A392572 Decimal expansion of the probability that a straight line drawn through a point selected uniformly at random on the perimeter of a regular hexagon, with a direction selected independently and uniformly at random, intersects the side opposite to the side on which the point lies.

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

Offset

0,2

Comments

A solution to a problem proposed by the Spanish engineer, mathematician, and economic theorist José Gallego-Díaz Moreno (1913-1965) in 1962. The problem was not well-defined, and this constant is the solution proposed by William Funkenbusch.

Links

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

J. Gallego-Diaz, Problem 469, Mathematics Magazine, Vol. 35, No. 1 (1962), p. 55; A Random Probability, Solution to Problem 469 by W. W. Funkenbusch, ibid., Vol. 35, No. 4 (1962), p. 252.

Formula

Equals 1/3 - sqrt(3)*log(4/3)/Pi.

Example

0.174725894095841002879090941277862458197971077374855...

Mathematica

RealDigits[1/3 - Sqrt[3]*Log[4/3]/Pi, 10, 120][[1]]

Prog

(PARI) 1/3 - sqrt(3)*log(4/3)/Pi

Crossrefs

Cf. A083679, A284983 (square), A394923 (pentagon), A394921 (cube).

Sequence in context: A160575 A194361 A153586 * A388777 A319883 A153186

Adjacent sequences: A392569 A392570 A392571 * A392573 A392574 A392575

Keyword

nonn,cons

Author

Amiram Eldar, Apr 13 2026

Status

approved