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 A165953 Decimal expansion of (5sqrt(3)+sqrt(15))/(6Pi). 4
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS Weisstein, Eric W., "Dodecahedron." FORMULA Equals (5*A002194 + A010472)/(6*A000796). Equals (5*A002194 + A010472)*A049541/6. Equals (10*A010527 + A010472)*A049541/6. Equals (5 + sqrt(5))/(2Pi*sqrt(3)). Equals (5 + A002163)*A049541*A020760/2. EXAMPLE 0.6649088942053266431144284467086337161648765805556919381057592605722964718... MATHEMATICA RealDigits[(5*Sqrt[3]+Sqrt[15])/(6*Pi), 10, 120][[1]] (* Harvey P. Dale, Feb 16 2018 *) PROG (PARI) (5*sqrt(3)+sqrt(15))/(6*Pi) CROSSREFS Cf. A000796, A002194, A010472, A165922, A049541, A165952, A165954, A063723, A002163, A020760, A010527. Sequence in context: A245297 A002421 A209938 * A045885 A019118 A019126 Adjacent sequences:  A165950 A165951 A165952 * A165954 A165955 A165956 KEYWORD cons,nonn AUTHOR Rick L. Shepherd, Oct 02 2009 STATUS approved

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Last modified December 19 02:36 EST 2018. Contains 318245 sequences. (Running on oeis4.)