## Monday Morning Math: the witch of Agnesi

by

Happy Halloween!  For this day, it seems appropriate to talk about the Witch of Agnesi. Oooohhhhh!  Spooky!

But this witch is a curve.  It’s described with the algebraic formula:   $y = \frac{64}{x^2+16}$ (or, more generally, as $y = \frac{8a^3}{x^2+4a^2}$ – in the previous equation I used $a=2$).

The original construction is described geometrically, starting with a circle of radius $a$.  Here’s a short video of how it is constructed

So how did this curve get its name?   Maria Gaetana Agnesi was a wicked smart woman who was born in Milan, Italy, in 1718, about 15 years after this curve was first studied by Pierre de Fermat and Guido Grandi.  By the time she entered her teens she spoke 7 languages, and by the time she entered her twenties she was also accomplished at philosophy and mathematics, which she discussed with her father’s visitors, part of an intellectual salon.  After her mother died Maria Agnesi took over running the house and wrote a calculus book for some of her 20 younger siblings.  This book was published when she was 30, when the study of Calculus itself was only decades old.  It was over one thousand pages, and Agnesi was granted an honorary appointment at the University of Bologna.  Agnesi spent most of her adult life focused on theology and serving others, particularly people who were poor or sick.

In 1901, John Colson translated it into English, and here is where a significant mistranslation occurred.  Agnesi had called the above curve averisera (related to the word for “turning”), but the word for “witch” is similar, avversiera, and that’s what Colson used.

(Public domain from Wikimedia)

Sources: