A394608 Decimal expansion of the median of the distribution of distances between two points in a unit square.

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

Offset

0,1

Comments

The median of the probability density function f(x) = 4*x*(Pi/2 - 2*x + x^2/2) for x <= 1, and 4*x*(arcsin(1/x) - arccos(1/x) + 2*sqrt(x^2-1) - (x^2+2)/2) for 1 <= x <= sqrt(2) (Ghosh, 1951).

The second root of 3*x^4 - 16*x^3 + 6*Pi*x^2 - 3 = 0.

Links

Table of n, a(n) for n=0..105.

Birendranath Ghosh, Random distances within a rectangle and between two rectangles, Bulletin of Calcutta Mathematical Society, Vol. 43 (1951), pp. 17-24.

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

Index entries for transcendental numbers.

Example

0.512003269083333882131081199474793545179390944060415...

Mathematica

RealDigits[Root[3*x^4 - 16*x^3 + 6*Pi*x^2 - 3, 2], 10, 120][[1]]

Prog

(PARI) solve(x = 1/2, 1, 3*x^4 - 16*x^3 + 6*Pi*x^2 - 3)

Crossrefs

Cf. A091505 (mean), A394606 (disk), A394607 (mode).

Sequence in context: A156952 A158748 A351241 * A273874 A086039 A265824

Adjacent sequences: A394605 A394606 A394607 * A394609 A394610 A394611

Keyword

nonn,cons

Author

Amiram Eldar, Mar 26 2026

Status

approved