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Going in Circles

What is a circle? When you see a circle, how do you know it's a circle? When you want to make a circle, how do you do it?

Click Go. Each of the turtles walks forward. Together, they make an ever-expanding circle.

This example highlights one way of thinking about circles: A circle is all of the points at a fixed distance from a given point. Since all of the turtles start at the same place, and all walk at the same speed, they stay equidistant from the starting point. So they always make a circle.

This is just one of many ways of thinking about circles. In this essay, we'll be exploring many other ways of making circles. Each approach will highlight a different aspect of "circleness."

In the process, we will explore not only how to make circles, but also how to think about circles -- and perhaps how to think about things in general.

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Last modified: November 17, 2003
by Rupert Russell