Expert: Paul Klarreich - 10/1/2005

Question
I need to draw a cogwheel (needs to be accurate). I think that involves dividing a circle into equal parts. How can I divide a circle of any size into equal parts?

Thought I'd ask a mathematician. I'd be grateful for any information!

Answer
Hi, Emile,
Your question was:
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I need to draw a cogwheel (needs to be accurate). I think that involves dividing a circle into equal parts. How can I divide a circle of any size into equal parts?
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I'm not sure exactly what a cogwheel looks like, but  dividing a circle into n equal parts is not a known construction.  In fact, I believe it is impossible to do in general.  To divide a circle into n parts you will want to construct an angle of  360/n degrees.

But an angle of 20 degrees is known to be non-constructible.  (Something about it being impossible to trisect an angle.)