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.
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.