When I saw this question on the 2015 Common Core Geometry Regents exam, I couldn’t help but think of mathematician and author Steven Strogatz.

Strogatz wrote a popular series on math in the New York Times, and in his piece “*Take it to the Limit*“, he shares a beautiful and intuitive derivation of the formula for the area of a circle. That technique involves slicing the circle up into sectors and re-arranging them into a shape that approximates a rectangle.

I’m certain his piece inspired this question (which I like), just as it inspired me when I was cutting up my homemade pizza!

Maybe we can add *test prep* to the long list of reasons to be reading Steve’s work!

It also reminds me of the treatment of area in AoPS pre algebra. I’m not sure which came first.

It’s a well-known argument. Neither Strogatz nor AoPS would claim to be the originator.

Indeed, it is a standard argument, which I might have first seen in Chakerian, Stein, and Crbill’s _Geometry: A Guided Inguiry_.

In fact, never having seen Strogatz’s post, I put a GeoGebra animation of this argument on my Web site, in honor of π day 2015: http://www.mathedpage.org/constructions/pi/

This argument is essentially what was used by Archimedes with 96-gons inscribed and circumscribed about a circle to get the approximation 22/7 < π < 223/71.