Wednesday, December 14, 2011

How do you construct a 57-gon?

If you mean a regular 57-gon, constructed with ruler and comp, then don't bother trying because Gauss proved that it is not possible. The only constructable regular polygons with fewer than 65000 sides are ones with 3, 5, 17, 257 or some power of 2 times one of those numbers, for the number of sides. Since 57 = 3*19 is not in that list you are out of luck.

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