A395018 - OEIS

%I #6 Apr 10 2026 08:14:12

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

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

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

%N Decimal expansion of the mode of the distribution of distances between two points in the interior of a unit cube.

%C The second of the 4 roots of 5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x = 0.

%H Arak M. Mathai, Peter Moschopoulos, and Giorgio Pederzoli, <a href="https://rivista-statistica.unibo.it/article/view/1104">Distance between random points in a cube</a>, Statistica, Vol. 59, No. 1 (1999), pp. 61-81; <a href="https://www.researchgate.net/publication/268489321">ResearchGate link</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubeLinePicking.html">Cube Line Picking</a>.		

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

%e 0.675230751991264244633196900774754334312565525608912...

%t RealDigits[x /. FindRoot[5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x, {x, 1/2}, WorkingPrecision -> 120]][[1]]

%o (PARI) solve(x = 1/2, 1, 5*x^4 - 32*x^3 + 18*Pi*x^2 - 8*Pi*x)

%Y Cf. A073012 (mean), A395017 (median), A394605 (disk), A394607 (square), A395019 (ball), A395016.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Apr 10 2026