I've been very fortunate — I've attended every NCTM Annual Meeting since 1995. I usually arrive exhausted, having put in long hours in preparation during the weeeks leading up to the meeting. While I'm at the meeting, I keep late hours, so I leave even more exhausted.

But the preparation is worth it. I get exhilirated giving presentations and interacting with enthusiastic teachers.

And the late hours are worth it, too. Those hours are often spent in conversation with some of the greatest math educators in the country, sharing problems and ideas.

And the math! Oh, the math! It just oozes! I always look at the world through mathematical eyes… but while interacting with math folks for a week, my eyes seem even more wide open.

I arrived yesterday to Philadelphia, and I had a great math experience. Just outside the convention center are fire hydrants that have interesting bolts on them:

Originally, fire hydrant bolts were square or hexagonal, but any standard wrench could be used to open those. Nowadays, most fire hydrants have pentagonal bolts, in an effort to thwart attempts by common citizens to open the hydrants. But even pentagonal bolts are not foolproof. A diligent delinquent, using three boards arranged correctly, could force open a pentagonal bolt. So many of the fire hydrants in Philadelphia, like the one above, now have a bolt in the shape of a Reuleaux triangle. A Reuleaux triangle is constructed by forming an arc on each side of an equilateral triangle. Like a circle, a Reuleaux triangle has constant diameter. (For that reason, this shape is occasionally used as a manhole cover.) The shape is very effective as a fire hydrant bolt — try to put some straight boards around a Reuleaux triangle, and they'll just slip off. Even a diligent delinquent can't open the hydrant without a specially made wrench that fits the shape exactly.

I'm very excited for the meeting… I'm hoping that finding a Reuleaux triangle is just the first of many exciting math experiences I have this week!