OFFSET
1,2
COMMENTS
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
LINKS
Eric Weisstein's World of Mathematics, Bow
EXAMPLE
1.9215113651725125701...
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 23 2006
EXTENSIONS
More digits from R. J. Mathar, Mar 23 2010
STATUS
approved