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Floating bodies in neutral equilibrium
Robert Finn and Mattie Sloss
In the paper just preceding in this issue, Finn proved that if the contact angle γ of a convex body B with a given liquid is π/2, and if B can be made to float in “neutral equilibrium” in the liquid in any orientation, then B is a metric ball. The present work extends that result, with an independent proof, to any contact angle in the range 0 < γ < π. Our result is equivalent to the general geometric theorem that if for every orientation of a plane, it can be translated to meet a given strictly convex body B in a fixed angle γ within the above range, then B is a metric ball.