Gems in STEM: The Liar’s Paradox and Fuzzy Logic

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…


Gems in STEM: Tessellations

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…


Gems in STEM: The History of the Abacus

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…


Gems in STEM: A Discussion of Fractals

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.

The Mandelbrot set

The Mandelbrot Set (image taken from Wikipedia)

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…


Gems in STEM: A Discussion of Partitions

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. …


Hi everyone! Quick recap: this bi-weekly column, Gems in STEM, is a place to learn about various STEM topics that I find exciting, and that I hope will excite you too. Future columns may include social issues in STEM, its intersections with other subjects, and various other topics that are prominent in these fields.

Note: this is a transcript of my talk at the Youth STEM Summit 2020, edited for clarity. Also included are images from the presentation, icons by Flaticon.

When I was in third grade at my very first math competition, a random boy asked me, “What’re you…


Gems in STEM: The History of Zero

What are we going to talk about today? Nothing!

Okay, okay, today we’ll be briefly discussing the fascinating history of the number zero. Now, using the term “number” is a little presumptuous, because it first came into play as a placeholder.

In particular, the first known appearance of this idea of zero was in Mesopotamia, around 5,000 years ago. The Sumerians used a counting system for practicality — to count their goods and to keep track of things like wild horses and cattle. In writing, scribes used spaces to denote the absence of a number in a place (hence the…


Gems in STEM: An Introduction to Knot Theory

As I mentioned in the last article about primes, this column, Gems in STEM, is a place to learn about various STEM topics that I find exciting, and that I hope will excite you too! This column will always be written to be fairly accessible (with a few advanced details), so you don’t have to worry about not having background knowledge. Now, onto today’s topic…knots! First, a disclaimer: the diagrams included are not mine, they are photos taken from the Internet.

What are knots?

When you think of knots, you might think of your double-knotted shoelaces or your hopelessly tangled earbuds. I personally…


Gems in STEM: A Discussion of Primes

Hi everyone! I’m Apoorva, a high-schooler who enjoys mathematics (and terrible jokes, as seen from the title). I’ve loved math ever since I was a kid, and have been involved in math competitions since elementary school. Additionally, I’ve co-authored two published papers in number theory. I’ll be using this platform to share STEM topics I’m excited about, and that I hope will excite you too. These articles are published in my local newspaper in my column, Gems in STEM, and I figured I might as well upload them here for anyone interested! Everything…

Apoorva Panidapu

16 year-old mathematics student, artist, and advocate for youth and gender minorities in STEAM.

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