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

symbol, or figure eight.

It has equation It was studied by Camille-Christophe Gerono.

Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that is Another representation is which reveals that this lemniscate is a special case of a Lissajous figure.

The dual curve (see Plücker formula), pictured below, has therefore a somewhat different character.