## Archive for March, 2010

### March Math-ness

A problem for the NCAA tournament:

There are 65 teams in the tournament. How many games are necessary to determine a champion?

In high school, this problem was presented to us by our psychology teacher. Nathan Horstman (voted “most likely to succeed”) and I (voted “most studious” and “most likely to become a millionaire”) worked together on this problem for five minutes before solving it. Had we been thinking, we would have solved it in five seconds… like the pot-heads in the back of the room had. I have no idea what point our teacher was trying to make by giving us that problem, but if the lesson was “you can’t judge a book by its cover,” then mission accomplished.

### Rational Thoughts

I saw the word *irrational* a lot on Pi Day, and my friend Patrick Flynn recently invited me to join the Global Anti-Rationalization Foundation (GARF) on Facebook. Both of these things reminded me of the following story, which comes from a four-decade veteran of the classroom, John Benson of Evanston Township High School.

A student of John’s solved a problem and obtained a fractional answer that contained the square root of pi in the denominator. But then the student did a curious thing. He started to multiply the numerator and denominator by the square root of pi.

“What are you doing?” John asked.

“Rationalizing the denominator,” the student responded.

(If you don’t understand why that’s funny, you may be too young.)

Thanks to calculators, the process of rationalizing denominators is no longer necessary. One could make the argument that it wasn’t really necessary before the days of calculators, either, but there was at least some reason for doing it back then — converting a fractional result to a decimal was difficult if the denominator was irrational. If the denominator could be converted to a rational number, then the division would be less arduous.

When I worked for MathCounts, I was fortunate to spend two memorable years with John Benson. He served as a member of the MathCounts Question Writing Committee. John wrote phenomenal problems, had keen mathematical insight, and could put you on the path to a solution for every problem. But most importantly, John was inspirational. I once attended a presentation by John, and I loved the quote he displayed at the end of his talk: “You can’t get burnt out unless you were once on fire.” When he talked about his classroom, you realized what’s possible in math education. His philosophy has kept both he and his students inspired for nearly 40 years, and the following statement from John, which he claims to repeat often at parent-teacher conferences, will help you understand why:

I promise that I will try hard to make sure that something happens every day in class that cannot be replicated anywhere else. If a student is not in class, that student will never be able to recapture that teachable moment. They will have missed something.

### Jokes for Pi Day

Today is Pi Day (3/14) as well as Albert Einstein’s birthday. Numerologists surely believe that’s no coincidence.

Here are a couple of jokes for today:

- I’m like pi… irrational, but well‑rounded!
- What is the ratio of the circumference of a jack‑o‑lantern to its diameter? Pumpkin pi.

### What Makes Math Funny

The following joke comes from Harold Reiter, a math professor at the University of North Carolina–Charlotte:

Last night, I was working on a difficult problem, and getting nowhere with it. So I went to bed. When I woke up this morning, it was dark; but then it dawned on me!

Despite public perception, Harold contends that most mathematicians have a keenly developed sense of humor. I love Harold’s description for why math things are funny:

For mathematicians, technical words have a specific meaning that are sometimes quite different from the colloquial meaning, and often that distinction can be emphasized in a humorous way. Take the word

dawn. Two meanings come to mind, a “brainstorm” and “the start of a new day.” So, it makes sense to try to get both meanings into a one-liner:When I woke up , it was dark; but then it dawned on me!