OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Ampersand Curve
EXAMPLE
9.1975597439...
MATHEMATICA
eq = (y^2 - x^2)(x - 1)(2 x - 3) == 4(x^2 + y^2 - 2 x)^2 ; sy = Solve[eq, y]; f1[x_] = y /. sy[[2]]; f2[x_] = y /. sy[[4]]; x1 = x /. FindRoot[f1'[x] == 1, {x, 31/21}, WorkingPrecision -> 120] ; y1 = y /. Solve[eq /. x -> x1][[3]]; y2 = y /. Solve[eq /. x -> x1][[4]]; sx = Solve[eq, x]; g1[y_] = x /. sx[[1]]; g2[y_] = x /. sx[[4]] // Simplify[#, y1 < y < y2] &; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1+f1'[x]^2], {x, 0, 1}] + ni[Sqrt[1+f1'[x]^2], {x, 1, x1}]; i2 = ni[Sqrt[1+f2'[x]^2], {x, 0, 1}] + ni[Sqrt[1+f2'[x]^2], {x, 1, x1}]; i3 = ni[Sqrt[1+g1'[y]^2], {y, 0, Sqrt[3]/2}]; i4 = ni[Sqrt[1+g2'[y]^2], {y, y1, y2}]; Take[RealDigits[2(i1+i2+i3+i4)][[1]], 105]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Aug 02 2011
STATUS
approved