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 A165954 Decimal expansion of sqrt(10 + 2*sqrt(5))/(2*Pi). 4
 6, 0, 5, 4, 6, 1, 3, 8, 2, 9, 1, 2, 5, 2, 5, 5, 8, 3, 3, 8, 6, 2, 6, 5, 2, 0, 5, 1, 2, 8, 0, 4, 4, 4, 9, 0, 3, 0, 0, 8, 4, 5, 4, 0, 8, 8, 0, 1, 4, 2, 8, 8, 9, 3, 3, 2, 0, 0, 9, 3, 5, 0, 0, 0, 8, 3, 8, 2, 9, 5, 6, 8, 3, 8, 2, 0, 7, 2, 7, 2, 7, 8, 5, 3, 6, 2, 4, 2, 6, 2, 5, 9, 6, 8, 8, 1, 3, 0, 5, 1, 9, 3, 2, 4, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The ratio of the volume of a regular icosahedron to the volume of the circumscribed sphere (with circumradius a*sqrt(10 + 2*sqrt(5))/4 = a*A019881, where a is the icosahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165953. A063723 shows the order of these by size. LINKS Eric Weisstein's World of Mathematics, Icosahedron. FORMULA sqrt(10 + 2*sqrt(5))/(2*Pi) = sqrt(10 + 2*A002163)/(2*A000796) = 2*sin(2*Pi/5)/Pi = 2*sin(A019694)/A000796 = 2*sin(72 deg)/Pi = 2*A019881/A000796 = 2*A019881*A049541 = (2/Pi)*sin(72 deg) = A060294*A019881. EXAMPLE 0.6054613829125255833862652051280444903008454088014288933200935000838295683... MATHEMATICA RealDigits[Sqrt[10+2Sqrt[5]]/(2Pi), 10, 120][[1]] (* Harvey P. Dale, Aug 27 2013 *) PROG (PARI) sqrt(10+2*sqrt(5))/(2*Pi) CROSSREFS Cf. A000796, A002163, A165922, A049541, A165952, A165953, A063723, A019881, A019694, A060294. Sequence in context: A011492 A274419 A131329 * A340576 A104288 A198995 Adjacent sequences: A165951 A165952 A165953 * A165955 A165956 A165957 KEYWORD cons,nonn AUTHOR Rick L. Shepherd, Oct 04 2009 STATUS approved

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Last modified April 2 00:39 EDT 2023. Contains 361723 sequences. (Running on oeis4.)