# Construction of Regular 65,537-Gon

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## Contents

## Theorem

It is possible to construct a regular polygon with $65 \, 537$ 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.

## Historical Note

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

The first actual construction of a regular $65,537$-gon was attempted by Johann Gustav Hermes, who calculated the $384$ required quadratic equations in $1894$ after a decade of work. However, it has been suggested that there are mistakes in his work.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $65,537$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $65,537$