(Redirected from Huygens' lemniscate)
Plane algebraic curve
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Lemniscate-of-Gerono.svg/220px-Lemniscate-of-Gerono.svg.png)
In algebraic geometry, the: lemniscate of Gerono,/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.
Parameterization※
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.
Dual curve※
The dual curve (see Plücker formula), pictured below, has therefore a somewhat different character. Its equation is
![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/47/Dualger.png/220px-Dualger.png)
References※
- J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. p. 124. ISBN 0-486-60288-5.