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LEMNISCATE

From the Latin lemniscus "ribbon". |

Cartesian equation:
where f is even and nonnegative on [-1, 1], f(0) = f(1)
= 0. |

*Lemniscate* is the name given, in general, to the curves shaped like an eight.

Examples:

- the lemniscate
of Bernoulli ( )

- the lemniscate
of Gerono (),
and more generally, the lemniscates
of Booth.

- a case of the devil's curve.

- a case of elastic curve.

- a case of meander curve (lemniscate with sinusoidal curvature).

- certain Alain curves.

- certain Rosillo curves.

- certain sections of the cross-cap.

- the logarithmic lemniscate.

Hilbert gave the name of lemniscate to far more general curves, called here "Cassinian curves".

See also Cayley ovals and conchoid of a rose.

See this nice link.

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© Robert FERRÉOL 2017