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 A091505 #33 Feb 16 2025 08:32:52 %S A091505 5,2,1,4,0,5,4,3,3,1,6,4,7,2,0,6,7,8,3,3,0,9,8,2,3,5,6,6,0,7,2,4,3,9, %T A091505 7,4,9,1,4,0,3,1,5,6,7,7,7,9,0,0,8,3,4,1,7,9,6,2,1,0,5,1,8,7,5,0,5,0, %U A091505 7,8,9,3,3,0,4,8,1,5,8,3,1,8,6,7,9,2,8,1,3,2,9,2,5,2,6,1,4,5,2,4,6,7 %N A091505 Decimal expansion of (2 + sqrt(2) + 5*arcsinh(1))/15. %C A091505 Or equally, decimal expansion of (2 + sqrt(2) + 5*log(1+sqrt(2)))/15. %C A091505 Average distance between two points chosen at random in a unit square. %D A091505 S. R. Finch, Mathematical Constants, Cambridge, 2003, Sections 8.1 p. 479 and 8.5 p.498. %D A091505 L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 49. %H A091505 G. C. Greubel, <a href="/A091505/b091505.txt">Table of n, a(n) for n = 0..5000</a> %H A091505 Uwe Bäsel, <a href="https://arxiv.org/abs/2101.03815">The moments of the distance between two random points in a regular polygon</a>, arXiv:2101.03815 [math.PR], 2021. %H A091505 Jens Egholm Pedersen, Jörg Conradt, and Tony Lindeberg, <a href="https://arxiv.org/abs/2405.00318">Covariant spatio-temporal receptive fields for neuromorphic computing</a>, arXiv:2405.00318 [cs.NE], 2024. See p. 12. %H A091505 Michael Penn, <a href="https://www.youtube.com/watch?v=YJU4iy3cnK4">The average distance between points on a square</a>, video (2022). %H A091505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquareLinePicking.html">Square Line Picking</a> %H A091505 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A091505 0.5214054331647206783309823566... %t A091505 RealDigits[(2+Sqrt[2]+5ArcSinh[1])/15,10,120][[1]] (* _Harvey P. Dale_, Jul 18 2011 *) %o A091505 (PARI) (2 + sqrt(2) + 5*asinh(1))/15 \\ _G. C. Greubel_, Jan 11 2017 %o A091505 (PARI) (2 + sqrt(2) + 5*log(sqrt(2)+1))/15 \\ _Charles R Greathouse IV_, Nov 21 2024 %Y A091505 Cf. A091506, A073012. %K A091505 nonn,cons %O A091505 0,1 %A A091505 _Eric W. Weisstein_, Jan 16 2004