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 A093525 #23 Feb 16 2025 08:32:53
%S A093525 0,1,7,3,9,8,2,3,9,2,4,5,1,2,6,6,9,3,8,4,2,6,7,9,4,6,5,5,7,8,8,7,3,8,
%T A093525 2,7,2,0,8,2,1,5,3,1,5,8,3,4,7,9,3,5,9,8,1,3,7,8,7,9,0,0,8,8,1,0,5,5,
%U A093525 2,5,5,5,5,6,7,3,8,2,4,4,8,3,1,3,2,6,4,3,9,5,1,5,5,7,0,7,5,0,0,1,2,8,8
%N A093525 Decimal expansion of 13/720 - Pi^2/15015.
%C A093525 Average volume of a tetrahedron picked at random in a tetrahedron with unit volume.
%C A093525 Buchta & Reitzner announced this result in 1992, and Mannion (independently) proved it in 1994. Buchta & Reitzner proved a more general result in 2001. - _Charles R Greathouse IV_, Sep 04 2015
%C A093525 Klee (1969) conjectured that the average volume is 1/60 and stated that according to Monte Carlo experiments 1/57 is the integer-reciprocal closest to this value. - _Amiram Eldar_, Apr 09 2022
%H A093525 Christian Buchta and Matthias Reitzner, <a href="https://www.zobodat.at/publikation_volumes.php?id=53573">What is the expected volume of a tetrahedron whose vertices are chosen at random from a given tetrahedron</a>, Österreichische Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse, Vol. 129 (1992), pp. 63-68.
%H A093525 Christian Buchta and Matthias Reitzner, <a href="https://doi.org/10.1515/crll.2001.050">The convex hull of random points in a tetrahedron: Solution of Blaschke's problem and more general results</a>, J. reine angew. Math., Vol. 536 (2001), pp. 1-29.
%H A093525 Victor Klee, <a href="https://www.jstor.org/stable/2316377">What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body?</a>, The American Mathematical Monthly, Vol. 76, No. 3 (1969), pp. 286-288.
%H A093525 David Mannion, <a href="https://www.jstor.org/stable/1427809">The volume of a tetrahedron whose vertices are chosen at random in the interior of a parent tetrahedron</a>, Advances in Applied Probability, Vol. 26, No. 3 (Sep 1994), pp. 577-596.
%H A093525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedronTetrahedronPicking.html">Tetrahedron Tetrahedron Picking</a>.
%H A093525 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A093525 0.0173982392...
%t A093525 Join[{0}, RealDigits[13/720 - Pi^2/15015, 10, 100][[1]]] (* _Amiram Eldar_, Apr 09 2022 *)
%o A093525 (PARI) 13/720 - Pi^2/15015 \\ _Charles R Greathouse IV_, Sep 04 2015
%Y A093525 Cf. A020829, A093524, A093591.
%K A093525 nonn,cons
%O A093525 0,3
%A A093525 _Eric W. Weisstein_, Mar 30 2004
%E A093525 Added initial 0 to make offset correct. - _N. J. A. Sloane_, Feb 08 2015