A394812 - OEIS

%I #4 Apr 03 2026 00:21:15

%S 5,6,8,2,9,1,5,9,2,5,8,3,8,9,3,4,8,5,3,4,6,8,9,2,8,8,2,9,6,6,5,3,6,6,

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

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

%N Decimal expansion of 3 - 24/Pi^2.

%C The solution to Sylvester's four-point problem on a hemisphere: the probability that four points independently and uniformly selected at random on a hemisphere form a convex spherical quadrilateral (Santaló, 2004).

%D Luis A. Santaló, Integral Geometry and Geometric Probability, 2nd ed., Cambridge University Press, 2004, p. 313, note 9.

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

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

%F Equals 3 - 1/A222171.

%e 0.568291592583893485346892882966536666295389407866082...

%t RealDigits[3 - 24/Pi^2, 10, 120][[1]]

%o (PARI) 3 - 24/Pi^2

%Y Cf. A222171, A242780.

%Y Cf. A394808, A394809, A394810, A394811.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Apr 02 2026