Witch of Agnesi

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

Related Topics:
Mathematics - Maria Agnesi

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

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or in general:

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:y=rac{a^3}{x^2+a^2}

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and parametrically:

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: x = a t ; , y = {aover t^2 + 1} ; ,

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which consists of a small bump at the y intercept.

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Notice that, analytically, the equation

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: y = {1 over {x^2 + 1}}

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is the derivative of the arctangent function

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: Y = an^{-1} x .

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In Italian, this curve is called la versiera di Agnesi which means "the curve of Agnesi". This was once interpreted by a Cambridge professor to mean "l'avversiera di Agnesi" where "avversiera" means "witch", and the mistranslation stuck.

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