Math with Art Supplies

The Center of a Circle

After teaching this in a number of classes, I hear that I’ve been getting credit for this method of finding the center of a circle. Just setting the record straight: thanks goes to Greek mathematician Thales of Miletus, who lived just under 3000 years ago.

This is for anyone who has ever used a lid to make a circle, then is left wondering where exactly is the center. What makes this method so accessible is that we all have the essential tools: a pencil, a straight edge, and a piece of paper that has corners.

The surprise is that if you touch the perimeter of a circle with the regular corner of a piece of paper (which is typically 90 degrees, a right angle), draw in the edges of the paper to the point where they intersect the circle,…

…then connect those intersecting points with each other, you end up with a line that is not only the longest side of a triangle, but it’s also the diameter of the circle. Who would have thought that this would be true? Well, Miletus did.

What good is a diameter for finding the center of the circle? Not a whole lot of good, actually. But what if you repeat all of the steps above, but, second time around, start out touching a different part of your circle with the corner of your paper?

Look! The diameters intersect, and that’s the center of the circle.

Just to be sure, there’s no reason not to make a whole lot more of these right triangles.

Great. Now what?

Do whatever you want. That part is up to you.

If you want to give me credit, instead of calling this Thales Circle Theorem, feel free to call it Paula’s way of finding the center of a circle. I’m good with that.

7 thoughts on “The Center of a Circle

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