pi = 3.14159… while 22/7 = 3.14285… so 22/7 is bigger. But here's a cute proof that 22/7 is bigger.

The integral that gives 22/7 – pi is surprisingly elegant, and it's clearly positive since you're integrating a positive function. pic.twitter.com/Dj2HJMYRJD

It was an nicely timed tweet for me because my son is beginning a long review of calculus ideas this year. Tonight I finally got around to sharing the idea with him.

We began by talking about some basic properties of the function:

Next we talked about how you could approach integrating the function and then used Mathematica to help with the polynomial division:

Finally, we went to the whiteboard to work through the integral and talk about the nice surprise:

I really like this integral. It is both a neat “fun fact” and a great example to share with kids learning calculus.