OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Burnside Curve
EXAMPLE
3.878554858741...
MATHEMATICA
f[x_, y_] = y^2 - x (x^4 - 1); f[x_] = Sqrt[-x + x^5]; x1 = -5/6; y1 = f[x1]; x2 = -1/4; y2 = f[x2]; eq = Eliminate[f[g[y], y] == 0 && D[f[g[y], y], y] == 0, g[y]]; dg1[y_] = g'[y] /. Solve[eq, g'[y]][[3]]; dg2[y_] = g'[y] /. Solve[eq, g'[y]][[1]]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + dg1[y]^2], {y, 0, y1}]; i2 = ni[Sqrt[1 + f'[x]^2], {x, x1, x2}]; i3 = ni[Sqrt[1 + dg2[y]^2], {y, 0, y2}]; Take[RealDigits[2(i1+i2+i3)][[1]], 105]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Aug 03 2011
EXTENSIONS
Mathematica program simplified by Jean-François Alcover, Aug 26 2011
STATUS
approved