A396819 Decimal expansion of 2*(18 - sqrt(5))/45.

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

Offset

0,1

Comments

The probability that the convex hull of four points independently and uniformly selected at random in the interior of a regular pentagon is a quadrilateral.

Links

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

Eric Weisstein's World of Mathematics, Sylvester's Four-Point Problem.

Index entries for algebraic numbers, degree 2.

Formula

Equals 1 - 4*A396660.

Minimal polynomial: 2025*x^2 - 3240*x + 1276.

Example

0.700619201000009346826258948056387722869305850683932...

Mathematica

RealDigits[2*(18 - Sqrt[5])/45, 10, 120][[1]]

Prog

(PARI) 2*(18 - sqrt(5))/45

Crossrefs

Cf. A051050, A051051, A242780 (disk), A394805, A396660, A396820 (regular octagon), A396821 (regular 10-gon).

Sequence in context: A019933 A067840 A132712 * A021592 A235140 A249119

Adjacent sequences: A396816 A396817 A396818 * A396820 A396821 A396822

Keyword

nonn,cons

Author

Amiram Eldar, Jun 07 2026

Status

approved