#Non-Euclidean

[knotty-et-al]

Pseudosphere and dini surface

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

v Pseudosphere

[acrossdimension]

Hyperbolica (Snow Fight)

[ngeruma]

"A Touch Unreal - Non-Euclidean" | Perpetual Testing | Portal 2 Community Maps & Mods

By SkyGlass

A Non-Euclidean exploration of spaces that should not be, but do in fact, be. Some of them with really nice views too.

Full Video

More Test Chambers

[maybeasunflower]

Very nice. :-)

(Also: there are no squares on a sphere, because the interior angles of any quadrilateral with side lengths must add up to strictly more than 4 * 90 degrees on a surface with everywhere positive curvature, such as a sphere.)

(Aka why Saskatchewan isn't actually a rectangle)

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

[bumblebeebats]

"Don't just throw ripped jeans away, you can repair them using these 10 cute Visible Mending techniques!!" unfortunately my friend the first point of failure for every single pair of jeans i have owned in my life has been the Crotch and Ass. Knees: fine, cuffs: fine; but 3 years in, and all that stands between the world and my astronaut-patterned taint is 0.5µm of denim worn so thin that every squat threatens to tear it to shreds like wet toilet paper. If the Tiktok craft community could figure out a way to resurrect jeans afflicted in such a way that doesn't involve adding a whole ass buttpatch like some sort of inverse assless chaps situation then that'd be great

[swagrum76]

I have a terrible idea - Non-Euclidean straws. You couldn't even drink from them properly, as the liquid that is sucked up into it might come out somewhere else.

[himmurf]

This cryptid's addition has funny consequences. Like vampires not being able to echolocate like bats since their sounds would be immune to reflect and bounce. Does this mean they are also immune to the reflection of noise not their own? Can a vampire home in on your location by sound without the possibility of being turned around by confusing acoustics? Like Tolkien elves and their non-Euclidean eye balls?

Can a vampire see since visual perception is the reflection of light into the eyes? Do they somehow still see things as if they were devoid of light as a concept? Does the vampire themself reflect any light?

What if you throw something at the vampire that should bounce off? Does the projectile's path warp and bend around the vampire so the objects flies harmlessly around and past them?

What happens if a vampire washes a spoon face up under a heavy tap?

hypothesis: vampires are magically vulnerable to light originating from the sun

observation: moonlight has no effect on vampires, despite being a reflection of the sun

conclusion: this aversion is not a result of light or its origin, but some property of sunlight only present in direct contact

hypothesis: vampires are extremely sensitive to uv radiation

[the-barefoot-hatter]

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

[pep-the-artemis]

Scientists want to ignore the fact that the earth could very well be flat.

note, I'm not a flat earth believer despite what the click bait title says, I just realised that everyone who is a flat earth believer is illiterate and was curious about if I could do a better job at the flat earth.

The core of the globe earth model is the assumption that space-time is euclidean; but it doesn't have to be and all studies conducted trying to prove it have only heavily implied the universe is euclidean. But what if it wasn't? Then it's entirely possible to have a flat plane with the properties of a sphere; elliptical space has this property but we don't live in one of those due to use observing properties of space (mainly other planets exist) which show we don't.

So, are flat earth believers justifiable in their madness, no. Although possible we have insufficient evidence to make any claim that we live in a non-euclidean world so its crazy to jump to bold claims.

[etheasavatar]

What is Ethea?

I'mma just pretend that one of ya'll asked me this question. What IS Ethea?

Ethea is a parallel reality to that of Earth's, though only occupied by a single planet. Sorry fellas, due to size restrictions, I couldn't fit a sun nor moon into there. We got a lighthouse that emulates them. Magic, a fix-all to every problem.

That planet. That planet is also named Ethea. It features one primary Pangaea-like continent. It is also named Ethea. Don't worry, that's all the Etheas.

So, what's it like? Alright, imagine a stereotypical fantasy environment. Now throw in a few kingdoms. Three, actually. Well, one of them is a kingdom-sized refugee camp, and one of them prepares for a war...and then prepares for a war some more. Now divide it into different biomes, cities, and different general locales. Now throw away your map because those do NOT work here.

Traveling in Ethea quite genuinely requires you to use an atlas. Standard single-page paper maps do not work. You can't just travel between regions, you have to find Paths, else you'd walk into a procedurally generated null-energy dreamscape and nobody gets anything good out of those. Put simply, each region is larger on the inside, by a large volume.

Paths are points in space that connect two locations, though many of them require specific criteria to activate and utilize. They, of course, only trigger if you're aware of them and want to use them.

I could go on, but I think that's good enough for now. Nice to meet ya'll, I hope I enjoy this platform.

[knotty-et-al]

Knotty's art of today [2023/08/07]

[typhlonectes]

[prism-forgone]

frisky

[kermit-coded]

gorgunit shippers rise up

[chanceofwhat]

@the-barefoot-hatter if you liked my other one you’re gonna love this

I couldn’t stop picturing it and laughing so I drew a little comic for my version of the non-Euclidean geometry au. ¯\_(ツ)_/¯ It’s a bit of a mess, but I enjoyed making it and I think it turned out okay considering I don’t tend to make comics. Long story short, a new player has arrived.

[giulliadella]

Speculative Biology of Euclydians (and Bill Cipher) part 1

Part 2

We're doing this, babies!

This analysis is based on two assumptions:

Before Bill Cipher became a demigod, he was a biological, living organism and so were the rest of his species.

Even after Bill Cipher became a demigod, he still retained some physical characteristics of his biological form.

I will clearly specify which of his abilities are innate abilities of his species, which ones are definitely his divine abilities and which ones could be both.

This is part one. This analysis became VERY long, so I'll separate it into FIVE parts:

Part 1: What is Euclydia and what are Euclydians?

Part 2: How Euclydians function as animals? (This is where I explain how are they built, what their organs do, how they feed, move, speak etc.)

Part 3: Reproduction NSFW (this one I separated because it's NSFW. It'll be nothing explicit, but I doubt your boss would be thrilled if he found out that you're reading about how triangles fuck in your office)

Part 4: Growth and development (here I will also talk about Bill's deformity and Euclydean society)

Part 5: How Bill Cipher destroyed Euclydia and got his god like powers?

SO, without further ado:

What is Euclydia and what are Euclydians?

I'm gonna drop a bomb first.

Euclydia IS NOT a flat two dimensional plane. Before you load your shotguns, let me explain!

There are many proofs both in the Gravity Falls show and The Book of Bill that Euclydia isn't a flat plane like the imaginary two dimensional world from Flatland by Edwin A. Abbot.

The first one is actually Bill himself. Bill's species has complex camera lens type of eyes. Such eyes are possible in 2D world, but not on the front, like Bill has. He was born like that, so that is proof that Euclydia isn't 2D.

Next, when Bill is talking about his home in Weirdmageddon part 3, he shows an image of his home planet:

This planet has RINGS. That is COMPLETELY impossible in 2D. Even if the planet was completely flat, the rings would go through it. They would never be able to actually encircle this planet. So, if Euclydia was two dimensional, Bill's home planet would not be able to exist.

In the Book of Bill, we see image of Bill as a baby. In that image he's standing on some kind of field with grass and you can clearly see that there's grass in front of him and behind him, and that's impossible in 2D:

(also sorry for the shit quality of this pic)

But the best proof is that image from thisisnotawebsitedotcom.com that you get when you type VALLIS CINERIS in the computer. It shows Bill Cipher as a child with his parents. The parents are holding him in a manner that is completely impossible in 2D:

The image quality sucks, but you can clearly see that his parent's hands are IN FRONT OF him and he is also IN FRONT OF his parents. The position of "in front of" isn't possible in two dimensions and yet on this image the overlap happens many times. (I circled his parents' hands in red where they overlap with Bill and I circled him in blue where he overlaps with his parents. Bill's bow tie is also in front of him.).

With all that being said, what is Euclydia?

Well, just like Bill said, it's a flat world. Not two dimensional, but flat. The third dimension of Euclydia is limited somehow. Basically, in 3D, creatures are defined by 3 axis:

x axis is left and right (width)

y axis is up and down (height)

z axis is towards and away from (depth)

All three dimensional objects have both width, height and depth. Two dimensional objects have just width and height, so just x and y axis. And Bill has depth. It's a very limited depth, but it is depth nonetheless. So he's not really a triangle, more like a very thin pyramid. This is his side profile lmao:

So Euclydeans have some depth, but for whatever reason, they can't move on z axis. They can only move left, right, up and down. They also can't turn around.

This is how thisisnotawebsitedotcom.com explains Euclydian movements:

Two dimension to and fro, you always know which way to go. If you're lost, don't be afraid, in Euclydia you've got it made. Run too far right to right of frame, you'll appear on left again. Jump too high don’t cry or fret, pop up from the ground I bet. In this place, there is no fear, loved ones will be ever near. Roles and rules always flea/clear. Euclydia, we hold you dear.

So, if they move too far left, they'll come from the other side. This is actually something that in possible ONLY in non-euclidean geometry, which means that Euclydia, ironically, is a non-euclidean place. It's actually a sphere (or a similar elliptical body).

In non-euclidean geometry of the sphere, there exists something that sounds paradoxical: a straight line is actually a circle. But it's actually very easy to understand with this example:

Imagine that you're flying a plane in a straight line. You feel like you're going in a straight line, but your plane is actually following the curvature of the Earth. If you manage to fly around the entire Earth, you will appear on the same spot where you started flying. You were flying in a straight line, but because Earth is a non-euclidean sphere, you were actually flying in a circle. And both of those are true!

The plane is very very small compared to the size of the Earth. So, to the plane, Earth's curvature is so negligent that we could say that in a small radius around it the Earth is actually a flat plane. So, for example, houses, neighborhoods, even cities are built relying only on euclidean geometry (the geometry of a flat plane) because the Earth is so goddamn big.

And Euclydia is actually a whole fucking dimension. Let's say that our dimension is our universe. Our universe is approximately 93 billion light-years wide. So let's say that that's the size of Euclydia. How tiny is Earth compared to the Universe? That's why planets and everything else in Euclydia can be treated as a flat plane: every object is so small compared to the size of this giant sphere that the curvature could be completely omitted from the equation.

Now this is my theory, but I imagine that Euclydia looks like a giant soap bubble. Soap bubbles are made when two thin layers of soap molecules trap a thin layer of water:

Euclydia is the water - that thin layer is where all the planets, stars and living beings on them are located. That's why movement on z axis is so limited. The soap molecules are membranes that separate Euclydia from the other dimensions, one inside the bubble and one outside.

Since Euclydians can't move across z axis, they have eyes on their sides that can see only left and right. Their vision is limited to one dimension. But Bill's eye is located in a spot that allows him to see both left and right, but also up and down. He can see two dimensions, just like us! Here's a diagram I made, so you can understand better:

(there are stars outside too, but I didn't want to clutter this image more)

So, now that I've spent SO MUCH TIME explaining what is Euclydia, let me tell you what are Euclydeans.

Euclideans are animals (or their equivalent in their dimension). Animals are defined as multicellular heterotrophic organisms with an internal digestive tract. This basically means multicellular organisms that eat.

Euclydeans have to be multicellular because they have extremely complex structures such as: camera lens eyes, teeth, fingerprints, exoskeleton and so on. These traits cannot be achieved by a unicellular organism. And they definitely eat their food, we've seen Bill do it. So they are (their dimension's equivalent of) animals.

And how they function? What type of animal are they? Well, see you at part two, if this didn't bore you to death already!

Thank you to @forseenconsequences @extremereader and @ok1237 for asking me to do this. Hope you like it, guys!