most recent 30 from http://mathoverflow.net 2013-06-18T07:39:34Z http://mathoverflow.net/feeds/question/82331 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82331/smallest-containing-simplex Vladimir Reshetnikov 2011-12-01T00:02:36Z 2013-05-22T20:33:57Z

<p>Let $V_n$ be the least real number such that for every convex subset of $\mathbb{R}^n$ with hypervolume $1$ there is a containing simplex with hypervolume $V_n$. What is known about $V_n$? Is there a known general formula? If not, then what is the best known bounds on $V_n$?</p>

http://mathoverflow.net/questions/82331/smallest-containing-simplex/82356#82356 Michael Biro 2011-12-01T08:33:56Z 2011-12-01T08:40:32Z

<p>The paper <a href="http://www.springerlink.com/content/cu7rvr8m7vnlhgtr/" rel="nofollow">Parallelotopes of Maximum Volume in a Simplex</a> by Lassak gives the maximum possible volume of a parallelotope in a simplex as $n!/n^n$ times the volume of the simplex. This gives us a bound of $V_n \geq n^n/n!$, which I suspect is tight.</p>

http://mathoverflow.net/questions/82331/smallest-containing-simplex/131505#131505 TauMu 2013-05-22T20:33:57Z 2013-05-22T20:33:57Z

<p>The problem seems to be still open even for $n=3$:<br> <em>Weisstein, Eric W. <a href="http://mathworld.wolfram.com/TetrahedronCircumscribing.html" rel="nofollow">"Tetrahedron Circumscribing."</a></em></p>