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A118322
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Decimal expansion of perimeter of the closed portion of the bow curve.
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0
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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 23 2010]
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LINKS
| Eric Weisstein's World of Mathematics, Bow
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EXAMPLE
| 1.9215113651725125701...
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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(%) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 23 2010]
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CROSSREFS
| Sequence in context: A010160 A093962 A198984 * A199507 A154993 A197488
Adjacent sequences: A118319 A118320 A118321 * A118323 A118324 A118325
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KEYWORD
| nonn,cons
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 23, 2006
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EXTENSIONS
| More digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 23 2010
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