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?
Can a regular heptagon be constructed using a compass, straightedge, and angle trisector?
18
$\begingroup$
geometry
euclidean-geometry
galois-theory
geometric-construction
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6[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