A197688 Decimal expansion of 2*Pi/(4+Pi).

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, 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, 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

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

Comments

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.

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

Examples

			x=0.8798016929768852481790427490274267675983748864...
		

References

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

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 1; c = Pi/4;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .8, .9}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197688 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
RealDigits[(2 Pi)/(4+Pi),10,120][[1]] (* Harvey P. Dale, Dec 30 2023 *)

PARI

2*Pi/(4+Pi) \\ Charles R Greathouse IV, Jul 22 2014