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22 votes
2 answers
5k views

Surface equivalent of catenary curve

A catenary curve is the shape taken by an idealized hanging chain or rope under the influence of gravity. It has the equation $y= a \cosh (x/a)$. My question is: What is the shape taken by an ...
Joseph O'Rourke's user avatar
8 votes
1 answer
787 views

The rain hull and the rain ridge

Rain falls steadily on an island, a 2-manifold $M$, which you may assume, as you prefer, is: (a) smooth, or (b) a PL-manifold, or perhaps even (c) a triangulated irregular network (TIN). After a time,...
Joseph O'Rourke's user avatar