A394597 - OEIS

%I #7 Jul 20 2026 23:07:24

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

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

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

%N Decimal expansion of the mean distance between two points selected independently at random within the interior of a regular hexagon 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 Gilles Bonnet, Anna Gusakova, Christoph Thäle, and Dmitry Zaporozhets, <a href="https://doi.org/10.1016/j.aim.2021.107813">Sharp inequalities for the mean distance of random points in convex bodies</a>, Advances in Mathematics, Vol. 386 (2021), Article 107813. See p. 5, eq. (5).

%H Yanyan Zhuang and Jianping Pan, <a href="https://arxiv.org/abs/1106.2200">Random Distances Associated with Hexagons</a>, arXiv:1106.2200 [math.GM], 2011-2021.

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

%F Equals 7/(10*sqrt(3)) - 7/90 + 19*log(3)/40 - log(2+sqrt(3))/60.

%e 0.826258949490232082314283750323326010149318430219325...

%t RealDigits[7/(10*Sqrt[3]) - 7/90 + 19*Log[3]/40 - Log[2 + Sqrt[3]]/60, 10, 120][[1]]

%o (PARI) 7/(10*sqrt(3)) - 7/90 + 19*log(3)/40 - log(2+sqrt(3))/60

%Y Cf. A091505 (square), A093064 (triangle), A093070 (disk), A394596 (pentagon), this constant (hexagon), A394598 (octagon), A394599 (10-gon), A394600 (12-gon), A394601 (rhombus), A394602 (rectangle).

%K nonn,cons,changed

%O 0,1

%A _Amiram Eldar_, Mar 26 2026