## Posts tagged ‘infinity’

### Points of Intersection

In sixth grade, I overheard two teachers talking about a new school policy. We had just moved into an elementary school that was four stories tall, and it was decided that any time a class needed to move between floors via the staircases, students should always stay to the right — “just as your parents do when driving on a road,” we were told.

One teacher said to another, “Given our principal, I’m surprised it isn’t up on the right, down on the left!”

Nothing like a little administration-bashing to cleanse the soul, eh?

I was reminded of this over the weekend, when my sons and I participated in Bike DC, a family-friendly event in which thousands of riders were given the privilege of riding along the streets of Washington, DC, on a beautiful Sunday morning, during which the streets were closed to traffic. It was quite a thrill for Alex and Eli to ride in front of the President’s house. We turned around before the designated turn-around spot, but I was rather proud that my five-year-old sons were able to log 7.5 miles.

Unfortunately, there was a problem with the course design. See map below.

We followed a simple out-and-back course along several major roads. As shown above, we went out via the blue line and returned via the green line. And just like driving, we spent the first several miles in the right lane. But as the blue line shows, we were asked to *switch* to the left side of the road at one point; then on the return trip, we were asked to *switch again* to the right side of the road. As indicated by the two red dots, this caused a problem — when you ask 10,000 bikers to cross each others’ paths, problems are bound to ensue. (You’ll note that two blue lines merge near the bottom of the map. Some bikers doing the full ride merged with those of us doing the family ride at this point.)

Today, I received an email from the ride organizers with the following explanation:

This was by far the biggest Bike DC yet, and some of the routing that had been adequate with a smaller ride was unsatisfactory for this larger group.

That made me chuckle. Crossing paths is never a good idea, with any size group. Even people who have never been very good with coordinate geometry know that non-parallel lines intersect. Parallel lines would have been a better option, unless the course was extremely long:

If parallel lines meet at infinity, then infinity must be a noisy place with all those lines crashing together!

The way to avoid the problem, as any statistician will tell you, is to pass through these points of intersection very quickly.

A statistician would always accelerate when coming to an intersection, fly through it, and then brake on the other side. A passenger asked him why he went so fast through intersections. The statistician replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”

### To Infinity, and Beyond…

The table in the board room at NCTM headquarters contains an extended infinity symbol:

The design is based on the stylized infinity symbol that appears in the NCTM logo: