http://openproblemgarden.org/op/the_double_cap_conjecture Comments for "The Double Cap Conjecture" en http://openproblemgarden.org/op/the_double_cap_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/kalai_gil">Kalai</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; The largest measure of a Lebesgue measurable subset of the unit sphere of <img class="teximage" src="/files/tex/2010c953180b3521ec2f66d10e1f40ec71d44574.png" alt="$ \mathbb{R}^n $" /> containing no pair of orthogonal vectors is attained by two open caps of geodesic radius <img class="teximage" src="/files/tex/01608ea3b80f85b77096d16610a43e184782386c.png" alt="$ \pi/4 $" /> around the north and south poles. </div> </tr></td> </table> </td> </tr> </table> Kalai, Gil combinatorial geometry independent set orthogonality projective plane sphere Combinatorics http://openproblemgarden.org/op/the_double_cap_conjecture#comment Tue, 15 Sep 2015 09:55:23 +0200 Jon Noel 60000 at http://openproblemgarden.org