  We construct the hyperbolic plane with its geodesic flow as the scale plus
symmetry reduction of a three-body problem in the Euclidean plane. The
potential is $-I/\Delta^2$ where $I$ is the triangle's moment of inertia and
$\Delta$ its area. The reduction method uses the Jacobi-Maupertuis metric,
following the author's earlier paper "Putting Hyperbolic Pants on a Three-body
Problem".
