From time to time I will post interesting math problems.

Feel free to try these problems. Share them with friends and colleagues. Use them however you see fit!

I will post the answer to the problems two days later, after people have had time to respond.

To post your response, simply send an email to me @ info@SingingTurtle.com

and make your Subject: **Fun Problem**.

The problem: Which provides the fuller fit? Putting a circular peg in a square hole, or putting a square peg in a circular hole? To get credit, show all work, and justify your answer by expressing each “fit” as a percent.

A few term-clarifications, to help you do this correctly:

a) By “fit,” I mean the ratio of the smaller shape to the larger shape, expressed as a percent. For

example, if a ratio is 4 to 5, that would represent a “fit” of 80 percent.

b) For the circular peg in the square hole, assume that the diameter of the circle equals the side of the

square. For the square peg in a circular hole, assume that the diameter of the circle equals the diagonal of the square.

c) By “fuller fit,” I mean the larger of the two ratios.

Have fun!

The circle in the square is the better fit at ~78%, opposed to the square in the circle’s ~63%.

I tried working this problem with x as the circle’s radius, which gave a fit ratio of 2/(pi*x) for the square in circle and a fit ratio of pi/4 for the circle in square.

A comparison between numbers and variables felt a little “apples and oranges”, so I re-did the problem with radius 1, which led to the 78% and 63% fit ratios.

Algebra is more my thing than Geometry, so I know there’s the real possibility for mitake in my calculations! Please, don’t hold back! I’d love to know the “right” way to do this!

Hi ZeroSum,

Good work! Yes, your answer is correct. I would just round each off to the hundredths place and get 64% and 79%. But your work is correct. You can see my method of getting the answer on my 4/14 answer post.

Thanks for participating in the Fun Math Problem!

— Josh