Calculating Pi with Real Pies - Numberphile

[MUSIC PLAYING] My goal is to not actually do any measurements other than using pie. So the entire thing is going to pie based. We get the circumference in the exact number of pies-- give or take-- we get the diameter in number of pies. Divide one by the other, we get pi. [MUSIC PLAYING] Pi was historically rarely calculated this way, because it's notoriously inaccurate to try and get-- I know, we're idiots-- it's notoriously inaccurate to try and calculate pi by measuring a circle. [MUSIC PLAYING] To get any kind of accuracy on our final answer we have to be as precise as we can be. [MUSIC PLAYING] This is a mild problem, because I want to go 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 PLAYING] So that's 84 and 1/3. 264 and 2/3 pies around, we have the diameter, is 84 and 1/3 pie. To get pi, we just divide the circumference by the diameter. OK, and if we actually work out what that is, it equals-- that's pretty good. Pi from pies, we got 3.13834, which is approximately 3.14. So using pies, we've got pi to be 3.14. I am a very happy man right now. With the diameter, and if I know that ratio, I can just measure the diameter. That's the easy bit to measure. The center point will be my pen, and the outside will be the chalk. So the pies, in theory, are a fairly consistent size. So they're all-- yeah they're about the same. OK. [MUSIC PLAYING]