A118289 Decimal expansion of the arc length of the bifoliate.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Bifoliate

Example

6.4799119598464165599...

Mathematica

f1[x_] := Sqrt[x + Sqrt[x^2 - x^4]]; f2[x_] := Sqrt[x - Sqrt[x^2 - x^4]]; g1[y_] = x /. Solve[y == f1[x], x][[4]]; g2[y_] = x /. Solve[y == f2[x], x][[4]]; x1 = 7/8; y1 = f1[x1]; y2 = f2[x1]; ni[f_, x_] := NIntegrate[f, x, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + f1'[x]^2], {x, 0, x1}]; i2 = ni[Sqrt[1 + f2'[x]^2], {x, 0, x1}]; i3 = ni[Sqrt[1 + g1'[y]^2], {y, 1, y1}]; i4 = ni[Sqrt[1 + g2'[y]^2], {y, y2, 1}]; Take[RealDigits[2(i1+i2+i3+i4)][[1]], 105] (* Jean-François Alcover, Nov 25 2011 *)

Crossrefs

Sequence in context: A153306 A092160 A303134 * A075495 A070652 A195487

Adjacent sequences: A118286 A118287 A118288 * A118290 A118291 A118292

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 22 2006

Status

approved