# Bending an elastic, inextensible sheet of paper into a teardrop shape

I take an rectangular sheet of paper, of height $H$ and Young's Modulus $E$, and in the absence of gravity, I bend it into a "teardrop" shape so that the edges along the top and bottom touch only along a single line.

What analytic function describes this "teardrop" shape?

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Are you specifying the boundary condition that the tangent cones of the edges coincide, or that they form some specified dihedral angle? –  S. Carnahan Jan 24 '12 at 23:45
You may find this question on MSE useful: math.stackexchange.com/questions/51539/… –  Samuel Reid Jan 25 '12 at 0:02