A254604 - OEIS

%I #21 Jul 02 2023 02:25:14

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

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

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

%N Decimal expansion of the half of a single half-wave constant.

%C By the definition this constant takes the value 0 < x < Pi such that the horizontal line y = sin x divides the region bounded by the sine curve and the interval [0,Pi] on the x-axis into two shapes of equal area.

%F 2*cos(x) - (Pi - 2*x)*sin(x) = 1, 0 < x < Pi.

%e x = 0.368305390596661399946991689932336338080760158209792727276899496553...

%t FindRoot[2 Cos[x] - (Pi - 2 x) Sin[x] - 1 == 0, {x, 0, Pi}, WorkingPrecision -> 150] (* _Bruno Berselli_, Feb 03 2015 *)

%o (PARI) solve(x=0, Pi, 2*cos(x) - (Pi - 2*x)*sin(x) - 1) \\ _Michel Marcus_, Feb 03 2015

%K nonn,cons

%O 0,1

%A _Roman Witula_, Feb 02 2015