A118322 - OEIS

%I #12 Aug 15 2015 14:58:48

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

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

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

%N Decimal expansion of perimeter of the closed portion of the bow curve.

%C Writing x=r*cos(phi), y=r*sin(phi), r=sin(phi)*(1-2*sin^2(phi))/cos^4(phi) in circular coordinates gives the arc length of one wing of int_{phi = 0 .. Pi/4} sqrt( (dx/dphi)^2 + (dy/dphi)^2)) dphi = int_{s=0..1/sqrt(2)} sqrt(1-5*s^2+20*s^6) / (1-s^2)^3 ds. - _R. J. Mathar_, Mar 23 2010

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Bow.html">Bow</a>

%e 1.9215113651725125701...

%p Digits := 120 : f := 2*sqrt(1-5*x^2+20*x^6)/(1-x^2)^3 ; Int(f,x=0..1/sqrt(2.0)) ; x := evalf(%) ; # _R. J. Mathar_, Mar 23 2010

%t f[x_] := 2*Sqrt[1-5*x^2+20*x^6]/(1-x^2)^3; First[ RealDigits[ NIntegrate[f[x], {x, 0, 1/Sqrt[2]}, WorkingPrecision -> 120], 10, 105]](* _Jean-François Alcover_, Jun 08 2012, after _R. J. Mathar_ *)

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Apr 23 2006

%E More digits from _R. J. Mathar_, Mar 23 2010