Construction of Regular 257-Gon

Theorem

It is possible to construct a regular polygon with $257$ sides using a compass and straightedge construction.


Proof

257 is a Fermat prime.

From Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime it is known that this construction is possible.

$\blacksquare$


Historical Note

It was proved by Carl Friedrich Gauss in $1801$ that the construction is possible.

The first actual constructions of a regular $257$-gon were given by Magnus Georg Paucker in $1822$ and Friedrich Julius Richelot in $1832$.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $257$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$
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