A fun and challenging geometry problem from twitter

Saw this problem posted on Twitter earlier today (via a John Golden retweet) –

Does square or circle have greater perimeter? A surprisingly hard prob for HS: http://t.co/vwLIs26pcC #mathchat #math pic.twitter.com/Vpjop8yU7G

— Greg Schwanbeck (@GregSchwanbeck) March 16, 2015

Not the easiest problem in the world, but since my son and I are studying a new section about circles in our Introduction to Geometry book, I thought I’d give it a try.

If you are interested in watching the thoughts of a kid as he struggles through a tough problem, today is your lucky day 🙂

First, an introduction to the problem and maybe 5 minutes of his initial thoughts. He’s walking towards the solution the whole way – slowly to be sure, but steadily.

 

So, I just turned the camera on and off to break the last video at approximately 5 minutes. In this second video he continues working towards the solution. Eventually he sees that the circle is the circumcircle of the triangle he’s drawn. That plus the area formula:

Area = A * B * C / 4R, where A, B, and C are the side lengths and R is the radius of the circumscribed circle gets him to the finish line.

Finding the approximate value of (5/2) * confused him a little at the end, but he eventually was able to conclude that this expression was less than 8.

 

So, a fun exercise for me watching my son work through this problem, and a pretty challenging problem for him. Made for a good night. Thanks, as always, Twitter!