A165953 Decimal expansion of (5*sqrt(3) + sqrt(15))/(6*Pi).

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

Offset: 0

Author

Rick L. Shepherd, Oct 02 2009

Keywords

• cons
• nonn

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.

Examples

			0.6649088942053266431144284467086337161648765805556919381057592605722964718...
		

Links

• Eric Weisstein's World of Mathematics, Dodecahedron.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796, A002194, A010472, A165922, A049541, A165952, A165954, A063723, A002163, A020760, A010527.

Programs

Mathematica

RealDigits[(5*Sqrt[3]+Sqrt[15])/(6*Pi),10,120][[1]] (* Harvey P. Dale, Feb 16 2018 *)

PARI

(5*sqrt(3)+sqrt(15))/(6*Pi)

Formula

Equals (5*A002194 + A010472)/(6*A000796).

Equals (5*A002194 + A010472)*A049541/6.

Equals (10*A010527 + A010472)*A049541/6.

Equals (5 + sqrt(5))/(2*Pi*sqrt(3)).

Equals (5 + A002163)*A049541*A020760/2.