A354249 - OEIS

%I #23 Aug 04 2024 08:46:21

%S 7,4,4,2,9,4,0,0,8,8,1,9,4,1,9,2,6,6,8,4,0,2,9,0,7,7,2,7,2,2,5,0,8,7,

%T 4,5,8,8,6,4,7,1,7,4,8,4,9,4,9,6,4,8,8,1,2,7,9,1,4,4,1,2,7,3,9,2,8,9,

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

%N Decimal expansion of 27*sqrt(3) / (2*Pi).

%C For any triangle ABC (see Crux Mathematicorum):

%C (sin(A) + sin(B) + sin(C)) * (1/A + 1/B + 1/C) >= 27*sqrt(3) / (2*Pi),

%C where (A,B,C) are the angles in radians.

%C Equality stands iff triangle ABC is equilateral.

%H Shi-Chang Chi and Ji Chen, Douglas L. Grant, <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv22n1.pdf">Problem 2015</a>, Crux Mathematicorum, Vol. 22, No. 1 (1996), pp. 47-48.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A010527 * A132717.

%e 7.442940088194192668402907727...

%p evalf(27*sqrt(3)/(2*Pi),110);

%t RealDigits[(27*Sqrt[3]/(2*Pi)), 10, 110][[1]] (* _Amiram Eldar_, May 21 2022; corrected by _Georg Fischer_, Aug 04 2024 *)

%Y Cf. A010527, A132702, A132717.

%K nonn,cons

%O 1,1

%A _Bernard Schott_, May 20 2022

%E a(100) corrected by _Georg Fischer_, Aug 04 2024