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Euclid has a magical compass with which he can trisect any angle. Together with a regular compass and a straightedge, can he construct a regular heptagon?

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    [Apparently, you can.](http://math.fau.edu/yiu/regularheptagontrisection070424.pdf) (see page 44 onwards). The idea is to start with trisecting the angle of a right triangle with hypotenuse $1$ and one leg of length equal to $\frac1{2\sqrt 7}$. See the link for more details.2011-12-22

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