#mathed-potatoes

[encryptiondecryption]

Writing a math thesis proposal is strange

If it was honest, it would say “I wanna find out stuff about this thingy. I don’t know what other thingys would help, and I can’t describe the properties of the thingy. If I could, then I wouldn’t be writing a proposal on it. Please give me money.” Note: This is for a Master’s degree. I am allowed to not know things about the thingy. That’s the point.

[xfayewrites]

mathed-potatoes replied to your post:mathed-potatoes: I was explaining this post by...

YES! ME TOOO!

@mathed-potatoes Honestly, I knew that I was gonna be in that category after "Can't do arithmetic for h*ck" ok xD also, am I the only one mentally categorizing my math colleagues according to this post?

[transistorgrimoir]

Play. Play with [your subjects] all the time.

Mathed-Potatoes

[servantofthewrittenword]

The Witch of Agnesi

I’m gonna let my math geek flag fly for a bit, because I’m completely fascinated by this curve:

First studied by Fermat around 1630, and first named the “versiera” by Guido Grandi in the early 1700′s, the curve’s modern name came from Maria Gaetana Agnesi, in a really roundabout way. Grandi called it the “versiera,” both as a reference to a sailing term from the Latin “versoria” (what wasn’t related to sailing back then?) and the versed sine function used in the (his) construction of this curve. Agnesi also used this term in her book, Instituzioni analitiche ad uso della gioventù italiana, or Analytical Institutions for the Use of Italian Youth. Now, “versiera” is also a shorter form of a then-common Italian word “avversiera,” derived from the Latin “Adversarius.” This was a nickname for the Devil, the “Adversary of God,” and at the time was synonymous with “witch.” Cambridge professor John Colson, in translating Agnesi’s work, mistranslated “versiera” as “witch.” Thus, the curve came to be known as “The Witch of Agnesi.”

Now, etymology are fun, but math is equally fun, so how do you make The Witch of Agnesi? Start with a circle of radius a in the Cartesian (x-y) plane. Put the bottom of the circle on the origin O, and center it on the y-axis. Where the circle crosses the y-axis again at the top of the circle, label that point M, and draw its tangent line. Now, take any point A on the circle, and draw the secant line OA. Look at the point where the line tangent to the circle at M and OA cross. Label that point N. Now, we need a line parallel to the y-axis crossing N, and another line parallel to the x-axis crossing A. Label the point at which these two lines cross P. So, we should have a circle of radius a centered on the y-axis, crossing at O and M, and a right triangle NPA. If I lost you somewhere in this construction, consult the picture below:

Now, if we vary the position of A and trace the path of P, the Witch appears in the trace. Pretty cool, right?

That’s all fine and good if you’re into geometry. But what’s the explicit curve, with y as a function of x?

(Remember, a is the radius of the circle). When a = 1/2, the curve resembles something many statisticians should be familiar with:

Yep, it’s the probability density function of the Cauchy distribution (without the constant)! Since I’m a physicist by major, we sometimes call it the Lorentzian, or Lorentz distribution, but I’m not picky. Especially because I am forever going to call it the Witch. It’s a much cooler name, if you ask me.

(All images from Wikipedia page, Witch of Agnesi)