## Archive for April 29, 2011

### On the Road Again

The summer driving season is just around the corner, and a gallon of gas costs a dollar more than it did at this time last year. We can all take solace in the fact that Exxon isn’t feeling any ill effects.

Hopefully the following driving-related math jokes will make you feel a little less depressed.

Which American highway is related to the length of the vector (1, 8, 1)?

Route (root) 66.

Perhaps the next one hits a little too close to home.

A large group of math majors were headed to a party, but they only had one car. Consequently, one person served as the driver and shuttled folks to the party in groups. When the last of them arrived, they realized they didn’t really feel like interacting with any of the other party-goers. So, they repeated the process of returning home one group at a time, in their only car.

In short, they commute but don’t associate.

How is the group described above like the averaging function *x* AVG *y* = ½(*x* + *y*)? The averaging function is commutative:

*x* AVG *y* = *y* AVG *x*

However, it is not associative:

(*x* AVG* y*) AVG *z* ≠ *x* AVG (*y* AVG *z*)