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 A237603 #19 Feb 07 2025 13:20:21 %S A237603 1,1,1,3,5,1,6,3,6,4,4,1,1,6,0,6,7,3,5,1,9,4,3,7,5,0,3,9,4,8,6,9,4,9, %T A237603 3,7,5,8,8,3,1,5,0,3,6,9,8,8,6,4,8,7,7,7,2,6,0,1,2,0,8,0,0,3,9,9,8,4, %U A237603 8,9,6,2,0,5,6,5,5,6,5,9,7,5,8,8 %N A237603 Decimal expansion of the inscribed sphere radius in a regular dodecahedron with unit edge. %C A237603 Equals phi^2/(2*xi), where phi is the golden ratio (A001622, 2*cos(Pi/5)) and xi is its associate (A182007, 2*sin(Pi/5)). %D A237603 Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง12.4 Theorems and Formulas (Solid Geometry), p. 451. %H A237603 Stanislav Sykora, <a href="/A237603/b237603.txt">Table of n, a(n) for n = 1..2000</a> %H A237603 Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>. %H A237603 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A237603 Equals A001622^2/A182007 = (cos(Pi/5))^2/sin(Pi/5) = A019863^2/A019845 = cos(Pi/5)*cotan(Pi/5) = A019863*A019952 = 1/sin(Pi/5) - sin(Pi/5) = A019845^(-1) - A019845 = sqrt(250+110*sqrt(5))/20. %e A237603 1.1135163644116067351943750394869493758831503698864877726012080... %t A237603 RealDigits[ Cos[Pi/5]^2 / Sin[Pi/5], 10, 111][[1]] (* Or *) %t A237603 RealDigits[ Sqrt[5/8 + 11/(8 Sqrt[5])], 10, 111][[1]] (* _Robert G. Wilson v_, Feb 28 2014 *) %o A237603 (PARI) sqrt(250+110*sqrt(5))/20 %Y A237603 Cf. A001622, A182007, A019863, A019863, A019952, A374771 (sphere volume). %Y A237603 Cf. Platonic solids inradii: A020781 (tetrahedron), A020763 (octahedron), A179294 (icosahedron). %K A237603 nonn,cons,easy %O A237603 1,4 %A A237603 _Stanislav Sykora_, Feb 25 2014