A341942 Decimal expansion of (388 + 15*Pi)/(212 - 15*Pi).

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

Offset: 1

Author

Peter Kagey, Feb 24 2021

Keywords

• nonn
• cons

Comments

The constant is equal to lim_{n -> oo} A190020(n)/A190019(n), which is the ratio of the probability of an obtuse triangle to an acute triangle, when all three vertices are drawn uniformly at random in a square.

Examples

			2.6390960417866483205308889755825371915092...
		

Links

• Code Golf Stack Exchange, Ratio of obtuse triangles to acute triangles in the square.
• Eric Langford, The probability that a random triangle is obtuse, Biometrika, 56(3), 1969, p. 689.
• Plot of A190020(n)/A190019(n) vs n using OEIS Plot2.
• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A190019, A190020.

Programs

Mathematica

RealDigits[(388 + 15*Pi)/(212 - 15*Pi), 10, 100][[1]]

PARI

(388 + 15*Pi)/(212 - 15*Pi) \\ Michel Marcus, Feb 25 2021