OFFSET
1,1
COMMENTS
The Cartesian equation used here is y^2*(t^2-x^2) = (x^2+2*t*y-t^2)^2, with t=1. The arc length (perimeter) is proportional to the parameter t.
LINKS
EXAMPLE
5.056530032121244973270164896660474468785901065654375492013745802986533576904...
MATHEMATICA
digits = 100; y1[x_] := (1 - x^2)/(2 - Sqrt[1 - x^2]); y2[x_] := (1 - x^2)/(2 + Sqrt[1 - x^2]); i1 = NIntegrate[Sqrt[1 + y1'[x]^2], {x, -1, 1}, WorkingPrecision -> digits+5]; i2 = NIntegrate[Sqrt[1 + y2'[x]^2], {x, -1, 1}, WorkingPrecision -> digits+5]; RealDigits[i1 + i2][[1]][[1 ;; digits]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 03 2013
STATUS
approved