Pi with Pies (director's slice) - Numberphile

Key Takeaways

To celebrate the mathematical constant of pi, we're going to attempt the most accurate calculation ever of pi using pies. Now, before we do our pi based pi calculation, we'll have a quick crash course in circles and why pi is so important. Now, to do that, uh because we're in the UK, home of many famous circles, we've come to one of the oldest and greatest circles, which is of course this one. It's the uh football circle here at Knots County uh football club. Apparently, they are the world's oldest football league club. There's a giant sign that says that right behind me, which does mean for a while there, I guess they had no one else to play, but you know, who knows? Uh so this uh circle here, as you can see, there's two things going on with the circle. First of all, there's the diameter. So, it's this nice uh wonderful straight line here that goes right through the middle of the circle. And the great thing about a diameter is it's a nice straight line. So if I wanted to, I could get a measuring tape and I could measure from the start all the way across here to the finish and get a very precise measurement of the distance across the circle. Now around here we have the circumference. Now this is a lot harder to measure. As you can see, it's a curved line. So instead of having to measure it directly, we can use pi. Now pi is the ratio of the straight line diameter to the total distance all the way around the outside. And if we know that ratio, we can do one measurement for the diameter, multiply it by pi, and get the exact distance all the way around the outside. All right, enough messing around on a football pitch. Let's go get our pies out. All right, first thing we need is a circle. People find it notoriously hard to draw circles. How do you get around this problem? Uh actually we were talking to the guy who does the uh circle on the pitch for the football stadium here and he uh does it the same way I think most people do. Gets a bit of string, makes the middle bit of the string remain perfectly still in what will become the center of the circle and then use that to draw a nice equal distance line all the way around. In fact, I guess that's the best way to define a circle. It's the line of all the points the same distance away from a center point. The center point will be my pen and the outside will be the chalk. [Music] [Music] All right, let's do this. My goal is to not actually do any measurements other than using pi. So the entire thing is going to be pi based. We get the circumference in an exact number of pies give or take. We get the diameter and number of pies. Divide one by the other we get pi. Pi was historically rarely calculated this way because it's notoriously inaccurate to try and get I know we're idiots. Uh it's notoriously inaccurate to try and calculate pi uh by measuring a circle. [Music] To get any kind of accuracy on our final answer, we we have to be as precise as we can be. This is this is a mild problem cuz I want to go from from the very edge of the circle, but as you can see, I've positioned all the pies exactly on the line as if they're little mini tangents. So, I'm going to have to move these two out. And then I can start doing the diameter exactly on the circumference there. Like that. [Music] So that's 84 and 1/3 of 264 and 2/3 pies around. We know the diameter is 84 and a3 pi. To get pi, we just divide the circumference by the diameter. Okay. And if we actually work out what that is, equals that's really good. pi from pies we got 3.1 3834 which is approximately 3.14. Uh so using pies we've got pi to be 3.14. We I am a very happy man right now. I on anything between 3.1 and 3.2 I would have been happy but to get 3.14 I'm downright ecstatic. Uh so there you are. And that is officially the world's most accurate calculation of pi using pies. It wasn't really something we planned to make part of the video, but as a lot of you have asked, the pies we used were donated and were no longer fit for human consumption. So, we couldn't give them to charity like we did, for example, with all the baked beans that Hines donated us earlier. However, in the spirit of Pi Day, we did attempt to make some kind of gesture and we donated £314, of course, £314, to a local charity here in Nottingham that helps give food to people in times of crisis. Now, a lot of you have expressed a lot of interest in charity. And we'd really encourage you, if you're in a position to do so, to also make a donation. And we've put some links under the video. And because we're all number files here, why not make your donation a multiple of pi in some way? 15 16 17 18. This is length L. Okay. And that means that the distance here is 2 L. Okay.