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