#non-euclidean geometry

[typhlonectes]

[knotty-et-al]

Pseudosphere and dini surface

^ Visualization about the transformation of a pseudosphere into a dini surface.

v Pseudosphere

[emperornorton47]

[internetgiraffekid1673]

Featured today on "Everyone In My Family, Including Me, Is Crazy and Likes It!"

I inform my brother that quadrilaterals are polygons and circles are not. This devolves into an conversation where my dad and my brother attempt to argue it is possible for a curve to be a straight line, and I attempt to explain that 1) no it's not, and 2) Planet Earth has Non-Euclidean geometry and should not be counted in purely mathematical discussions of polygons. The conclusion of this debate? It is mathematically, but not functionally, inaccurate to say you went straight up a hill.

[mathsbian]

Favorite genre of math?

I’m a huge slut for number theory. There’s so much cool shit there.

Non-Euclidean Geometry was also super interesting.

And with my computer science degree as well, I of course really like Computational Theory, which is right on the line between math and computer science.

[highladyluck]

Past me had the kind of fun current me no longer comprehends

[mausuwinasa]

Ooh I wanna make some stimboards for various non-euclidean geometries! I think I’ll start with Nil or Hyperbolic, since those are my favorites :3 I want some other suggestions tho!

Just pick a number from 1-7 (or a specific geometry if you know what they are lol) and a fun color or theme to go with it, and maybe I can make a stimboard for it!

Comment your requests on this post or put them in my asks, even if you don’t understand non-euclidean geometry it would be fun to get some random prompts :3

[ruberine]

@bexbashie figure you might enjoy this one

I love seeing a meme and being like oh, tumblrs going to love this one

[silenthades]

Song: “end of the world” by sompner

Part 2 of the previous post.

All throughout my life I’ve had odd dreams as well. I’m never lucid in my dreams and it never occurs to me that I’m dreaming, but they are very real. I can touch, taste, smell, read, write, and tell time. Had sleep studies done. They’re consistent in their rules, to get to each place I have to travel, the stories are cohesive, and I’m not always “myself” in my dreams. Was recorded on camera for a while. No sleepwalking, no apnea, etc, but sometimes I’d wake up with the bruises and such from my dreams like they just carried over.

My favorite dreams were the ones I call my “Void” dreams. They’re a special kind of dream that feels even less dreamlike than usual.

Backing up a little, I used to be an insomniac. Never did sleep well growing up. Plagued by nightmares and visions, I’d often wake up screaming, crying, gasping, and upset. When I’d lay down it would feel like someone put itching powder and wax in my blankets. I’d wake up frozen often as well. It wasn’t until later in life that I realized the reason for that was overstimulation giving me brain shocks, which was waking me up constantly and giving me panic attacks in my sleep. Didn’t help that we had a resident entity terrorizing my family and causing all sorts of issues. Made it difficult to separate the genuine health issue from the ‘maybe it’s ghosts’ excuse.

Either way I did end up finding a way to guarantee sleep.

It was by returning to that stirring, of course. Sensory deprivation. I’d turn out every light so there was nothing to see. Earplugs in so all I could hear was the rush of blood through my ears and my own breathing. Soft shirt and undergarment so I couldn’t feel the cloth on my skin. Soft blankets so I couldn’t feel the bed beneath me, and more than one blanket above for my body temperature to never plummet.

When I’d close my eyes, at first I would stop being in my room. I was in a dark space and that stirring inside me was at peace all around me. I felt like I had gone home, so I’d stay there for a while before my mind finally slipped into dreams.

And that is how we get to Void dreams.

They’re a different sort of dream than my normal vivid ones. I’m myself in these ones, and I am a wanderer and witness, according to those who have spoken to me in these dreams. The individuals in these dreams are most often not human, and if they are they’re usually fleeting dreamers themselves. Some of these individuals who speak with me give me very interesting conversations about time, impermanence, and transformation. Tell me their own stories while we sit at the edge of a cliff in the deserts of some dead realm, or the sum of their eternity as they take form in the basement of an inn at the edge of reality built above where lost things collect together and form consciousness from the memories held within them. I used to be scared in these areas. I’d get lost trying to navigate the non-euclidean geometries and end up in places I shouldn’t. I’ve learned how to navigate them now, though. I know how to get back to where I started or get lost in the folds to end up somewhere new.

The worst ones, however, were the ones with what I call The Shed.

The Shed is what I’ve drawn above. It was a little building made of a single layer of rotted wood panels and a now ill-fitting door. I’d be having normal dreams, or void dreams, and this one building would change everything.

The first time I saw it was in a realm with no stars. It was an eternal twilight after the sun had already vanished before the horizon and greyed the skies to near black. I was in a sandy desert and the shed was the only thing to be seen for miles. It sat there silently, surrounded by an old fashioned wooden livestock fence that was mostly rotted apart and half buried in the sand. It only had three real ‘rooms’. Once I was in the doorway, a short length of dark hallway led to another door inside. You could see the greying light from outside peek through the panels of the wall and sand only collected in the immediate entry. It was all old, greying wood. Inside, the air was heavy and stagnant. Dry, though, as though fresh air and dampness hadn’t come in for a long time.

I felt like I was being watched as I proceeded inside, past the first doorway. There was a room there, empty save for a few small things of faded, long-discarded trash, like paper that had soaked through and dried many times over years.

There was another door on the same wall as the door I entered in through. This door had nothing but darkness beyond it, but I opened it anyway. There was a staircase down.

It was a loop like that, with the bottom of the staircase leading to a mirror image of the room above- but instead of a hallway out, it was just another staircase down.

I would have headed back up, but behind me, two coyotes formed from the sand and hunted me every time I tried to turn back.

As I went down, details were lost. The trash, the size of the room, the width of the stairs- and then finally the wood disappeared entirely. The room was goon and I was walking down a steep, narrow pathway with stone stairs long since eroded into smooth steps down, down, down. I stopped hearing the coyotes a long time ago, but something else drew me on. The stirring I felt in my daily life wasn’t in me. It was outside of me, pulling me down toward it.

My path ended in a smooth sandstone wall. The space was so small I had a hard time being there and every shape was rounded and tight, like an unfinished tunnel. I didn’t feel like this was a wall in front of me, though. I felt like it was a doorway only I could open and that something was waiting on the other side. More than that, it felt like I was waiting on the other side.

I woke up.

The Shed invaded a lot of dreams after that. Something normal, then suddenly that same twilight would overtake the skies and everyone else would be gone. Those coyotes would form and force me back into the Shed and I’d come face to face with that door again.

It finally stopped when the last dream came. I ended up on an island off one of the coasts. Small island, likely unnamed. There’s a manor there that looked like it had been built in the time of those stupid sliding doors with the really crap latches. It looked abandoned, filled with dust, but there were scorch marks over certain areas as though there had been several small fires inside. Things had just been left there, papers strewn about and personal affects like journals, family pictures, and so on left behind. As I travelled through the rooms, it became clear to me that these scorch marks were probably once people and that something had hunted them down one by one.

There was one room at its center with that stupid sliding door. Everything I’d found in the multitude of other rooms had led to increased activity and struggle right near this room, where a message had been scrawled over it. I can’t remember what it said exactly, though. ‘Do not open’ maybe?

Of course I had to open it, though.

There was a monitoring room inside. Multiple computer monitors on two long white desks, old office chairs, papers and blood scattered about. Glass and all manner of things were below.

The adjacent wall was metal with a large glass pane now shattered and all around the room. Observation into… a twilight grey void without any stars. Impossibly, there was a rolling grass hill, and on it, the Shed. It felt angry somehow.

I haven’t seen it since then, but I still think about it often.

Anyway, the void stirs before I sleep. Now I’m tired and it’s time to rest.

[kris-and-the-pnictogens]

Chara's favorite number, and my own fictive exomemories of the Underground

so...I've been thinking hard about the whole...highest number thing.

it's a very haunting bit of text but I feel as though I can safely say now that it does not line up with my exomemories. so that's a definite point of difference. to a great degree my Undertale fictive exomemories are entirely consonant with canon and I've felt very strange about that, as if I were somehow obliged to choose a point of divergence. but now here's a point of divergence with canonical material that seems quite definite to me. I have different notions about numbers.

however, seeing that text has me convinced that there was some other issue of a mathematical nature that I stumbled into in the Underground, for you see, at some point I clued into the fact that things weren't linear down there.

at the time that I "fell", even as a child, I'd had a lot of experience in reading about mathematics and science—I was already clued into to certain...possibilities, you might say, that others might not notice. so at some point I realized fully that I inhabited some sort of non-Euclidean space, I think, and...I think it kind of messed with my mind. I could grasp it, but I was NOT okay with it, if that makes any sense.

but I can't remember what it was. it might have been realizing that Asriel and the other Monsters simply had a different math, a different geometry. like...what would it be like to live in a world where the "parallel postulate" wasn't the same as the Euclidean one? (this is a famous mathematical paradox: the parallel postulate can't be proved in terms of the other Euclidean postulates, and therefore one is free to define some other definition of what parallel lines are—and thus we have "non-Euclidean geometry", like hyperbolic geometry.)

but other possibilities occur to me. what would it be like to learn that the Monsters didn't have...oh, a concept of zero, say? or a concept of infinity?

humanity didn't always have these things. what if the Monsters didn't?

~Chara of Pnictogen

[felixwylde]

Dimensional Breaches and Biological Anomalies: Empirical Evidence from the Backrooms Exploration Initiative By Dr. Alexey Petrovitch Ivanoff, Dr. Serina Zhang, Dr. Micheal Torrez, Dr. Emilie Rousseaux, and Dr. Rajj Patel. Abstract:The recent empirical validation of the Backrooms, a complex network of extradimensional spaces, has revolutionized multidisciplinary scientific research, presenting…

[florbo-0]

Buncha squares if you ask me.

So am I actually, but I have 5 sides

[tagitables]

🤍

[laejoh]

First I was thinking Lovecraft!

[the-barefoot-hatter]

c'mon Sixer, it's like the World's Greatest Playpen! 100% safe!

[megarhyssa-sp]

from this:

@iowntheworldandyou you are so right. he was probably keeping it in his pocket. these two should not be parents 😂