OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Dumbbell Curve
EXAMPLE
5.54100277...
MATHEMATICA
f[x_, y_] = y^2 - x^4 (1 - x^2); f[x_] = Sqrt[x^4 - x^6]; x0 = 9/10; y0 = f[x0]; g[y_] = x /. Solve[f[x, y] == 0, x][[2]]; i1 = NIntegrate[ Sqrt[1 + f'[x]^2], {x, 0, x0}, WorkingPrecision -> 120]; i2 = NIntegrate[ Sqrt[1 + g'[y]^2], {y, 0, y0}, WorkingPrecision -> 120]; Take[ RealDigits[4(i1+i2)][[1]], 105]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Aug 03 2011
STATUS
approved