--

I don't know.

I think people like the fact that it's different and that

they're going, oh, whoa, whoa, whoa-- everyone

else has got it wrong.

We can change this.

And tau is better.

And oh, people try and do maths and they

think pi's all that.

No, they're wrong.

But I don't think there's any great advantage other than it

can be a bit more exclusive to say, oh, we're all over tau--

[RINGING]

MATT PARKER: --when I think pi works just

as well in all cases.

It's got the--

I know--

historical--

the fact that it's got a bit of heritage doesn't mean we

should keep it around necessarily.

But it's worked for a very long time.

And it's there for very good reasons.

[RINGING]

MATT PARKER: Nothing people have thrown at me in terms of

tau, saying it's better--

you gain as much as you lose from--

[RINGING]

MATT PARKER: --switching from-- both of them have their

disadvantages and their advantages.

[RINGING]

MATT PARKER: I don't think there's enough for an entire

overhaul of the subject because people think, oh,

what, this particular equation looks a bit nicer.

Oh, but we've lost the fact that you get negative numbers

in Euler's identity.

And even your arguments with circles--

this is my clincher.

This is why I genuinely think pi is nicer.

If you've got tau, right?

If you do tau radians--

you do an entire revolution--

you end up right back where you started.

Tau gets you nowhere, right?

[RINGING]

STEVE MOULD: [CHUCKLING].

MATT PARKER: With pi, if you do pi radians, you actually

get somewhere.

And I think if you want a unit to measure things, the unit

shouldn't be the whole thing.

[RINGING]

STEVE MOULD: What?

[LAUGHING].

MATT PARKER: A unit should be a section of it.

And so it's more nuanced.

And for that reason--

STEVE MOULD: Oh, then in that case--

MATT PARKER: I think pi is better.

STEVE MOULD: --divide it by-- you know--360.