One of the "Problems of Antiquity" is to construct a regular heptagon with a compass and straightedge. I know of two good ways to do this. The first, which I created, is reasonably accurate like the second, from a Geometry text.
It is accepted as being impossible to construct a heptagon. In fact, it has been proven. To view the proof as well as how mathematicians prove other similar things impossible, click here. Heptagon Proof.
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