## Archive for October, 2010

### Greek Math (OK, just Greek)

October 28, 2010

TwoPi and I just got back from a long-anticipated trip across the Atlantic.  And, except for the fact that camels are about fifty times taller than they look and really really scary to ride (unless you’re ten.  Then, apparently, they’re totally cool.) the trip was amazing.  Especially because we found mathy things, and who doesn’t like mathy things???

This, by the way, might be my favorite photo:

Two of the days we spent in Greece, and everything was in Greek.   Which is obvious, but it made it seem like there was math everywhere.  Even on Sprite bottles.

Plus a lot of the signs were posted in both Greek and Latin alphabets, so I could try to sound out the Greek and then see if I was right.  [I spent a similar amount of time reading signs in Montreal, once, and then checking myself on the English subtitles].

It was like all these years I’ve spent learning and teaching math symbols paid off in a completely unexpected way.  (Even though, ummm, joining a sorority might have had the same effect.  But I digress.)

Unfortunately, with only a couple days, we didn’t do anything that had any actual math content during this portion of the trip.  But I did find this sign, which made me really happy.  (I blacked out the Latin part so that you could sound it out.)

October 25, 2010

Actually, it’s been up for almost a month, but I’m just now getting around to telling anyone.  See it here, and as usual, it’s probably more interesting for our current students and alumni than others.  But also as usual, we have a few fun problems to ponder:

Problem 5.1.1: (2000 AIME I) Let $a, b$ be relatively prime positive integers and suppose that the coefficients of  $x^2$ and $x^3$ are equal in the expansion of $(ax+b)^{2000}$.  What is $a+b$?

Problem 5.1.2: An envelope contains 12 bills: 3 ones, 3 fives, 3 tens, and 3 twenties.  Two bills are drawn at random without replacement.  What is the probability that their sum is at least \$20?

Problem 5.1.3: (From a Martin Gardner collection) An absentminded teller switched the dollars and cents when cashing a check for Mr. Brown. After buying a 5-cent newspaper [this is an old problem], Mr. Brown found that he had exactly twice as much as his original check. What was the amount of the check?