OFFSET
1,1
COMMENTS
The piriform curve Cartesian equation used is a^4*y^2 = b^2*x^3*(2*a-x) with a=b=1, i.e., y^2 = x^3*(2-x).
LINKS
Eric Weisstein's World of Mathematics, Piriform
EXAMPLE
7.042494468...
MATHEMATICA
f[x_] := Sqrt[2*x^3 - x^4]; g[y_] = x /. Solve[f[x] == y, x][[4]]; i1 = NIntegrate[ Sqrt[1 + f'[x]^2], {x, 0, 7/4}, WorkingPrecision -> 120]; i2 = NIntegrate[ Sqrt[1 + g'[y]^2], {y, 0, f[7/4]}, WorkingPrecision -> 120]; Take[ RealDigits[2(i1+i2)][[1]], 105]
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Dec 01 2011
STATUS
approved