The Witch of (Maria) Agnesi

 Consider a circle that fits perfectly between two parallel lines. One of the easiest pairs of parallel lines to picture is a top and a bottom. In this picture, the point O is the point tangent to the bottom and the point M is the point tangent to the top.

Take any point on the circle and call it A. The line drawn from O to A is called a secant and it will cross the line at the top at a point we call N. We can create a right triangle by making a line parallel to both top and bottom. The point P is the corner of the right triangle that has the 90° angle. For every new A, there is a new N and a new P. We are interested in the curve created by all the points P.
  

This may seem like a very strange and roundabout way to make a curve in the plane. You wouldn't be wrong to think so. In the early days of the xy-plane, mathematicians worked on these kinds of very strange curves. The first work on this was done by Pierre De Fermat, an amateur mathematician working with Rene Decartes at the beginning of the discovery of the Cartesian plane, named for Descartes ("of the cards" in French.) The formula for the curve is given by the formula in x, y and a, where a is the radius of the circle.

The simplest version of the equation is when the radius is ½, so the diameter is 1.

The curves are sometimes called bell-shaped curves, but this is not the formula for the most famous of the bell-shaped curves, the most studied version of that being called the normal curve. This curve is called the Witch of Maria Agnesi.

The name comes about by a mistranslation of Italian to English, a mistranslation that might have been intentional but has most certainly lasted until today.

Fermat's first work on the curve is done is 1630, but in 1703, the Italian Guido Grandi also studies the shape and names it in Latin, the versoria, which is also the name for one of the ropes that holds a sail in place, usually called a sheet in English.

Move forward again to 1748 and a very odd occurrence at the time, an important mathematical paper written by a woman, the Italian mathematician Maria Agnesi. She writes her paper in Italian and calls the curve "versiera", the Italian translation for Grandi's Latin word "versoria". Here comes the confusion, possibly done on purpose.

The Italian for adversary is "aversiera" is sometimes shortened to "versiera". The adversary of God is the Devil, but because this is the feminine form, it can be translated to "witch". The translation by Cambridge professor John Colson, a contemporary of Maria Agnesi, turns the name for a rope on a boat to witch, a play on words that likely was done at the expense of the very rare female mathematician.

So here is to Maria Agnesi, not an originator of an idea but, like so many of us in mathematics, a worker in the field, doing her best to preserve knowledge for future generations. Her name lasts to this day in a somewhat mocking form, but at least we remember her, one of the few women in all of Europe to publish a mathematical work that has lasted from an era when women were not allowed to get a degree from any university on the continent.