cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A242780 Decimal expansion of the maximum probability that the convex hull of four points, chosen at random inside a convex planar region, is a quadrilateral (Sylvester's four-point problem).

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%I A242780 #14 Feb 16 2025 08:33:22
%S A242780 7,0,4,4,7,9,8,8,1,0,4,3,1,8,1,4,9,9,9,5,5,3,5,1,5,6,5,6,3,8,2,9,4,3,
%T A242780 8,6,5,2,8,9,5,3,5,7,3,8,7,2,6,1,4,2,3,2,5,3,3,6,4,0,3,2,3,6,4,1,9,9,
%U A242780 5,0,6,3,8,6,0,1,4,6,6,2,9,8,5,8,9,7,2,9,5,1,0,5,0,2,6,9,6,4,0,2,9,3,6
%N A242780 Decimal expansion of the maximum probability that the convex hull of four points, chosen at random inside a convex planar region, is a quadrilateral (Sylvester's four-point problem).
%C A242780 It is proved that this maximum probability is achieved when the region is an ellipse (or a disk). [after Steven Finch]
%D A242780 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.18, p. 533.
%H A242780 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem</a>.
%F A242780 Equals 1 - 35/(12*Pi^2).
%e A242780 0.70447988104318149995535...
%t A242780 RealDigits[1 - 35/(12*Pi^2), 10, 103] // First
%o A242780 (PARI) 1 - 35/(12*Pi^2) \\ _Stefano Spezia_, Dec 26 2024
%Y A242780 Cf. A004677, A004824, A004936, A005017, A051050, A051051.
%K A242780 nonn,cons
%O A242780 0,1
%A A242780 _Jean-François Alcover_, May 22 2014