Witch of Agnesi Curve

Date: 09/25/2003 at 09:19:51
From: Rebecca
Subject: witch of Agnesi curve

I have searched the Internet and books, but I still can't find an 
everyday use for the witch of Agnesi curve. Do you know of any? 

The graph looks like that of a bell curve. Is that a use and if so are
there more or is that all?

Date: 09/25/2003 at 10:50:58
From: Doctor Douglas
Subject: Re: Witch of Agnesi curve

Hi Rebecca.

Thanks for writing to the Math Forum.

The witch of Agnesi is sometimes used in spectroscopy (from physics)
for fitting the shape of spectral lines in situations where the bell 
curve (a "Gaussian") is not quite right:

Applications to the Witch (PDF file)
<http://www.cs.appstate.edu/~sjg/womenandminoritiesinmath/final/agnesifinal/applications.pdf

I have also heard of its use as a model for a bump-shaped disturbance 
in fluid flow models of the atmosphere.  This bump might, for example, 
be a mountain on the ground that affects wind patterns around it.

And yes, there is also mention of the use of curves related to the 
witch of Agnesi used in statistics.  This is one area where the bell 
curve is often seen, but it seems that the witch of Agnesi makes its 
appearance as well.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/