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

Author

Eric W. Weisstein, Apr 22 2006

Keywords

• nonn
• cons

Examples

			6.4799119598464165599...
		

Links

• Eric Weisstein's World of Mathematics, Bifoliate

Programs

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 *)