Good MORNING (or afternoon or evening), readers! I am so psyched you’re here and ready to work that brain–now let’s ride! Let’s start off slow by first defining what an elliptic curve is. (To quickly catch you up, we’re going to learn about elliptic curves as though we are in a SoulCycle class and I’m the infuriatingly energetic instructor. This may or may not be a result of me laughing about “elliptic” continuously being autocorrected to “elliptical.”)

Surprisingly, elliptic curves have (almost) nothing to do with ellipses (or elliptical machines, for that matter).

Last time, I left you all on a bit of a cliff-hanger (totally my bad). In particular, we had defined the basic tools of spherical geometry (i.e. great circles), but didn’t answer some other questions about other objects on spheres! For example, if there are no straight lines in this geometry, what happens to angles? Or shapes? (Note: If you’re not sure what spherical geometry is about, I recommend you first read my last article which introduces everything we work with here!)

First, a warning: FLAT-EARTHERS BEWARE, THE FOLLOWING (SCIENTIFICALLY ACCURATE) INFORMATION MAY BE UPSETTING.

Now, let’s start with the…

Who run the world? Girls! (As Beyonce dictates.) But, I am *personally* not a good runner, so I want to know the shortest possible distance required to “run” the world. In particular, given any two points on the globe (which we assume is a sphere, for simplicity), I need to know what the shortest path between them is so I don’t have to run for too long. (Yeah, yeah, I should build my endurance, *whatever*, I’m not in the Olympics.)

While at first glance this question doesn’t seem so difficult, it’s a little harder than it looks! Unfortunately, we can’t…

I remember watching *Spy Kids* when I was younger and wishing that I, too, was a spy. I would daydream about doing killer gymnastics between sharp red laser beams and flying with those insane gadgets that they somehow let tiny children use. Then I grew up and realized that I am not at all physically fit enough for all the running they do, and that it was essentially free child labor (not once did I see those kids receive monetary compensation for their hard work).

Anyways, a lot of the trouble in spy movies seems to lie within the inability…

Before we get started, let me tell you why I’ve decided that it is my duty to help equip the masses with the basics of cryptography by writing this column. My sister is a major Swiftie and literally every week she claims that Taylor Swift will be releasing something huge! (Every week she is wrong.) Apparently, the legendary T. Swift is notorious for the hidden messages within her beautiful lyrics, stunning music videos, and general social media presence, and I unashamedly admit that I have recently gotten caught in her web of intrigue.

So far, the messages (at least the…

I seem to have found myself in a…complicated situation. I’ll save you from the details of how, but I’m trapped in the Pinocchio movie and I need to find a way to get out. I don’t have the patience to play through the movie, so I just have to find some way to break the system. Oh, how lucky, Jiminy Cricket just walked by! If there’s anyone in this crazy story who could give me some advice, it’s him!

“Hey Jiminy, Jiminy–how do I get out of here?”

Jiminy Cricket studies me, then ominously hands me a paper, a pencil…

Before we get started, I need some help. I keep hearing about Harry’s Tiles *everywhere I go*, and I can’t for the life of me figure out what people are talking about?! Let me give you some examples:

*“Wow, did you see that Vogue featured Harry’s Tiles?”* I thought Vogue was about fashion, not interior design?

*“I’m such a big fan of Harry’s Tiles music!”* So like, clinks? I don’t get the appeal.

*“I think I’m in love with Harry’s Tiles…”* Wow, they must be really beautiful!

Naturally, I wanted to figure out what all the hype was about. I…

Unfortunately, during the pandemic, most of us are unable to enjoy the beaches. It’s a shame we can’t see the beautiful waves, feel the refreshing wind on our faces, and move pebbles between lines in the sand to painstakingly and meticulously count our cattle and goods. What? You don’t do that? Oh, of course, of course, neither do I! Haha…

To clarify, today we’re talking about the rich history of the abacus (and not my endeavors with sand on beaches, though there seems to be some strange overlap)!

I think the beginning purpose of the abacus is beautifully summarized by…

It’s time for our souls to spiral in frozen fractals all around, as Idina Menzel iconically sings in Frozen’s “Let it Go.” In particular, this week we’re taking a look at fractals! It’s only fitting that we go back in time to look at the first visualization of a famous fractal.

On March 1st, 1980, in the IBM research center of Yorktown Heights, NY, mathematician Benoit (B.) Mandelbrot caught the first glimpse of what would later be known as the **Mandelbrot set**, a celebrity in the gorgeous world of fractals. If I had seen it, I might’ve thought it was…

Now it’s time for a breakdown… (cue En Vogue’s *My Lovin’ (You’re Never Gonna Get It)*)

In particular, a breakdown of numbers! Today we’ll be talking about partitions of numbers. At first glance, they’re a fairly simple concept: a **partition** of a positive number n is a way to break it up into a sum of positive integers. For example, the partitions of 5 are 1+1+1+1+1, 2+1+1+1, 2+2+1, 3+1+1, 3+2, 4+1, and 5, for a total of 7 partitions. Note that 5 still counts as a partition of 5. …