  The purpose of this paper is to explore the asymptotics of the eigenvalue
spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving
strong experimental evidence for a conjecture of the second author
\cite{strichartz2016}. We computed and analyzed the eigenvalue spectra of
several different regions in Euclidean, Hyperbolic, and Spherical space under
Dirichlet, Neumann, and mixed boundary conditions and in particular we found
that the average of the difference between the eigenvalue counting function and
a 3-term prediction has the expected nice behavior. All computational code and
data is available on our companion website \cite{murray2015results}
