Bending an elastic, inextensible sheet of paper into a teardrop shape - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T18:16:43Z http://mathoverflow.net/feeds/question/86588 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86588/bending-an-elastic-inextensible-sheet-of-paper-into-a-teardrop-shape Bending an elastic, inextensible sheet of paper into a teardrop shape PaperHouse 2012-01-24T23:30:20Z 2012-01-25T01:09:25Z <p>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. </p> <p>What analytic function describes this "teardrop" shape?</p> http://mathoverflow.net/questions/86588/bending-an-elastic-inextensible-sheet-of-paper-into-a-teardrop-shape/86589#86589 Answer by Paul B for Bending an elastic, inextensible sheet of paper into a teardrop shape Paul B 2012-01-24T23:53:35Z 2012-01-25T01:09:25Z <p>All in here (if using Euler Bernoulli beam theory)</p> <p><a href="http://sci-toys.com/bent_paper_problem.pdf" rel="nofollow">http://sci-toys.com/bent_paper_problem.pdf</a></p> <p><hr /> (<em>Added by Joseph O'Rourke</em>). 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. <br /> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <img src="http://cs.smith.edu/~orourke/MathOverflow/TearDrop.jpg" alt="Tear Drop"></p>