A165954 Decimal expansion of sqrt(10 + 2*sqrt(5))/(2*Pi).

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

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

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Icosahedron.

Index entries for transcendental numbers.

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