login
Decimal expansion of 2*Pi/(4+Pi).
2

%I #20 Dec 30 2023 15:05:50

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

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

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

%N Decimal expansion of 2*Pi/(4+Pi).

%C Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1 and c=pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

%C This number is the pressure drag coefficient for Kirchhoff flow past a plate, calculated by Kirchhoff (1969) for an infinitely long plate; see References. - _Peter J. C. Moses_ and _Clark Kimberling_, Sep 07 2013

%D Herbert Oertel and P. Erhard, Prandtl-Essentials of Fluid Mechanics, Springer, 2010, pages 163-164.

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

%e x=0.8798016929768852481790427490274267675983748864...

%t b = 1; c = Pi/4;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .8, .9}]

%t N[Pi/(2*b + 2*c), 110]

%t RealDigits[%] (* A197688 *)

%t Simplify[Pi/(2*b + 2*c)]

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

%t RealDigits[(2 Pi)/(4+Pi),10,120][[1]] (* _Harvey P. Dale_, Dec 30 2023 *)

%o (PARI) 2*Pi/(4+Pi) \\ _Charles R Greathouse IV_, Jul 22 2014

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011