Constructing the Hyperbolic Plane as the reduction of a three-body problem

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 $-I/Δ^2$ where $I$ is the triangle's moment of inertia and $Δ$ its area. The reduction method uses the Jacobi-Maupertuis metric, following the author's earlier paper "Putting Hyperbolic Pants on a Three-body Problem".

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