## Monday, July 30, 2012

There is two hour parking all around University of Saskatchewan. I once went to move my car (to avoid a ticket) and found that the parking attendant had marked--in chalk--the top of my tire. I wanted to erase the mark so began driving through as many puddles as possible.

I then convinced myself to find a puddle longer than the circumference of my tire--to guarantee a clean slate and a fresh two hours.

As I walked back to campus, I got thinking about the pattern left behind by my tires. For simplicity, let's take the case of a smaller vehicle--a bike.

If you were to ride a bike through a puddle of a certain width, the trail would look like this:
Is this model correct? Evenly spaced iterations of puddle-width splotches.

Assume that:
width(puddle) < circumference(tire)

and consider the following bike-ish contraptions. Can you predict the pattern? Better yet, can you draw an accurate prediction on graph paper? Assume a six-inch puddle (why not?)

That is the task I present to the students. The emerging patterns are interesting.

Unicycles--one wheel; one pattern.

But now combine them. (Of course, the bike goes in a perfectly straight line...)

A standard bicycle-- two wheels; same size.

Alter it slightly. (You may want to encourage colour coding for overlapping paths...)

Old school--two wheels; different sizes.

Exaggerate the difference.

Crazy old school--two wheels; way different sizes.

How does the pattern change? Is it important to know how far apart the wheels are? (Experiment...)

Just for fun--4 wheels; 3 tracks; 2 sizes.

What do you notice about certain radii? What causes certain patterns to "line-up"?

An interesting task to give a class working on circles, algebraic manipulation, factors, etc.

NatBanting