There are 2 plausible stories about the origin of the name for this curve which was used as an example in a calculus textbook by Maria Agnesi on how to do an integral with partial fractions. The website gives one version of the story, that the curve is named after the latin for a coil of rope which Agnesi then turned into Italian as la versaria. The other possibility is that since the curve was in a problem, she meant l’aversaria (our adversary/opponent, but crucially the feminine version of this noun). In any case, when it was translated into English, the person translating said something along the lines of “Well aversario is the devil, so aversaria must mean ‘witch’” and so the curve became known as the “Witch of Agnesi”.

This curve (the folium/leaf of Descartes) is also very cool. https://www.2dcurves.com/cubic/cubicf.html#folium%20of%20Des...

Decartes and Fermat had a massive falling out via letters over trying to get a method of deriving the tangents of this curve, with Decartes insulting Fermat because Fermat’s method was insufficiently rigorous even though Decartes was unable to take the tangent using his method and a modern calculus student would recognize Fermat’s method as very similar to the modern definition of the derivative as the limit of the difference quotient. Decartes was very uncomfortable with the fact that it seemed to be dividing by zero.

I find it quite funny that clicking "the author" brings us to Linkedin, feels like going back to reality.

I think it should be:

(x^2+y^2) * (x^2+y^2+bx)^2 - a^2 (x^2-y^2)^2 = 0

Also the plot images seem inverted (reflected) along y axis. See plot of the above function in desmos [2].

1. https://www.2dcurves.com/sextic/sexticsc.html

2. https://www.desmos.com/calculator/esrche1qtv

But I was somewhat surprised when my first click in this encyclopedia of 2d curves landed me on a 3d sponge https://www.2dcurves.com/3d/3dm.html