#integ

[gaspriceboner]

Hi friends!! My lovely sister @anarchist4lien has helped me develop a website (she did ALL THE CODING LIKE THE ABSOLUTE GOAT SHE IS) for my comic/book universe! Theres only one singular comic and blip(chapter) on it currently and it’s still greatly in development! I’m going to leave the link to my neocities here! Hope you enjoy!!

TW for: uncanny/cryptid type characters and themes, gor3 kinda? It’s mostly black and white apart from some early panels but most is implied Very implied.)

If you have any questions ask me here! And if I don’t reply it’s entirely on accident I don’t check tumblr a lot!

Much love friends! Have fun, don’t get lost in the archiiiiveeesssssss~~/JK THERES LITERALLY NO WAY TO GET LOST ITS NOT THAT BIG YET 😭😭

(Side note: I know it’s a bit hard to read the next blip will be exclusively with text rather than handwriting!)

[nonotoff]

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

[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

[eulerseverything]

I love math I wish numbers were real

[ozdical]

wip :]

[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!

[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

[kevin-weezhlewig-dot]

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

[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.

[secondwheel]

The  |  stands for the absolute value of an integer. In this case, it makes anything positive. 

[xxyv3]

quick pi doodle, i forgkt to put my signatur on my last art

[sleekwind]

What I don't understand is when math teacher says -1 is the largest negative integer. What about -0.1? Or -0.000534? Are they not right side enough in the integer scale for them to be large? If there is a math side of Tumblr pls explain

[dino--draws]

IF TWO ONES MAKE TWO AND TWO TWOS MAKE FOUR WHAT'S TO DO WHEN TWO TWOS WON'T MAKE FOUR ANYMORE?

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"It's 11 PM, I'm just going to do a sketch for this idea" <- the words of a liar who then spent 30 minutes borderline painting a Creaturified verison of the LOGICIAN from scp

I will make fucking ANYTHING a dragon if you let me, even a formless multiuniversal semiontological bureaucratohazard

Tempted to also post this over on the wiki. God I need an art page for all my miscellaneous stuff like this <- still needs to make a damn author page god someone yell at me to do that

[lurking-latinist]

never forget when Seven/Time went canon <3

(No Future by Paul Cornell)

[painted-bees]

okee good morning...answering this for real now lmao

Required reading for context first!:

https://www.tumblr.com/painted-bees/714138097261150208/lark-wren-lark-needs-to-drag-her-focus-kicking

https://www.tumblr.com/painted-bees/713687883290214400/thinkin-more-about-magritte-and-rafael-because-of

Raf and Magritte, before meeting Cortes, had become pretty iron clad as a pair. As skittish/paranoid as Raf can be, Magritte had proven time and time again that she adores Raf for being Raf, and not what he can be used for nor what she imagines he should be. He’s no longer waiting for that other shoe to drop with her, like he’s usually waiting on with literally anyone else. Magritte’s love, so far as he can tell--and deliberately elects to believe in--is completely unconditional. Raf has only ever had three...four people he trusts to see him as himself and do well by him: his grandmother, his uncle, Magritte, and Cortes.

Magritte, of course, genuinely does adore Raf, thinks he’s very sweet--thinks he’s got a -lot- of baggage and needs some proper patience and a gentle kind of love. But he’s very patient with her, doesn’t yell at her for forgetting things or forgetting to -do- things, and just seems to genuinely love having her around, and doesn’t get annoyed when she’s excited about stuff and it’s just...so refreshing.

Needless to say, Raf and Magritte are ride or die for each other. Raf is extremely protective of Magritte’s infectious enthusiasm, optimism, and her overall penchant to see the best in every situation and every person. Magritte just wants to see Raf have an easier time of things and find joy in the stuff that is joyful again.

Raf and Magritte met Cortes...strangely: https://www.tumblr.com/painted-bees/715850323888160768/the-water-between-the-discovery-islands-off-the

Cortes is their...adopted cryptid gf, they kinda have this inherent understanding that Cortes is more a force of nature than anything else. She comes and goes as she pleases, is wholly aloof to the world around her outside of Raf and Magritte (whom are the clear objects of her affection during her little ‘human-kind’ cosplay adventure). Sometimes Cortes is gone for a month or so at a time, with no indication of where she went or what she’s doing. But Magritte and Raf both inherently kinda...know...she’ll be back and she’s fine. 

Raf and Cortes have a very quiet, chill kind of relationship--very low energy in the comforting way. The relationship version of “lowfi beats to study to” lmao. 

Magritte and Cortes have a very playful, mischievous relationship and Cortes encourages Magritte’s childish impulses--both good and peevish lmao they are a chaotic duo...but they somehow always get away with what ever trouble they end up finding themselves in together. 

Neither Magritte nor Raf (nor anyone, really) find anything unsettlingly strange or off putting about Cortes--she’s not even all that weird, really. Just a unique kind of charisma.