In the book The Math Instinct by Keith Devlin, the story is told of frisbee dogs that run mathematically optimal pursuit paths when chasing frisbees. Most of us have seen dogs do this. But then he describes what happens to dogs that chase frisbees at the seashore.

Let's say you throw the frisbee out over the water. He says the dog will adjust her path to get the edge of the shore as quickly as possible, then change direction as she swims out to get the frisbee. This means the path is not a straight line since the dog travels more slowly in the water. The dog still comes up with an optimal pursuit path, meaning she has taken the difference in speeds into account.

Have you ever seen a dog do this? I thought this could make a funky field trip if we brought the students to the shore with a frisbee dog and a video camera. It'd be fun to see if it is really true. Makes for sort of an interesting lesson plan, explaining about the pursuit theory. You also hit some experimental design standards.

(I know of at least one person on this board who had Frisbee Dog as a hobby interest).

Cheers --

Mark,

I happen to have frisbee loving dogs and would say that what you have read is true. If you don't have time to do the field trip you may even be able to find something on Youtube and show it.

Another thing that I remeber doing in math class was looking at a pool table and figuring out all the math for where the ball travels based on angles.

Good luck!

Karen Niemela

I have a dog who has spent much time chasing bumpers into rivers.  Almost instinctively, he will judge the speed of the water and determine his pursuit angle before he gets to the shore.

Fast moving water = more time on land running up/downstream, opposite for slow. 

If the bumper is thrown upstream he will pick a point of interception and stick to it.

It might make a better animal psychology question than a mathematic model, but it would be interesting to look at these ideas!