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 A165953 #20 Feb 25 2023 11:45:52 %S A165953 6,6,4,9,0,8,8,9,4,2,0,5,3,2,6,6,4,3,1,1,4,4,2,8,4,4,6,7,0,8,6,3,3,7, %T A165953 1,6,1,6,4,8,7,6,5,8,0,5,5,5,6,9,1,9,3,8,1,0,5,7,5,9,2,6,0,5,7,2,2,9, %U A165953 6,4,7,1,8,1,8,7,7,3,2,5,9,7,4,9,7,0,8,9,0,0,2,6,9,2,0,9,2,5,9,8,9,8,2,8,0 %N A165953 Decimal expansion of (5*sqrt(3) + sqrt(15))/(6*Pi). %C A165953 The ratio of the volume of a regular dodecahedron to the volume of the circumscribed sphere (which has circumradius a*(sqrt(3) + sqrt(15))/4 = a*(A002194 + A010472)/4, where a is the dodecahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165954. A063723 shows the order of these by size. %H A165953 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dodecahedron.html">Dodecahedron</a>. %H A165953 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>. %F A165953 Equals (5*A002194 + A010472)/(6*A000796). %F A165953 Equals (5*A002194 + A010472)*A049541/6. %F A165953 Equals (10*A010527 + A010472)*A049541/6. %F A165953 Equals (5 + sqrt(5))/(2*Pi*sqrt(3)). %F A165953 Equals (5 + A002163)*A049541*A020760/2. %e A165953 0.6649088942053266431144284467086337161648765805556919381057592605722964718... %t A165953 RealDigits[(5*Sqrt[3]+Sqrt[15])/(6*Pi),10,120][[1]] (* _Harvey P. Dale_, Feb 16 2018 *) %o A165953 (PARI) (5*sqrt(3)+sqrt(15))/(6*Pi) %Y A165953 Cf. A000796, A002194, A010472, A165922, A049541, A165952, A165954, A063723, A002163, A020760, A010527. %K A165953 cons,nonn %O A165953 0,1 %A A165953 _Rick L. Shepherd_, Oct 02 2009