Lemniscate of Gerono
In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve shaped like an [Infinity|] symbol, or figure eight. It has equation
It was studied by Camille-Christophe Gerono.
Parameterization
Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that isAnother representation is
which reveals that this lemniscate is a special case of a Lissajous figure.