Maths
I keep finding entertaining names for curves. It seems that the best way for a mathematician to be remembered is to stake a claim to some mathematical function or formula and squat on it, and then come up with a particularly silly name.
These are my favorites:
The Witch of Maria Agnesi
y=1/(1+x²)
Maria Agnesi was an 18th century Italian mathematician. She found this curve and wrote about it, but it seems the Italian word for curve, “la versiera,” is peculiarly close to the word for witch, “l’avversiera.” It was mistranslated into English, and so now we call it the “witch of Agnesi” instead of the “curve of Agnesi.”
Kampyle of Eudoxus:
r=asec²Θ
This one lacks the witch’s interesting backstory, but the name is too good to leave it out. It was apparently used by Eudoxus to try to solve the problem of cube duplication: If you have a cube, how large do you have to make a second cube if you want it to have double the volume?
The problem is trickier than it might at first appear, and it was a big deal to Athenians like Eudoxus. During a particularly nasty bout of plague, the Oracle told the Athenians that the gods were angered by the lackluster size of the altar to Apollo and commanded them to make a new altar, also cubical in shape, twice as large. The Athenians complied, building a new altar with each side twice as long - but of course, this only made the altar eight times as large as the original, since they increased each side by a factor of two. The plague remained, and the greatest minds of the day sought to solve this cube duplication problem.
They never really figured it out, unfortunately. In fact, no one would figure it out for over 2,000 years, since the “Delian constant,” the number used to multiply the sides to double the cube, isn’t actually a Euclidean number - it’s the cube root of 2. That’s not an easy number to come up with. Descartes figured out the answer in 1637, far too late for the Athenians.
Tschirnhausen cubic
y² = x³ + 3x²
So this one has neither interesting backstory in itself nor particularly fascinating applications. It’s definitely a pretty curve, though, and Tschirnhausen is a lot of fun to say. The esteemed Ehrenfried Walther von Tschirnhaus has one of the best names in math (which is saying a lot) and did quite a bit in his time. He figured out the details of how light works when reflected off of curved surfaces, helping develop advanced lenses and telescopes and wrote a philosophical text trying to unite deduction and empiricism. But his greatest claim to fame was probably his invention of European porcelain, which was previously an exotic import from the east.
Swallowtail Catastrophe
This ought to be the name of a book. It already is the name of a painting - Salvador Dali’s last painting, in fact, which is at the right. The actual swallowtail catastrophe, though, graphically shown four-dimensionally, so all you get is this painting.
Catastrophe theory is a branch of math explored in the 60s that looks at the mathematical and geometrical points at which systems suddenly collapse and change. In the case of this painting, that point (called the “cusp”) is in the lower-middle, where all the lines cross over a single point. The swallowtail catastrophe, which you can play with and look at here, is a particular example of this. Dali made this painting because he believed that catastrophe theory was “the most beautiful aesthetic theory in the world.”
Cornu Spirals
This is actually a genre of curves formed from the projection of Fresnel functions, a function used in optics to study diffraction. They’re named after Marie Alfred Cornu, a French physics professor from the 19th century. The uses of Cornu spirals are fairly esoteric, but they are pretty.
