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!
Math Tutors, Santa Fe, NM
MathChat 
Comments on: "FUN MATH PROBLEM — Circling the Square & Vice-Versa" (2)
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!
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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
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