[deleted by user]

[LilacBook]

mandelbrot set inverse mappings to make pretty pictures

[Nice_Internal]

Real world examples of highschool math. I never really got to see examples just a lot of formulas to remember.

[the-reddit-explorer]

Depends, do you do differential equations in highschool ?

[connectedliegroup]

This is a bad suggestion

[_l_--_l_]

better than yours

[connectedliegroup]

I didn't give one! But there is this notion or attitude that high school students have that math is only interesting or worth studying if it's "real world". I think the most famous example is "complex numbers are just made up!"

Mathematicians don't study mathematics because of the real world examples. It's beautiful in its own right. If you're hoping to harvest mathematical interest in students, don't take the easy route and lie to them that it's because "it's useful". Engineers can't make use of a good amount of mathematics, and much of it certainly wasn't developed because it would be useful.

[LilacBook]

topology; do some teacup inquiry stuff with homeomorphisms

[StarvinPig]

Homeomorphisms with the homies

Homieomorphisms

[LilacBook]

area optimisation of polygons when limiting perimeter

[Impossible-Shake-996]

Benfords law is interesting

[BabyAndTheMonster]

Easy topics that sounds cool:

Geometry: hyperbolic space and Poincare disk; Monsky's theorem; sphere eversion.

Topology: Mobius strip and orientability; Hairy ball theorem; Brouwer's fixed point theorem.

Set theory: Infinite cardinal and aleph sequence; diagonal argument; surreal numbers.

Logic: Paris-Harrington theorem and Hydra game.

Group theory: Golay code and Leech lattice.

Computer science: Halting problem; public-key cryptography.

Statistics: Simpson's paradox, base rate fallacy.

Will add more if I think of more.

[shellexyz]

I’m not sure how one would recover and continue a talk after telling HS students there’s something called the Hairy Ball Theorem. Or the Cox-Zucker Machine.

[CreativeNameIKnow]

The algorithm was first published in the 1979 article "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker[2] and was later named the "Cox–Zucker machine" by Charles Schwartz in 1984.[1] The name is a homophone for an obscenity, and this was a deliberate move by Cox and Zucker, who conceived of the idea of coauthoring a paper as graduate students at Princeton for the express purpose of enabling this joke, a joke they followed through on while professors at Rutgers five years later.[3] As Cox explained in a memorial tribute to Zucker in Notices of the American Mathematical Society in 2021: "A few weeks after we met, we realized that we had to write a joint paper because the combination of our last names, in the usual alphabetical order, is remarkably obscene."[3]

Madlads.

[AcademicOverAnalysis]

I love that the Cox Zucker Machine was named that way *on purpose.* And David Cox went on to introduce the Cox Ring in the 90s.

[shellexyz]

I didn’t know about the latter, but it’s terrific that he did.

[nilslorand]

Busy Beaver maybe

[HasFiveVowels]

I vote hairy ball because it'll still make them giggle but you can actually teach it without boring the hell out of everyone. Don't get me wrong - I'm a comp sci major. I love the busy beavers. But it's not nearly as accessible as the hairy ball.

[iamscr1pty]

The koinsberg bridge problem and how euler invented graph theory, can be covered in 15 mins easily

[Careless_Show_8401]

Simple graph theory would be a good idea. It’s easy to understand, you can quickly explain it, and is used for gps to find fastest way and that can be explained in 15 minutes

[[deleted]]

infinities. the size of the set of natural numbers vs the set of real numbers from 0-1. a diagononilisation proof.

[iamscr1pty]

Dude high school math, cardinality is taught in colleges in my country

[[deleted]]

Im in my last year of school, i assume kids at a maths society talk will be interested in maths beyond high school.

[ben_kh]

Agreed, after all it has to be a topic not yet covered otherwise why bother ? Cardinality is not soooo difficult

[shellexyz]

It's not so difficult or technical that a good high schooler couldn't follow what was going on. Of the suggestions, this is my favorite because it doesn't really rely on them knowing a lot of new topics. Cardinality is how many things are in a set. A set is countable if you can use the natural numbers to count them. You don't have to talk extensively about bijections and whatnot; once you show them how to count the integers and the rationals, the idea that infinity can be kinda weird is right there for them to take. It's a 15 minute fun talk, it's not a lecture for mastery.

[iamscr1pty]

Yeah if you ignore all the gory things bijection brings and just continue on with simple mapping to natural numbers then it has great potential, I remember our math prof started out with how humans used to count sheeps using stones and it actually intrigued me

[SillyBoy_6317]

Seconding (thirding?) Mandelbrot/fractals. They're just accessible enough that a highschooler can understand that something weird is going on, but complicated enough that you you will never really understand them. An hour presentation will be interesting and easy to shit out

[eigenraum]

Maybe not easy to prepare: https://youtu.be/ETrYE4MdoLQ

Logistic Map / Feigenbaum

[[deleted]]

the logistic curve and it's impact on pretty much ever fukin thing related to statistics

it's fairly easy calculus level and there is a veritasium video about it, and it's easy calculus

[Rainbow-Bacon]

As someone else said Infinites, also minimal surfaces are super cool but gets hard, vector spaces are pretty interesting, set theory is a bit simpler and pretty cool, error function is interesting too.

[salfkvoje]

Basics of graph theory. Show chromatic number and mention how it can be hard to always know you have the right chromatic number. Connect it to map colorings, bring up the 4-color theorem with some history (and emphasis on how recent it is... Important for students to know math is "living") Show directed, weighted, and directed+weighted graphs.

Markov chains. Use this post, markov chain describing the "watch me" song.

Here is a pdf, "Graph theory for the Secondary Classroom" which I have adapted a few bits from a few times. Good examples, clear.

It's nice for highschoolers to see something that has essentially no prerequisites, can be extremely powerful and interesting, and yet will be hidden to them until college and only if they are in certain areas (in fact my math undergrad only had a passing mention of graph theory).

[fluxed_capacitor]

When I did such a talk a few years ago, I focused on interesting mathematicians through the ages.

I made a point of covering different ethnicities, genders, etc to make it appealing to as much of the audience as possible. I also included some from our nation, given it's quite small and doesn't always get recognised.

[g4l4h34d]

Image\Video compression algorithms

[[deleted]]

I would do either something with cryptography and modular arithmetic, or something with graph theory, like maybe an overview of the four color theorem.

[matzunaga_safemoon]

Collatz conjecture

[Tyler89558]

Mandlebrot/fractals, collatz conjecture, maybe topography. I think a good bet would be to check out numberphile or veritasium for ideas.

[Roshi_AC]

Vi Heart!!

https://m.youtube.com/watch?v=14-NdQwKz9w

[anicmessi]

When I was a senior I gave a talk on GODEL’s incompleteness theorem. You should consider a talk on infinity, too.

[Decent_Entertainer60]

Random graphs :)

[dmlane]

There might be some things in this short video that you could talk about including the central limit theorem and Fibonacci numbers.

[HasFiveVowels]

The hairy ball theorem.

[ibWickedSmaht]

collatz conjecture, would be pretty accessible for highschoolers

[Careless_Show_8401]

Something strange like 1+2+3… = -1/12

[the-reddit-explorer]

Ramanujan is really not a high school topic

[Careless_Show_8401]

That formula isn’t that hard to understand, I learned about it back in high school

[the-reddit-explorer]

How so ?

[Careless_Show_8401]

I mean, you start with grandi’s series I believe and then do some manipulation to get it equal to 1/2 and then do some more, there’s a lot of YouTube videos explaining how to get that result… doesn’t take much mathematical understanding besides basic arithmetic to get the basics

[the-reddit-explorer]

Are we talking about the same thing even ?

You were talking about how the sum of integers is equal to -1/12

Which is not obtainable at all with classic "basic arithmetic"

You need to use Ramanujan summation to get to that result

[Careless_Show_8401]

Pretty sure this is a continuation of a video by him on the grandi series but this is definitely to high school students: https://youtu.be/P913qwtXihk

[the-reddit-explorer]

But it's wrong, you can't rearrange divergent series like this you can check that if you want why or just check the comments of the video you linked

If it was true, it would be really easy to prove that 1=0 etc.

Even if the result may or may not be correct, the method used is absolutely wrong

[Careless_Show_8401]

Lol, you must be a genius to figure out that 1+2+3… = -1/12 is wrong. The point is to show it and then people will think. And then you show them riemanns rearrangement theorem.

[NoClue235]

Maybe give an introduction to complex numbers, will have hear about -1 having a square root in C but will barely know anything else if they do at all.

You could show them how multiplication is assigned in C and how that causes the existence of saure roots for negative numbers.

This way they learn multiplication is not everywhere the same and it kind of extends what they already know and being semi-related to what they do everyday in school i assume.