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%I #17 Jun 15 2023 02:28:56
%S 8,2,1,0,2,1,0,5,3,8,7,4,2,2,8,7,5,6,5,2,4,1,4,1,3,9,3,2,2,9,1,5,4,9,
%T 0,6,4,4,7,0,1,0,1,3,4,0,3,3,7,5,2,3,4,5,9,4,8,2,4,9,3,2,6,6,0,1,5,5,
%U 5,8,7,7,8,7,2,2,9,4,9,8,2,0,5,3,3,2,5
%N Decimal expansion of 3*Pi/(2*Pi + sqrt(27)).
%C Given a segment, choose a point uniformly at random from the portion of the plane making it the middle leg of a triangle. This is the probability that the triangle is obtuse.
%H Richard K. Guy, <a href="http://www.jstor.org/stable/2690963">There are three times as many obtuse-angled triangles as there are acute-angled ones</a>, Mathematics Magazine 66 (1993), pp. 175-178.
%H Stephen Portnoy, <a href="http://mathfaculty.fullerton.edu/sbehseta/portnoy94.pdf">A Lewis Carroll pillow problem: Probability of an obtuse triangle</a>, Statistical Science 9:2 (1994), pp. 279-284.
%H Gilbert Strang, <a href="https://www.youtube.com/watch?v=XxHIrVTLubE">Are random triangles acute or obtuse?</a>, MIT BLOSSOMS video (2010).
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e 0.82102105387422875652414139322915490644701013403375234594824932660155587787...
%t RealDigits[3*Pi/(2*Pi + Sqrt[27]), 10, 120][[1]] (* _Amiram Eldar_, Jun 15 2023 *)
%o (PARI) 3/(2+sqrt(27)/Pi)
%Y Cf. A262041.
%K nonn,cons
%O 0,1
%A _Charles R Greathouse IV_, Sep 10 2015
%E More digits from _Jon E. Schoenfield_, Mar 16 2018
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