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 A179296 #38 Jan 28 2025 00:57:58 %S A179296 1,4,0,1,2,5,8,5,3,8,4,4,4,0,7,3,5,4,4,6,7,6,6,7,7,9,3,5,3,2,2,0,6,7, %T A179296 9,9,4,4,4,3,9,3,1,7,3,9,7,7,5,4,9,2,8,6,3,6,6,0,8,4,5,1,8,6,3,9,1,3, %U A179296 5,4,0,2,7,2,1,1,4,4,4,7,6,7,6,5,0,1,0,8,3,9,0,9,0,3,9,8,0,5,2,3,3,9,7,9,8 %N A179296 Decimal expansion of circumradius of a regular dodecahedron with edge length 1. %C A179296 Dodecahedron: A three-dimensional figure with 12 faces, 20 vertices, and 30 edges. %C A179296 Appears as a coordinate in a degree-7 quadrature formula on 12 points over the unit circle [Stroud & Secrest]. - _R. J. Mathar_, Oct 12 2011 %D A179296 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 A179296 Chai Wah Wu, <a href="/A179296/b179296.txt">Table of n, a(n) for n = 1..10001</a> %H A179296 A. H. Stroud and Don Secrest, <a href="http://dx.doi.org/10.1090/S0025-5718-1963-0161473-0">Approximate integration formulas for certain spherically symmetric regions</a>, Math. Comp. 17 (82) (1963) 105. %H A179296 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dodecahedron">Dodecahedron</a>. %H A179296 Wolfram Alpha, <a href="http://www.wolframalpha.com/input/?i=Dodecahedron">Dodecahedron</a>. %H A179296 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>. %F A179296 Equals (sqrt(3) + sqrt(15))/4 = sqrt((9 + 3*sqrt(5))/8). %F A179296 The minimal polynomial is 16*x^4 - 36*x^2 + 9. - _Joerg Arndt_, Feb 05 2014 %F A179296 Equals (sqrt(3)/2) * phi = A010527 * A001622. - _Amiram Eldar_, Jun 02 2023 %e A179296 1.40125853844407354467667793532206799444393173977549286366084518639135... %t A179296 RealDigits[(Sqrt[3]+Sqrt[15])/4, 10, 175][[1]] %o A179296 (PARI) (1+sqrt(5))*sqrt(3)/4 \\ _Stefano Spezia_, Jan 27 2025 %Y A179296 Cf. A001622, A102208, A102769, A131595, A179290, A179292, A179294. %Y A179296 Cf. Platonic solids circumradii: A010503 (octahedron), A010527 (cube), A019881 (icosahedron), A187110 (tetrahedron). - _Stanislav Sykora_, Feb 10 2014 %K A179296 nonn,cons,easy %O A179296 1,2 %A A179296 _Vladimir Joseph Stephan Orlovsky_, Jul 09 2010