OFFSET
1,1
COMMENTS
From Bernard Schott, Apr 17 2022: (Start)
For any triangle ABC, (see Crux Mathematicorum):
(b+c)/A + (c+a)/B + (a+b)/C >= (12/Pi) * s,
b*c/(A*(s-a)) + c*a/(B*(s-b)) + a*b/(C*(s-c)) >= (12/Pi) * s,
where (A,B,C) are the angles (measured in radians), (a,b,c) the side lengths of this triangle and s the semiperimeter.
Equality stands iff triangle ABC is equilateral. (End)
LINKS
S. Arslanagić and D. M. Milošević, Problem 1827, Crux Mathematicorum, Vol. 22, No. 1 (1996), p. 36.
FORMULA
EXAMPLE
3.819718634...
MAPLE
Digits:=100; evalf(12/Pi); # Wesley Ivan Hurt, Mar 26 2014
MATHEMATICA
RealDigits[N[12/Pi, 6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2009 *)
PROG
(PARI) 12/Pi \\ Charles R Greathouse IV, Dec 31 2011
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Omar E. Pol, Aug 26 2007
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Jun 19 2009
STATUS
approved