Talk:Witch of Agnesi

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What's so special about this curve?--Anakata 18:28, 25 June 2006 (UTC)

The Witch of Agnesi is functionally equivalent to the Cauchy-Lorentz Distribution, which has many uses in mathematics and physics. The one with which I am most familiar is the Lorentzian profile, or "natural broadening", of atomic emission and absorption spectral lines. I have added a link to the Cauchy Distribution page under "See Also". AmberRobot 21:04, 21 February 2007 (UTC)

I would say that the special nature is due to the geometric definition which was added a few days after Anakata's question. Note that the curve is not unilaterally scaleable: stretching it in (only) the horizontal or vertical direction will change the curve into a non-witch (unlike, say, an ellipse, which can be scaled arbitrarily). So only specific Cauchy-Lorentz distributions are actually witches. Cheers, Doctormatt 00:31, 22 February 2007 (UTC)