Witch of Agnesi

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The witch of Agnesi

In mathematics, the witch of Agnesi (named for Maria Agnesi) is the graph of the equation

$y = {1\over {x^2 + 1}} \; ,$

or in general:

$y=\frac{a^3}{x^2+a^2}$

and parametrically:

$x = a t \; , y = {a\over t^2 + 1} \; ,$

which consists of a small bump at the y intercept.

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See also: Witch of Agnesi, Maria Gaetana Agnesi, Mathematics