Georgia Institute of Technology College of Sciences

Video Conference David Alcaraz confernce. Newton's famous three-body problem defines dynamics on the space of congruence classes of triangles in the plane. This space is a three-dimensional non-Euclidean rotationally symmetric metric space ``centered'' on the shape sphere. The shape sphere is a two-dimensional sphere whose points represent oriented similarity classes of planar triangles. We describe how the sphere arises from the three-body problem and encodes its dynamics. We will see how the classical solutions of Euler and Lagrange, and the relatively recent figure 8 solution are encoded as points or curves on the sphere. Time permitting, we will show how the sphere pushes us to formulate natural topological-geometric questions about three-body solutions and helps supply the answer to some of these questions. We may take a brief foray into the planar N-body problem and its associated ``shape sphere'' : complex projective N-2 space.