A262041 Decimal expansion of 3/(8 - 6*sqrt(3)/Pi).

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, 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, 9, 6, 9, 9, 0

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

Table of n, a(n) for n=0..72.

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).

Index entries for transcendental numbers

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

Cf. A262080.

Sequence in context: A197511 A158606 A021065 * A243152 A093754 A135935

Adjacent sequences: A262038 A262039 A262040 * A262042 A262043 A262044

Keyword

nonn,cons

Author

Charles R Greathouse IV, Sep 08 2015

Status

approved