A118322 Decimal expansion of perimeter of the closed portion of the bow curve.

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, 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, 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

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

Table of n, a(n) for n=1..105.

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

Sequence in context: A350298 A230191 A198984 * A199507 A230156 A225446

Adjacent sequences: A118319 A118320 A118321 * A118323 A118324 A118325

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 23 2006

Extensions

More digits from R. J. Mathar, Mar 23 2010

Status

approved