A394597 Decimal expansion of the mean distance between two points selected independently at random within the interior of a regular hexagon with unit circumradius.

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, 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, 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

Offset

0,1

Links

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

Uwe Bäsel, The moments of the distance between two random points in a regular polygon, arXiv:2101.03815 [math.PR], 2021.

Gilles Bonnet, Anna Gusakova, Christoph Thäle, and Dmitry Zaporozhets, Sharp inequalities for the mean distance of random points in convex bodies, Advances in Mathematics, Vol. 386 (2021), Article 107813. See p. 5, eq. (5).

Yanyan Zhuang and Jianping Pan, Random Distances Associated with Hexagons, arXiv:1106.2200 [math.GM], 2011-2021.

Index entries for transcendental numbers.

Formula

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

Example

0.826258949490232082314283750323326010149318430219325...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A002994 A097408 A228818 * A195845 A093207 A178969

Adjacent sequences: A394594 A394595 A394596 * A394598 A394599 A394600

Keyword

nonn,cons,changed

Author

Amiram Eldar, Mar 26 2026

Status

approved