A073012 - OEIS

A073012

Decimal expansion of Robbins constant.

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

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OFFSET

0,1

COMMENTS

The average distance between two points chosen at random inside a unit cube.

This constant was named after the American mathematician David Peter Robbins (1942 - 2003). - Amiram Eldar, Aug 25 2020

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 479.

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 693.

Francois Le Lionnais, Les nombres remarquables, Paris: Hermann, 1983. See p. 30.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Simon Plouffe, The Robbins constant, in Miscellaneous Mathematical Constants, p. 173.

David P. Robbins, Problem E2629, The American Mathematical Monthly, Vol. 84, No. 1 (1977), p. 57, Theodore S. Bolis, Solution to problem E2629: Average distance between two points in a box, also solved by the proposer and by Günter Bach and Frank Piefke, ibid., Vol. 85, No. 4 (1978), pp. 277-278.

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

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

Eric Weisstein's World of Mathematics, Robbins Constant.

Wikipedia, Robbins constant.

FORMULA

4/105 + (17/105) * sqrt(2) - (2/35) * sqrt(3) + (1/5) * log(1+sqrt(2)) + (2/5) * log(2+sqrt(3)) - (1/15) * Pi. - Eric W. Weisstein, Mar 02 2005

EXAMPLE

0.66170718226717623515583113324841358174640013579095...

MATHEMATICA

RealDigits[ N[4/105 + 17/105*Sqrt[2] - 2/35*Sqrt[3] + 1/5*Log[1 + Sqrt[2]] + 2/5*Log[2 + Sqrt[3]] - 1/15*Pi, 110]] [[1]]

PROG

(PARI) (4 + 17*sqrt(2) - 6*sqrt(3) + 21*log(1 + sqrt(2)) + 42*log(2 + sqrt(3)) - 7*Pi)/105 \\ G. C. Greubel, Jan 11 2017