TheAstronomyDude Especially if the students can print for free!

TheAstronomyDude I would buy him another

TheAstronomyDude yeah these are amazing learning materials, and enjoyably explained

TheAstronomyDude I did not understand you

curiousme Filament is expensive, so the university is broke now. I meant it as a joke.

Now do that with your frying pan! 😀

Elliot Grey I can always fry it in my Klein bottle pan. (Yes IN the pan)

w8 how can it be in the pan if the pan is one sided?? shouldnt be on the pan?

john smith so you're assuming it has a top side?

Jack Le did you just assume my genus??

oh, 3d printing is actually really old used to be everywhere in universities, etc, just named a rapid prorotyping machine not 3d printer

Jenny Tokumei This is exactly what I thought too.

F

I was totally thinking how 3D printing must have revolutionized the field of topology.

Gameboygenius The Klein bottle guy took over the channel! xd

Not at all, visualization in 3D is only really useful for teaching and has been done with animations for a long time, + you can make those shapes without a 3D printer aswell, it's just not as easy.

This is what happens when you do that

True, it's very unlikely to have had a significant effect on topological research. But occasionally it's helpful.

Britt Berg me too.

LazerLord10 do you mean a 4d printer?

No it won't. A 3D printer makes an object using three spatial dimensions, and forms a solid 3D shape. A 4D printer would need to create a 4 dimensional object that we wouldn't be able to see completely due to the fact it has created it using a geometric space with four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space.Time is often quoted as the 4th dimension in physics, but in reality it is a separate dimension that we can use to animate a 2D shape on a computer screen to show a 3D shape and create animated movies and the like. In modern physics, space and time are unified in a four-dimensional Minkowski continuum called "spacetime", whose metric treats the time dimension differently from the three spatial dimensions. Spacetime is not a Euclidean space. But a 4D printer, (if it could ever be created) would use 4 spatial dimensions, in Euclidean geometry, which we can only see with our human eyes 3 dimensions of, in our 3D world we are part of. There may be more dimensions, special or otherwise, but as of yet have not been proven, only theorized in string theory and so on, but, well there you are!

And 4-dimensional space to print it into. Alternatively, if you can manage to print a 3-dimensional object that can warp itself over time, you can simulate a 4-dimensional object by stretching one of its 4th dimensions through time. What a klein bottle would look like in this case, I don't know, but I'd be interested to see.

and that one rule is....? (Also, most of this comment chain is jokey, btw)

More like a 4d printer⚠️

Kaffeebohnson I thought it was going to be about the tequila bottle with a shot glass for a cap. very disappointed.

same

Kaffeebohnson the doc brown of maths

I like this geezer hes pretty cool too

I know right? This would be the perfect Christmas gift for him though - Modular Klein Bottles... Actually, I wouldn't mind a set myself, when will these be available in stores?

The klein bottles are evolving...

Arthur Bernardo Coopi No, like, they're grotesque. Like something out of an artsy sci-fi film, where you're in an exhibition with every wall painted blinding white... And then the 1-sided monsters start showing up.

It sounds like you might have trypophobia.

they do bear a mild resemblance to innards

Cajer 1618 Not really, no. I mean, I do have the baseline gut reaction to repeating patterns, like every other human, but not to the level, that I actually notice it. Anadice Brown Yeah, it all looks so organic. No clear edges anywhere. I hate it.

yeeeup

MrAntieMatter proabably.

MrAntieMatter proabably.

It goes beyond a mere Klein Bottle - that's for beginners!

every video is a klein bottle video.

Kerbalnaught Step 3. Get a 3D printer.

Step one. Be obsessed with klien bottles Step 2. ??? Step 3. Profit.

Mr Perry Do you not understand that reference? Shame

Bordermemes I don't... please explain further

Juan Coria its a southpark reference.

puskajussi37 what animations?

dude, they are all over the video, those moments when the modules he has created where explained with a 3D animation to make it easier to understand for example at 3:32

puskajussi37 now what about that is hard?

You sure about that?

Would an ant really get cut if it tried to crawl over a border of a piece of paper or something?

what? you dont get it?

it's almost like half scottish, half... some part of scandinavia/germany

stormhunter77 yeah I heard that as well, Scottish/Scandinavia (first I thought Dutch, but a Danish accent comes very close to that). I looked it up, he's from Switzerland, but there isn't any French in his speech, so that makes it even weirder.

Well Swizz has 4 Languages - Italian, German French and Romansh(whatever this is).

baasmans Can confirm, it's swiss. He's probably from the german speaking part.

We do

Emil Macko it's his sexy swiss accent

What? I would have sworn it is Scottish

ikr?

Dav Emil. Du er da dansk?

Or 'Tetrahedron'

I think its about exploring the possibilities of 3 dimensional space

maybe circuit layouts?

it's used heavily in general relativity and even on advanced classical Mechanics

en.wikipedia.org/wiki/Topology#Applications ;) It's actually quite a broad and important field; it's probably one of the mathematical fields with the most practical applications.

3 blue 1 brown. "who cares about topology?"

Bob Bobson Mathematics in a nutshell.

pramitbanerjee Now it is a Groß Bottle. (This joke makes only sense in german. klein = small groß = big)

I'm surprised by how truly gleeful this idea makes me XD

klein pretzels!

I Should Get A Nickname Super duper pooper scooper bottle!

One side to rule them all

Bradthewinner That is actually an amazing idea. I nees this in my life.

i want the stl files so i can print these myself

AlucardNoir Because topology allows you to get donuts out of mugs.

Calm down, bra. Not much of a fan as well but this Carlo guy is very nice, at least. His video of regular polytopes in higher dimensions is among my Numberphile favorites.

well, i love it .D

Mmmmm, non-euclidean geometries...

you must not like pure math enough to enjoy it the way he does

That's okay; as soon as they move in they evict themselves.

Lol needs more upvotes

Jason Emmons And soda out of a three handle mug

John T It's the holes.

Flash Lol, it's not the holes! It's the twists in going from atrium to ventricle to atrium to ventricle with the flaps and like I said, the ability for things to pass through channels within the walls.

Unless you're a quantum-size particle, you're not going to naturally pass trough anything that doesn't have a hole.

That's true, but you have to look at it in different paradigms. The words that explain the macroscopic scale don't do justice to the microscopic and vice versa. There is a certain element of 4 dimensionality in that on the macroscopic scale, the heart is shaped somewhat like a variant of the klein bottle but on the microscopic scale, things pass through the walls to almost make it a true klein bottle.

Batfan1939 What's QGame?

K1naku5ana3R1ka Typo. I meant to say *A* game.

K1naku5ana3R1ka Fixed.

I know that you can't, but I don't know how to explain why.

Sebastian Cor I think genus is defined only for non negative integers. you'd need to refine the definition if you want to consider other values if genuses.

I'm curious to how you perceived the definition of a surface's genus.

Diglettoss Toss its mentioned in the video. something along the lines of the number of ways you can cut a 2-manifold without it falling apart.

You'd have to be a half-hole.

DeadFish37 I think they are explaining that changing the genus is not the same as changing the borders. Those numbers have to be listed separately for a reason.

Yeah they should have mentioned that it creates another border, might have been accidentally cut out?

DeadFish37 you are not thinking in the fourth dimension!!!, they are not talking about the shapes but properties they have

They explained it's only a border if it's going to another side, like with the flat paper, a hole when both "sides" are the same side, means its only a puncture

simsom4343 Thanks, must have missed that

I think since they are theoretically always "filled" or "connected" they don't act as holes. If you put another structure at the point it's just extending it's surface(s) at that point (that's how I see it)

When he talks about the stand for the genius 22 structure he never fills that hole on the bottom.

+Gasduster99 Yes but I think in theory it should or is - I guess that is just for presentation/simplicity - I mean Kleinbottles are weird in 3D, too.

Holes add borders, but that doesn't affect the number of sides or the genus. It's the latter two properties that are the point of the super bottles.

No, because you're still on the same "side"