A237558 - OEIS

%I #20 Jan 17 2018 03:16:46

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

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

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

%N Decimal expansion of (1/Pi)*arccos(1/sqrt(3)).

%C Known to be irrational. If m is a positive integer (1/Pi)*arccos(1/sqrt(m)) is rational iff m=1,2 or 4.

%C A constant giving the location (x = y) of the thermodynamic center (also called warmest point or "hot spot") of a unit isosceles right triangle. The thermodynamic center is the warmest point in a convex heat conductor with unitary initial temperature and with boundary grounded at zero temperature. The convex heat conductor here considered is the isosceles right triangle x>0, y>0, x+y <= 1. - _Jean-François Alcover_, Jul 26 2016

%D M. Aigner and G. M. Ziegler, Proofs from The Book, Chap. 7, p. 40, Springer-Verlag, Berlin, 1999.

%H Steven R. Finch, <a href="http://arxiv.org/abs/1406.0836">In limbo: Three triangle centers</a>, arXiv:1406.0836 [math.HO] 2014 p. 11.

%F 0 < x < 1/2 maximizing sin(Pi x)*sin(2Pi x), that is x = arctan(sqrt(2)) / Pi, solution to sin(Pi x) = 3 sin(3 Pi x). - _Jean-François Alcover_, Jul 26 2016

%e 0.30408672...

%p arccos(1/sqrt(3))/Pi; evalf(%) ; # _R. J. Mathar_, Aug 02 2016

%t Join[{0},RealDigits[1/Pi ArcCos[1/Sqrt[3]],10,120][[1]]] (* _Harvey P. Dale_, Feb 22 2015 *)

%Y Cf. A275336.

%K nonn,cons

%O 0,1

%A _Benoit Cloitre_, Feb 09 2014