#integity

[professorgtnt]

The supreme quality for leadership is unquestionably integrity. Without it, no real success is possible.

[realreadysetrose]

I’m afraid I can’t do that, Dirk

[nonotoff]

May not feel sexual/romantic attraction but that doesn’t mean we don’t exist

[eulerseverything]

I love math I wish numbers were real

[zorionbbq]

guy who says heh-heh!

[knightmareaceblue]

Cyberweek 2024 Day Five: Crossover

Pfft, I've been on an AvA kick recently, so I guess it's not too surprising that I chose this. On one hand, this crossover works well in theory. The stick figures are all fast, kinetic learners and really good at demonstrating their earned skills and knowledge.

On the other hand, the sheer tonal dissonance is hilarious.

[sufficientlylargen]

I've found my new favorite units chart (from wikimedia commons).

[fixing-bad-posts]

gawain updates?

the king hath made a knight of me

[jimmerzz0905]

YURI BLAST 💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥💥

meet Negative Four and L!! they’re basically just Four and X if their personalities were inverted and they were lesbians

i thought the concept of negative algebraliens with personalities the complete OPPOSITE of their positive counterparts would be interesting, and Negative Four is just one of like. 12 concepts I have LOL

as for L, she’s not actually X’s opposite in terms of value (which is CONSTANTLY CHANGING), but in terms of personality. she gets along with Negative Four pretty well, but would probably fucking HATE X (who may or may not be her sibling)

Negative Four is a musician (think Mitski), while L is just. kinda doing her own thing but hangs out at Negative Four’s apartment in Integer City sometimes

[ozdical]

wip :]

[positivelyprime]

Eisenstein primes (and integers)

You've heard of integer primes, but have you heard of different kind of primes? One of the most beautiful pictures in mathematics I've recently seen is this:

This is a picture displaying the Eisenstein primes and the rest of the post will be me explaining where this comes from.

Firstly, to understand what Eisenstein primes are, we need to know what Eisenstein integers are! An Eisenstein integer is a complex number of the form z = a + b w where a,b are integers and w = e^(2/3 pi i). Normally a small letter omega is used instead of w. Notice that w is a third root of unity, i.e. w³ = 1.

Appending this complex w to the regular integers has some consequences. In particular, we can now view the eligible numbers on the complex plane to get this picture:

The Eisenstein integers correspond exactly to places where two dotted lines cross. As such, where normally one can view integers as laying on a 1-d line, we can now view Eisenstein integers as laying on a 2-d lattice!

Now one may start to wonder if, just like in the integers, one can have Eisenstein integers which are not divisible by other Eisenstein integers. In more mathematics: We call a number p an Eisenstein prime if p cannot be written as a*b where a,b are Eisenstein numbers which are not +-1, +-w, +-w² (the units in this system).

It turns out that some regular primes are still primes in the Eisenstein integers. For example, 2 can still not be decomposed. However, 3 can! We may write 3 = -(1+2w)(1+2w) which means that 3 is not an Eisenstein prime. One may investigate this further (using abstract algebra) to arrive at the picture at the top of this post. The 6-fold rotational symmetry is due to the Eisenstein integers having 6 units.

Of course a natural question is why take a third root of unity and not an nth root? This is a very interesting question and leads to the study of (integer rings of) cyclotomic fields! This concludes fun math fact tuesday

[starflungwaddledee]

what is the name of the awtdy au? it looks to be an acronym of some sort

(any more stuff about the au in general is welcomed)

correct! here's the two page comic i made to answer this question instead of just typing out five words like a normal person because i am nothing if not committed!

[icy-saturday]

@biblicallyaccuratefour @1tzt3n10-b1gbr0 @differentsweetscreator @pibfb @dr-fizzovich @annabunnyisback @profily-and-friends @samuniverse108 @fourteenintegerfan @oneirophobes-nightmare @dimmydoodles @slime-water-shrew @willow-hart727

Merry early Christmas :)

Eat up moots 🪺🪺🪺🪺

[kalcifyrgomara]

these got damn . algebraliens

[shutinlear53]

plain janes are so undersexualized that they integer overflow to being the peak of perversion, like nuns and jon arbuckle

[kevin-weezhlewig-dot]

EVIL ARTSTYLE CHALLENGE. i couldnt think of anything to draw so tpot inscryption crossover