This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093524 #19 Feb 16 2025 08:32:53 %S A093524 0,1,3,8,4,2,7,7,5,7,4,0,2,3,6,4,0,8,0,4,6,8,3,5,8,8,3,7,9,6,3,5,3,6, %T A093524 3,3,7,3,3,6,5,1,0,6,5,0,8,9,2,4,0,3,7,4,7,0,9,9,9,3,8,1,9,7,3,3,2,3, %U A093524 1,4,6,0,7,3,0,3,6,1,4,7,9,0,5,4,1,6,5,8,4,5,6,4,6,4,2,6,5,9,6,1,8,8,9 %N A093524 Decimal expansion of 3977/216000 - Pi^2/2160. %C A093524 Average volume of a tetrahedron picked at random in a unit cube. %C A093524 From _Amiram Eldar_, Aug 25 2020: (Start) %C A093524 The exact value of this constant was first calculated by Zinani (2003). %C A093524 Equals (1/5) times the probability that 5 points independently and uniformly chosen in a cube are the vertices of a re-entrant (concave) polyhedron, i.e., one of the points falls within the tetrahedron formed by the other 4 points. Do and Solomon (1986) evaluated this probability using simulations, and their result is equivalent to an estimate of 0.0139 of this constant, with a 95% confidence interval of [0.01358, 0.01420] (Zinani, 2003). (End) %H A093524 Kim-Anh Do and Herbert Solomon, <a href="https://www.jstor.org/stable/3214192">A simulation study of Sylvester's problem in three dimensions</a>, Journal of applied probability, Vol. 23, No. 2 (1986), pp. 509-513, <a href="https://statistics.stanford.edu/sites/g/files/sbiybj6031/f/SOL%20ONR%20357.pdf">alternative link</a>. %H A093524 Johan Philip, <a href="https://people.kth.se/~johanph/ETC.pdf">The Expected Volume of a Random Tetrahedron in a Cube</a>, 2007. %H A093524 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubeTetrahedronPicking.html">Cube Tetrahedron Picking</a>. %H A093524 Alessandro Zinani, <a href="https://doi.org/10.1007/s00605-002-0531-y">The expected volume of a tetrahedron whose vertices are chosen at random in the interior of a cube</a>, Monatshefte für Mathematik, Vol. 139, No. 4 (2003), pp. 341-348. %H A093524 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A093524 0.0138427757... %t A093524 RealDigits[3977/216000-Pi^2/2160,10,120][[1]] (* _Harvey P. Dale_, Oct 31 2013 *) %Y A093524 Cf. A093591. %K A093524 nonn,cons %O A093524 0,3 %A A093524 _Eric W. Weisstein_, Mar 30 2004 %E A093524 Added initial 0 to match offset. - _N. J. A. Sloane_, Feb 08 2015