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 A270230 #22 Oct 01 2022 15:35:13 %S A270230 2,3,8,7,3,2,4,1,4,6,3,7,8,4,3,0,0,3,6,5,3,3,2,5,6,4,5,0,5,8,7,7,1,5, %T A270230 4,3,0,5,1,6,8,9,4,6,8,6,1,0,6,8,4,6,7,3,1,2,1,5,0,1,0,1,6,0,8,8,3,4, %U A270230 5,1,9,6,4,5,1,3,3,9,8,0,2,6,3,5,1,7,0,7,0,4,1,4,9,3,7,9,6,2,8,9,3,4,1,0,9 %N A270230 Decimal expansion of 3/(4*Pi). %C A270230 Consider generic prisms with triangular bases (tp), enclosed by a sphere, and let f(tp) be the fraction of the sphere volume occupied by any of them (i.e., the ratio of the prism volume to the sphere volume). Then this constant is the supremum of f(tp). It is attained by prisms which have as their base equilateral triangles with edge lengths r*sqrt(2), and rectangular side faces that are r*sqrt(2) wide and r*2/sqrt(3) high, where r is the radius of the enclosing, circumscribed sphere. %C A270230 An intriguing fact is that the volume of such a best-fitting prism is exactly r^3. Hence, 1/a is the volume of a sphere with radius 1. %C A270230 Examples of similar constants obtained for other shapes enclosed by spheres are: A020760 for cylinders and A165952 for cuboids. %H A270230 Stanislav Sykora, <a href="/A270230/b270230.txt">Table of n, a(n) for n = 0..2000</a> %H A270230 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A270230 0.238732414637843003653325645058771543051689468610684673121501016... %t A270230 First@ RealDigits[N[3/4/Pi, 120]] (* _Michael De Vlieger_, Mar 15 2016 *) %o A270230 (PARI) 3/4/Pi %Y A270230 Cf. A002193, A019699 (one tenth of 1/a), A020760, A020832 (one tenth of 2/sqrt(3)), A165952. %K A270230 nonn,cons %O A270230 0,1 %A A270230 _Stanislav Sykora_, Mar 13 2016