2-D Mathematical Curves

This has got one of my favourite curves in maths, the “Witch of Agnesi” https://www.2dcurves.com/cubic/cubicr.html#witch%20of%20agne...

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.

Beautiful and informative website from the old age: Tables, tiling background pictures, no fancy fonts or colors, even the formulas (equations) are typesetted as low-res bitmaps instead of contemporary MathML/JS/etc. For me, it feels like leafing throught an old vintage book (I have plenty of old math books left from my studies).

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

Related: Wolfram Alpha can generate Pokemon curves: https://www.wolframalpha.com/input?i=pikachu-like+curve

There's something wrong with the cartesian equation for scarabaeus [1].

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

A glimpse of old times, when the quality of the content mattered more than the presentation.

Reminds me of the Online Encyclopedia of Integer Sequences https://oeis.org/

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

Great collection of curves and articles about them. So many I'd never heard of, I'm enjoying all the pages. The formulae are only in tiny images though, I wish they were in text or MathML. But there's enough information that I can try producing some of my favorite curves and spirals.

I'm really curious what type of people find a practical use case for this? Graphic designers?