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Frostbite Theater

Pi from a Toothpick!

Learn how you can estimate the value of pi using a toothpick!

Announcer: Frostbite Theater presents... Cold Cuts! No baloney!

Joanna and Steve: Just science!

Joanna: Hi! I'm Joanna!

Steve: And I'm Steve!

Joanna: Today, we're going to show you how to estimate the value of pi... using a toothpick!

Steve: We learned this method on a video we found on Numberphile's channel. If you're unfamiliar with Numberphile, they have a lot of cool math videos.

You'll find a link to the video that we're borrowing from down in the description.

Joanna: The procedure is simple.

On a piece of paper, draw parallel lines two toothpick lengths apart.

Fill the paper with these lines.

Steve: Then, take a toothpick and randomly throw it on the paper.

Do this again.

And again.

And again, and again, and again.

Record how many times you threw the toothpick, and how many times the toothpick crossed one of the lines.

Joanna: Divide the number of throws by the number of times a line was crossed. This number will get closer to the value of pi the more throws you do.

Steve: So, why is pi showing up? I mean, we usually think of pi in terms of circles, right? But, the lines are straight. The toothpick is straight.

So, where's pi coming from?

Joanna: It turns out that the odds that the toothpick will cross a line is related to the angle of the toothpick with the line. It's more likely to cross if the toothpick is perpendicular to the line, and it's less likely to cross if the toothpick is parallel with the line.

But, the angle matters.

It's this angular dependency that causes pi to show up.

If you're interested in the full derivation, see the video linked in the description below.

Thanks for watching! I hope you'll join us again soon for another experiment!

Steve: Kinda cold out here...

Joanna: It's February.

Steve: I know... I know it's February. But, why are we shooting outside in February?

Joanna: I don't know!

Steve: I guess because Pi Day's in March.

Joanna: True.

Steve: Guaah...

Hey! So, yeah...

We want this video to be exactly three minutes and fourteen seconds. So, we need to add some buffer.

Joanna: I know!

Here, meet Mr. Mittens. That's his name because he has little white mittens.

He's such a good boy.

He's a Maine Coon and he just turned one year old. And he's a good boy. But also not interested in being in the video.

Bye, Mr. Mittens!

So, how much time do we have left?

Steve: That was about it.

Joanna: Oh! Cool!

Steve: I think...

If you're interested in why throwing a toothpick on a lined sheet of paper produces pi, please see the Numberphlie video referenced in this video.

Citation and linking information

For questions about this page, please contact Steve Gagnon.