A180308 Decimal expansion of the mean length of a line segment picked at random in a 30-60-90 (right) triangle.

2, 8, 8, 5, 7, 1, 7, 1, 8, 3, 4, 8, 3, 9, 4, 8, 5, 6, 2, 5, 4, 6, 8, 4, 9, 2, 4, 2, 8, 5, 2, 3, 5, 3, 4, 6, 4, 1, 7, 0, 4, 9, 6, 7, 4, 2, 3, 1, 0, 3, 9, 0, 0, 9, 2, 5, 9, 2, 6, 3, 3, 2, 2, 9, 7, 3, 5, 8, 1, 6, 3, 5, 8, 2, 2, 4, 6, 9, 3, 3, 0, 1, 1, 5, 5, 4, 5, 8, 9, 0, 7, 0, 5, 2, 7, 9, 4, 9, 4, 9, 0, 4, 5, 1, 1

Offset

0,1

Links

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

Eric Weisstein's World of Mathematics, 30-60-90 Triangle.

Eric Weisstein's World of Mathematics, Triangle Line Picking.

Formula

Equals (204 + 36*sqrt(3) + 81*log(3) + 2*(9 + 8*sqrt(3))*log(2 + sqrt(3)))/1440.

Example

0.28857171834839485625...

Mathematica

RealDigits[(204 + 36*Sqrt[3] + 81*Log[3] + 2*(9 + 8*Sqrt[3])*Log[2 + Sqrt[3]])/1440, 10, 120][[1]] (* Amiram Eldar, May 25 2023 *)

Crossrefs

Cf. A093063, A093064, A180307.

Sequence in context: A010596 A359699 A131920 * A155739 A197139 A198367

Adjacent sequences: A180305 A180306 A180307 * A180309 A180310 A180311

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 25 2010

Status

approved