OFFSET
1,1
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 30 2006
EXTENSIONS
Last digit corrected by Eric W. Weisstein, Jan 18 2012
STATUS
approved