A118811 Decimal expansion of arc length of the (first) butterfly curve.

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

Offset

1,1

Links

Table of n, a(n) for n=1..99.

Eric Weisstein's World of Mathematics, Butterfly Curve

Example

9.0173569856546976918...

Mathematica

eq = y^6 == x^2-x^6; f[x_] = y /. Solve[eq, y][[2]]; g[y_] = x /. Solve[eq, x][[2]]; h[y_] = x /. Solve[eq, x][[4]]; x1 = 3/8; y1 = f[x1]; x2 = 7/8; y2 = f[x2]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1+f'[x]^2], {x, x1, x2}]; i2 = ni[Sqrt[1+g'[y]^2], {y, 0, y2}]; i3 = ni[Sqrt[1+h'[y]^2], {y, 0, y1}]; Take[RealDigits[4(i1+i2+i3)][[1]], 99](* Jean-François Alcover, Jan 19 2012 *)

Prog

(PARI) 4*intnum(x=0, 1, sqrt(1+(x/3-x^5)^2/(x^2-x^6)^(5/3))) \\ Charles R Greathouse IV, Jan 17 2012

Crossrefs

Cf. A118292.

Sequence in context: A244593 A335415 A277524 * A200488 A249418 A256036

Adjacent sequences: A118808 A118809 A118810 * A118812 A118813 A118814

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 30 2006

Extensions

Last digit corrected by Eric W. Weisstein, Jan 18 2012

Status

approved