OFFSET
0,1
COMMENTS
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.
REFERENCES
C. L. Dodgson, Curiosa Mathematica. Part II, Pillow Problems Thought Out During Sleepless Nights. London: Horace Hart for Macmillan, 1893. Problem 58.
LINKS
Ruma Falk and Ester Samuel-Cahn, Lewis Carroll's obtuse problem, Teaching Statistics 23:3 (2001), pp. 72-75.
R. K. Guy, There are three times as many obtuse-angled triangles as there are acute-angled ones, Mathematics Magazine 66 (1993), pp. 175-178.
Michael Penn, are there more obtuse or acute triangles?, YouTube video, 2023.
Stephen Portnoy, A Lewis Carroll pillow problem: Probability of an obtuse triangle, Statistical Science 9:2 (1994), pp. 279-284.
Gilbert Strang, Are random triangles acute or obtuse?, MIT BLOSSOMS video (2010).
EXAMPLE
0.639382560711962302785777741019341412348113798482481993318778867868999699015893...
MATHEMATICA
RealDigits[3/(8-6 Sqrt[3]/Pi), 10, 120][[1]] (* Harvey P. Dale, Aug 04 2019 *)
PROG
(PARI) 3/(8-6*sqrt(3)/Pi)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Charles R Greathouse IV, Sep 08 2015
STATUS
approved