TITLE: Bending an elastic, inextensible sheet of paper into a teardrop shape
QUESTION [6 upvotes]: 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?

REPLY [8 votes]: All in here (if using Euler Bernoulli beam theory)
http://sci-toys.com/bent_paper_problem.pdf

(Added by Joseph O'Rourke).  Here is Fig.1 from the paper by Antoni Colom,
 "Analysis of the shape of a sheet of paper when two opposite edges are joined," PDF link above.