  The chromatic number of the plane is the chromatic number of the uncountably
infinite graph that has as its vertices the points of the plane and has an edge
between two points if their distance is 1. This chromatic number is denoted
$\chi(\mathcal{R}^2)$. The problem was introduced in 1950, and shortly
thereafter it was proved that $4\le \chi(\mathcal{R}^2)\le 7$. These bounds are
both easy to prove, but after more than 60 years they are still the best known.
In this paper, we investigate $\chi_f(\mathcal{R}^2)$, the fractional chromatic
number of the plane. The previous best bounds (rounded to five decimal places)
were $3.5556 \le \chi_f(\mathcal{R}^2)\le 4.3599$. Here we improve the lower
bound to $76/21\approx3.6190$.
