A394107 - OEIS

A394107

Decimal expansion of the probability that three points uniformly and independently selected at random from the interior of an equilateral triangle form the vertices of an obtuse triangle.

7, 4, 8, 1, 9, 7, 2, 2, 3, 3, 4, 2, 0, 2, 2, 9, 3, 0, 0, 3, 5, 5, 1, 9, 7, 2, 0, 3, 5, 8, 1, 3, 7, 2, 8, 1, 9, 7, 9, 7, 0, 6, 3, 6, 8, 2, 0, 0, 0, 5, 6, 9, 5, 4, 2, 7, 4, 8, 4, 3, 0, 2, 7, 5, 0, 2, 0, 7, 0, 4, 5, 0, 0, 9, 7, 1, 9, 3, 3, 6, 6, 0, 6, 3, 1, 3, 1, 2, 4, 6, 8, 1, 4, 9, 1, 9, 4, 7, 1, 6, 8, 7, 6, 3, 8

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

Dominik Beck, The Probability that a Random Triangle in a Cube is Obtuse, arXiv:2501.11611 [math.MG], 2025.

Dominik Beck, Random polytopes, doctoral thesis, Mathematical Institute of Charles University, Prague, 2025.

FORMULA

Equals 25/4 + Pi/(12*sqrt(3)) + (393/10)*log(sqrt(3)/2).

EXAMPLE

0.748197223342022930035519720358137281979706368200056...

MATHEMATICA