Mathematical properties When n is a positive rational number (in lowest terms), then each quadrant of the superellipse is a plane algebraic curve of order . In particular, when and n is an even integer, then it is a Fermat curve of degree n. In that case it is non-singular, but in general it will be singular. If the numerator is not even, then the curve is pieced together from portions of the same algebraic curve in different orientations.
mathematical properties when n is a positive rational number (in lowest terms) then each quadrant of the superellipse is a plane algebraic curve of order  in particular when and n is an even integer then it is a fermat curve of degree n in that case it is non-singular but in general it will be singular if the numerator is not even then the curve is pieced together from portions of the same algebraic curve in different orientations