OFFSET
0,1
COMMENTS
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.
LINKS
Richard K. Guy, There are three times as many obtuse-angled triangles as there are acute-angled ones, Mathematics Magazine 66 (1993), pp. 175-178.
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
0.82102105387422875652414139322915490644701013403375234594824932660155587787...
MATHEMATICA
RealDigits[3*Pi/(2*Pi + Sqrt[27]), 10, 120][[1]] (* Amiram Eldar, Jun 15 2023 *)
PROG
(PARI) 3/(2+sqrt(27)/Pi)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Charles R Greathouse IV, Sep 10 2015
EXTENSIONS
More digits from Jon E. Schoenfield, Mar 16 2018
STATUS
approved