A394600 - OEIS

%I #7 Jul 20 2026 23:31:36

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

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

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

%N Decimal expansion of the mean distance between two points selected independently at random within the interior of a regular 12-gon with unit circumradius.

%H Uwe Bäsel, <a href="https://arxiv.org/abs/2101.03815">The moments of the distance between two random points in a regular polygon</a>, arXiv:2101.03815 [math.PR], 2021.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals (504 - 660*sqrt(2) + 396*sqrt(3) - 4*sqrt(6) + 2*(3 + sqrt(3)) * sqrt(2 + sqrt(3)) + 6*(1 + 47*sqrt(3)) * sqrt(2 - sqrt(3)) - 27/2 * (15 + 11*sqrt(3)) * log(3) - 4*(27 - sqrt(3)) * log(1 + sqrt(2)) - 4*sqrt(3) * log(2 + sqrt(3)) + 2*(666 + 397*sqrt(3)) * log(2 - sqrt(3)) - (33 - 19*sqrt(3)) * log(2 + sqrt(2 + sqrt(3))) + 3*(899 + 523*sqrt(3)) * log(2 + sqrt(2 - sqrt(3))))/(1080*sqrt(2)).

%e 0.884953782114214064113523711258487868874291600958495...

%t RealDigits[(504 - 660*Sqrt[2] + 396*Sqrt[3] - 4*Sqrt[6] + 2*(3 + Sqrt[3])*Sqrt[2 + Sqrt[3]] + 6*(1 + 47*Sqrt[3])*Sqrt[2 - Sqrt[3]] - 27/2*(15 + 11*Sqrt[3])*Log[3] - 4*(27 - Sqrt[3])*Log[1 + Sqrt[2]] - 4*Sqrt[3]*Log[2 + Sqrt[3]] + 2*(666 + 397*Sqrt[3])*Log[2 - Sqrt[3]] - (33 - 19*Sqrt[3])*Log[2 + Sqrt[2 + Sqrt[3]]] + 3*(899 + 523*Sqrt[3])*Log[2 + Sqrt[2 - Sqrt[3]]])/(1080*Sqrt[2]), 10, 120][[1]]

%o (PARI) (504 - 660*sqrt(2) + 396*sqrt(3) - 4*sqrt(6) + 2*(3 + sqrt(3)) * sqrt(2 + sqrt(3)) + 6*(1 + 47*sqrt(3)) * sqrt(2 - sqrt(3)) - 27/2 * (15 + 11*sqrt(3)) * log(3) - 4*(27 - sqrt(3)) * log(1 + sqrt(2)) - 4*sqrt(3) * log(2 + sqrt(3)) + 2*(666 + 397*sqrt(3)) * log(2 - sqrt(3)) - (33 - 19*sqrt(3)) * log(2 + sqrt(2 + sqrt(3))) + 3*(899 + 523*sqrt(3)) * log(2 + sqrt(2 - sqrt(3))))/(1080*sqrt(2))

%Y Cf. A091505 (square), A093064 (triangle), A093070 (disk), A394596 (pentagon), A394597 (hexagon), A394598 (octagon), A394599 (10-gon), this constant (12-gon), A394601 (rhombus), A394602 (rectangle).

%K nonn,cons,changed

%O 0,1

%A _Amiram Eldar_, Mar 26 2026