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A262080 Decimal expansion of 3*Pi/(2*Pi + sqrt(27)). 1
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, 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, 5, 8, 7, 7, 8, 7, 2, 2, 9, 4, 9, 8, 2, 0, 5, 3, 3, 2, 5 (list; constant; graph; refs; listen; history; text; internal format)
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
Cf. A262041.
Sequence in context: A190404 A243433 A080729 * A164800 A011008 A010149
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More digits from Jon E. Schoenfield, Mar 16 2018
STATUS
approved

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Last modified June 21 23:48 EDT 2024. Contains 373560 sequences. (Running on oeis4.)