I'm here today calculating pi with darts, with the help of Veritasium.

So we're calculating pi using this, which is a target composed of a square and a circle inside the square that has a diameter the same length as one side of the square.

So the idea of calculating pi like this is that the number of darts that land in the circle divided by the number of darts that land in the entire square should be proportional to the area of the circle divided by the area of the square.

If the length of one side of the square is 1, that means the area of the square is 1.

That means the radius of the circle is 1/2.

So the area of the circle is pi r squared, so it's pi over 4.

Therefore, if we multiply the ratio of the number of darts that land inside the circle divided by the number of darts total by 4, we should get pi.

DEREK MULLER: So how'd we do?

We didn't do great.

[music playing] DEREK MULLER: We divide circles by the total.

DIANNA COWERN: 103.

Total is 103.

DEREK MULLER: Yeah.

88 by 103, and then we multiply by 4.

Yes.

Ooh.

DEREK MULLER: Is it bad?

No, it's kind of funny.

3.41.

[laughter] That is higher than pi.

That suggests that we're getting more of our random samples inside the circle than we should.

DEREK MULLER: I don't know.

Randomness is a tough thing to see, right?

DIANNA COWERN: I know.

DEREK MULLER: Does that look random to me?

DIANNA COWERN: What doesn't look random is this whole section right here.

DEREK MULLER: I do think these are centrally distributed, rather than evenly spread.

So we gotta try something else.

DEREK MULLER: Mm-hm.

We could try a bigger one and just try to be more random.

How do you try to be more random?

We can throw a lot of darts in a short amount of time.

The sun is setting.

We really need to make this happen.

And if you'll let me, I'll do my multi-dart spray.

You can do your multi-dart spray.

You can do eight darts at once.

Eight darts at once.

DEREK MULLER: 3, 2, 1.

DIANNA COWERN: Oh!

[laughter] Four?

[inaudible].

DEREK MULLER: Oh, I really don't know about this.

Why are you laughing so hard?

DEREK MULLER: Because of how ridiculous it is.

You don't even know how ridiculous this is.

Like that?

DIANNA COWERN: Like this.

How am I doing?

Like that?

DIANNA COWERN: Yeah.

Well, how do you hold one dart?

I don't know, but this is crazy.

Oh, yeah.

DIANNA COWERN: Look at that.

DEREK MULLER: Boo-yah!

DIANNA COWERN: Why does anyone buy a dartboard?

When you could do this?

DIANNA COWERN: When you could make one.

DEREK MULLER: Dollar Store.

Circles 2-- Here is the moment of truth.

We have 146 in the circle over a total number of 179.

DIANNA COWERN: Mm-hm.

Then we're gonna multiple by 4, and we should see pi.

3.26!

Oh, it's slightly better than our estimates all day.

I feel like there are better ways to measure pi than throwing darts at a board.

Don't do this method, kids.

I'm warning you.

This is not a good idea.

[music playing] [heavy sigh] So we're going to find the accurate value of pi using darts today?

I am so hopeful.

New day, new game plan.

I've drawn this pattern for Dianna.

But she doesn't know what it looks like.

That is to avoid her trying to aim it at anything.

So we're going to put this on the fence with it facing away from her, so she won't really know what she's trying to hit.

I'm going to try to aim as randomly as I can all over this board.

DEREK MULLER: All right.

Not bad.

Looks pretty random to me.

DEREK MULLER: Well done.

[music playing] Why don't we rotate the fence 90 degrees this way?

There's some sort of systematic error in the way that we are throwing.

OK. DEREK MULLER: This should fix it, right?

One.

DIANNA COWERN: Oh, ho.

I think this is actually easier to do.

DEREK MULLER: So you want to take the board off the fence and see how we did?

We're taking it off.

So my guess is it's right here.

Ready?

DEREK MULLER: Hang on.

OK, go for it.

Oh, ho, ho, ho!

I like this.

I like the grid.

DEREK MULLER: I figured this went with a strategy that we decided yesterday, where we wanted to have up and downs be able to hit, like-- DIANNA COWERN: Yeah.

DEREK MULLER: Plus we've got a center one that is probably going to be very dense.

And then we've got radially outer ones, which I thought would be less dense.

80.

DIANNA COWERN: Uh-huh.

DEREK MULLER: 85.

DIANNA COWERN: Mm-hm.

After trying so many different methods, it's now after sunset on the second day of trying to calculate pi with darts.

DEREK MULLER: So what is our estimate of pi?

DIANNA COWERN: 3.139.

[laughter] 3.139.

DEREK MULLER: (SHOUTING) Yeah!

That is awesome.

[laughter] Oh my gosh.

Check that out.

DEREK MULLER: How different is that from actual pi?

What percentage error is that?

Divide by pi.

[laughter] 0.07%.

Like 0.1%, if you round up, error.

DIANNA COWERN: Which is pretty good, if you're calculating pi with darts.

DEREK MULLER: Right?

I'm pretty happy with this.

I am really happy with this.

We spent two days of our lives doing this.

Happy Pi Day to you.

Happy Pi Day to you.

[music playing]