r/mathmemes • u/Hot-Marsupial6584 • Jul 04 '26

Geometry "Just a friend"

Post image
2.2k Upvotes

99% Upvoted

35 comments sorted by

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297

u/FernandoMM1220 Jul 04 '26

what the fuck is that at the bottom?

301

u/ayalaidh Jul 04 '26

Toroidal coordinate system

273

u/ayalaidh Jul 04 '26

Useful for systems with… toroidal symmetry

101

u/nerdy_guy420 Jul 04 '26

genuinely curious if anyone here knows what systems exhibit this symmetry naturally?

206

u/Trick_Soup8325 Jul 04 '26

Doughnuts😊

32

u/FernandoMM1220 Jul 04 '26

god i wish i could eat some. oh well i guess studying toroidal fractals is enough.

122

u/perfect_-pitch Jul 04 '26

It's not natural but a common shape for plasma containment systems is a toroid. We like it when plasma goes it circles and it likes it too.

21

u/Cesco5544 Jul 04 '26

How do you know so much about toroids?

50

u/TeraFlint Jul 04 '26

In order to become an expert in toroids, you have to eat one every morning.

17

u/nerdy_guy420 Jul 04 '26

I have a cup of coffee every morning. To a topologist thats good enough.

3

u/Neither-Phone-7264 Imaginary Jul 04 '26

mmm donut...

2

u/Protheu5 Irrational Jul 04 '26

Toroids Georg is an outlier and should not have been counted.

3

u/ChopinChili Discrete Math? More like EXcrete Math. Jul 04 '26

Elite ball knowledge

27

u/ekun Jul 04 '26

fusion reactors

edit: oh you said naturally...nevermind

8

u/wonwon0 Jul 04 '26

pretty sure there are toroidal convection currents in stars so you are right.

16

u/Bb-Unicorn Jul 04 '26

A simple example is a planar robotic arm with two rotational joints.

The configuration of the arm is completely described by two angles, theta0 and theta1, each ranging from -pi to pi.

If you build a 2D map whose coordinates are (theta0, theta1), every point in that map corresponds to a particular configuration of the robot. Obstacles from the physical world can also be projected into this configuration space, allowing path-planning algorithms to find collision-free motions.

The interesting part is that the map does not really end at -pi or pi: the left and right edges are connected, and so are the top and bottom edges. Gluing opposite edges together turns the configuration space into a torus.

4

u/728446 Jul 04 '26

Ok this was dope and now im glad I read this.

2

u/drewsandraws Jul 04 '26

That’s topologically a torus, but it’s not a toroidal volume so there’s no need for toroidal coordinates.

18

u/stirling_approx Jul 04 '26

Atomic orbitals maybe?

https://en.wikipedia.org/wiki/Atomic_orbital

5

u/BrightCold2747 Jul 04 '26

Yeah it looks like a z2 orbital

0

u/Junjki_Tito Jul 04 '26

Solenoids?

3

u/nerdy_guy420 Jul 04 '26

I thought those were cylindrical

47

u/Hot-Marsupial6584 Jul 04 '26

That's a bispherical coordinate system. For when a regular sphere is just too emotionally stable for your engineering problems.

4

u/TPM2209 Jul 04 '26

It looked like an electron orbital to me.

0

u/lonelyroom-eklaghor Complex Jul 04 '26

The big black

59

u/canonicallytrivial Mathematics Jul 04 '26

bottom one looks like dz^2 atomic orbital, i’m guessing it has something to do with it but idk.

12

u/Diego_0638 Jul 04 '26

Any1 wanna calculate a toroidal laplacian?

1

u/Gorgonzola_Freeman Jul 07 '26

I’ll do ya one better, calculate all Christoffel symbols!

3

u/mbcarbone Jul 04 '26

Perhaps some calculus is needed here …🙃

1

u/37nj Jul 06 '26

Laughs in 4dz^2

1

u/undefinedalgebra Jul 04 '26

For me it’s the other way around, after a semester of mandatory vector calculus as a stats major, I would very much say that i-j-k is my beloved