# Construction of Regular 257-Gon

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## Theorem

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

## Proof

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

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## 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): $257$