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Note that the family of closed curves C_N={(x,y)\in R^2;x^(2N)+y^(2N)=1} forN=1,2,3,... approaches the boundary of [-1,1]^2 as N \to \infty. In this paperwe exhibit a natural parameterization of these curves and generalize to alarger class of equations.

A parameterization of the Fermat curves satisfying x^(2N)+y^(2N)=1