OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Mandelbrot Set Lemniscate
EXAMPLE
8.8944968157...
MATHEMATICA
f[x_, y_] = (x^2 + y^2)*((x + 1)^2 + y^2) - 4; f[x_] = y /. Solve[f[x, y] == 0, y][[4]]; g[y_] = x /. Solve[f[x, y] == 0, x][[4]]; Take[RealDigits[ 4*NIntegrate[Sqrt[1 + f'[x]^2], {x, -1/2, 0}, WorkingPrecision -> 120] + 4*NIntegrate[Sqrt[1 + g'[y]^2], {y, 0, f[0]}, WorkingPrecision -> 120]][[1]], 105]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Aug 05 2011
STATUS
approved