Is Steven Strogatz Writing Regents Exam Questions?
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!
4 Comments
Ben · August 23, 2015 at 10:52 am
It also reminds me of the treatment of area in AoPS pre algebra. I’m not sure which came first.
MrHonner · August 23, 2015 at 1:17 pm
It’s a well-known argument. Neither Strogatz nor AoPS would claim to be the originator.
Henri Picciotto · August 24, 2015 at 9:14 am
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/
Dan Asimov · August 28, 2015 at 2:08 pm
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.