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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. Its equation is

- J. Dennis Lawrence (1972).
*A catalog of special plane curves*. Dover Publications. p. 124. ISBN 0-486-60288-5.

Wikimedia Commons has media related to Lemniscate of Gerono. |

- O'Connor, John J.; Robertson, Edmund F., "Figure Eight Curve",
*MacTutor History of Mathematics archive*, University of St Andrews