## Kiss those Math Headaches GOODBYE!

### FUN MATH PROBLEM — Circling the Square & Vice-Versa

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) 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!

### Problem of the Week – 10/18/2010

[Note:  I really am not getting a check from the New Mexico Tourism Department for this post, though I wouldn’t mind if they sent me one!]

Katja and Anthony are on a sightseeing trip in the western United States. Beginning where they land in Santa Fe, NM, they drive 80 miles east to see the historic wild west town of Las Vegas, NM. Then they travel 50 miles north to visit the Kiowa National Grasslands . Next they drive 140 miles west to visit Chaco Canyon National Historical Park. Finally they journey 130 miles south to visit El Malpais National Monument. When they reach El Malpais, how many miles are they from their starting point in Santa Fe?

Please explain how you found your answer, and send answers either as comments to this post, or as emails w/ subject POTW, sent to josh@SingingTurtle.com    I will not post your comments unless and until I determine that it is correct. And then, only on the day when I send out the answer on my blog.

Kivas in Chaco Canyon, New Mexico