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%I #16 Jan 28 2023 12:37:03
%S 6,3,9,3,8,2,5,6,0,7,1,1,9,6,2,3,0,2,7,8,5,7,7,7,7,4,1,0,1,9,3,4,1,4,
%T 1,2,3,4,8,1,1,3,7,9,8,4,8,2,4,8,1,9,9,3,3,1,8,7,7,8,8,6,7,8,6,8,9,9,
%U 9,6,9,9,0
%N Decimal expansion of 3/(8 - 6*sqrt(3)/Pi).
%C Given a segment, choose a point uniformly at random from the portion of the plane making it the longest leg of a triangle. This is the probability that the triangle is obtuse.
%D C. L. Dodgson, Curiosa Mathematica. Part II, Pillow Problems Thought Out During Sleepless Nights. London: Horace Hart for Macmillan, 1893. Problem 58.
%H Ruma Falk and Ester Samuel-Cahn, <a href="http://ratio.huji.ac.il/sites/default/files/publications/dp235.doc">Lewis Carroll's obtuse problem</a>, Teaching Statistics 23:3 (2001), pp. 72-75.
%H R. 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 Michael Penn, <a href="https://www.youtube.com/watch?v=uP666IjEo8E">are there more obtuse or acute triangles?</a>, YouTube video, 2023.
%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 0.639382560711962302785777741019341412348113798482481993318778867868999699015893...
%t RealDigits[3/(8-6 Sqrt[3]/Pi),10,120][[1]] (* _Harvey P. Dale_, Aug 04 2019 *)
%o (PARI) 3/(8-6*sqrt(3)/Pi)
%Y Cf. A262080.
%K nonn,cons
%O 0,1
%A _Charles R Greathouse IV_, Sep 08 2015