In My Workroom: Mathematical (Curve) Stitching Lesson 5

Curve of Pursuit

The parabola was the first curve that was introduced. In order to take the idea from abstract, inanimate things and forces to the real-life examples, one of the first examples that young children were introduced to was the Curve of Pursuit.

This story was explained in Mrs. Boole’s Lectures on the Logic of Arithmetic (Clarendon Press). Briefly, a dog sees a rabbit who is some distance away from his burrow. All three points, Dog, Rabbit and Burrow and marked on a piece of paper. The dog begins to run (in a straight line) toward the rabbit and the rabbit begins to hop in a straight line towards its burrow. They are both moving at the same speed. As the dog sees the rabbit change location, he changes his trajectory to realign his pursuit with the rabbit.

How to Draw the Curve of Pursuit (video)

Pursuit curves do not have to be about just two animals. There is also the predatory bug story. In this story, four bugs are in opposite corners of a square. They begin to chase each other in a counterclockwise direction.

To create the multiple curves of pursuit, you mark an equal distance on each side of the polygon and connect the marks. On the new, smaller polygon, mark the same equal distance again, going in a counterclockwise direction. Connect the new marks. Keep repeating this step until you can no longer measure the distance you’ve chosen on the side of the polygon. (you can rotate in either direction as long as you are consistent.

For a triangle you would have the following end result by using the same procedure:

You could do the same thing for any polygon: pentagon, hexagon, etc.

After making a pattern on lightweight paper, pierce the intersection points of the lines. These will become the sewing holes for your curves of pursuit. You could do each one in a different colour to make them stand out or keep them in the same colour for the optical illusion effect. You may have seen the square (4 curve) pattern as a zentangle pattern.

These curves can be tiled for interesting effects.

from instructables

You've seen the Curve of Pursuit in quilting also. It is known as the Twisted Log Cabin block.

It has also popped up in knitting patterns which can be found on Ravelry and Woolly Thoughts.

This is just FYI

If you'd like to learn even more about Curves of Pursuit and what happens if you change the variables, such as whether the dog and rabbit run at the same speed, do they run the same distance, do they change course, etc. Here is a link to an excellent article that will take you even further down the rabbit hole (pun intended). It will show you some developments in high end mathematics, computers and optical art from the late 1800's to the present day.

The Mathematical Tourist

Some interesting designs created by changing the variables.