  We discuss the relationship between Penner's $\lambda$-length and the norms
of Eisenstein integers. This leads to a geometric proof of the fact, attributed
to Fermat, that every prime $p$ of the form $3k + 1$ is the norm of an
Eisenstein integer that is can be written as $a^2 - ab + b^2$ for some $a,b \in
\mathbb{Z}$.
