A396819 - OEIS

%I #9 Jun 28 2026 15:50:58

%S 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,

%T 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,

%U 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

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

%C 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.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem</a>.

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%F Equals 1 - 4*A396660.

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

%e 0.700619201000009346826258948056387722869305850683932...

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

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

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jun 07 2026