# Everyday geometry: hat size

I don’t wear hats very often. Occasionally I wear a baseball hat. Twice a year I wear the hat that accompanies my academic regalia.

If you need to buy a hat, the first thing you need to know is your hat size. If you Google “hat size” then you can find many charts that match head circumference with hat size. For example, if your head measures $22\frac{1}{4}''$, then the charts tell you that you should get a hat of size $7 \frac{1}{8}$.

But what, if anything, does a hat size measure?

According to wikipedia, you can compute your hat size by dividing the circumference of your head by $\pi$. (Note: $22.25/\pi=7.08\ldots\approx 7.125=7\frac{1}{8}$.)

Hmmmm…. wait a minute. That is a familiar calculation.

Yes, your hat size is the diameter of the circle that has the same circumference as your head. In other words, if you took a hat of hat size H, and you forced it into a circular shape, then H would be the diameter of this circle. Wow, who knew?!?!

(Thanks to my mom for pointing out this $\pi$ calculation.)

[Photo by 2-dog-farm, published under CC license]