Maria Agnesi

Date: 03/15/97 at 22:34:51
From: Anonymous
Subject: Agnesi

Do you have or know where I can get information on the mathematician,
Maria Agnesi?  Also, what is the Witch of Agnesi?  Please help.  
Thank you.

Date: 03/16/97 at 10:17:09
From: Doctor Sarah
Subject: Re: Agnesi

Hello!

Here's some information from the MacTutor History of Mathematics 
archive at:

  http://www-groups.dcs.st-and.ac.uk:80/~history/   

Maria Gaetana Agnesi
   Born: 16 May 1718 in Milan, Habsburg Empire (now Italy)
   Died: 9 Jan 1799 in Milan, Habsburg Empire (now Italy)

Maria Agnesi is noted for her work in differential calculus. She 
mastered many languages, such as Latin, Greek, and Hebrew, at an early 
age. At the age of 9 she published a Latin discourse in defence of 
higher education for women. In 1738 she published _Propositiones 
Philosophicae_, a series of essays on philosophy and natural science. 

The text _Instituzioni analitiche ad uso della giovent italiana_ 
includes a discussion of the cubic curve now know as the 'witch of 
Agnesi'. The word 'witch' is in fact a mistranslation of 'versiera', 
which can mean either 'curve' or 'witch'. The paper was dedicated to 
the empress Maria Theresa. 

A commentary by Agnesi on de L'Hopital's _Traite analytique des
section coniques_ was never published. 

Agnesi occupied for a time (1750) the chair of mathematics in the
University of Bologna, thus becoming the first woman to occupy a chair 
of mathematics. The chair had been previously held by her father, 
Pietro Agnesi. After the death of her father in 1752, she devoted 
herself to charitable work. In 1771 she became director of Pio Albergo 
Trivulzio, a charitable trust.

The Witch of Agnesi

The Witch of Agnesi was studied and named 'versiera' (Italian for 
'she-devil' or 'witch') by Maria Agnesi in 1748 in her book 
_Istituzioni Analitiche_. It is also known as 'Cubique d'Agnesi' or 
'Agnesienne'. It is thought that Agnesi confused an old Italian word 
meaning 'free to move' with another meaning 'witch'.

The curve had been studied earlier by Fermat and Guido Grandi in 1703.

The curve lies between y = 0 and y = a. It has points of inflection at 
y = 3a/4. The line y = 0 is an asymptote to the curve.

The curve can be considered as the locus of a point P defined as
follows. Draw a circle C with centre at (0,a/2) through O. Draw a line
from O cutting C at L and the line y = a at M. Then P has the
x-coordinate of M and the y-coordinate of L.

To experiment interactively with this curve and its associated curves, 
see:

 http://www-groups.dcs.st-and.ac.uk/~history/Curves/Witch.html   

-Doctor Sarah,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/