Floating Bodies of Equilibrium
نویسنده
چکیده
A long cylindrical body of circular cross-section and homogeneous density may float in all orientations around the cylinder axis. It is shown that there are also bodies of non-circular cross-sections which may float in any direction. Apart from those found by Auerbach for ρ = 1/2 there are one-parameter families of cross-sections for ρ 6= 1/2 which have a p-fold rotation axis. For given p they exist for p− 2 densities ρ. There are strong indications, that for all p− 2 densities one has the same family of cross-sections.
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