Klein bottle embedded in R^4 - クラインの壷

[ThitanKhronos]

Klein Bottle + Möbius strip

[MrCGangsta]

lol those asians make even mathematics cute ....

[StrattonLOLfail]

WUT????

[marinepower]

LOL WHAT

[paullimbers123]

@TheK154321

ummmmm.

someone obviously doesnt know what they're talking about.

this is pretty clearly a representation of the klein bottle in theoretical 4-space. if you dont no what that is, then you should probably keep your racist comments to yourself.

[TheK154321]

@paullimbers123

Never mind then. thanks! I hate being this racist theese days, I didn't post this comment. someone must've hacked me. thank goodness I changed my code. thank you. It makes more sense now.

[L00NGB00W]

Wacky. I thought Klein Bottles were an impossibility.

But apparantly they can be mapped.

Great job!

[TheseEyesGod]

You, my friend, are a freakin genius... in your ability to present something like this, so beautifully. You satisfy (at least to some extent, ho ho) even the math-minded among us, as well as us right-brain types, with your excellent, sufficiently simple visuals.

Kudos, man. This is excellent! And though it's not my thing, in that I don't get the math - I freely admid - I'm glad to see it there for those who do. Beautiful... Ah, this is art :)

♥ ☼ ♥

[generatorium]

The music?

[gigioneumatica]

i dont get the idea of showing something from the R^4 in a video. the simple klein bottle in R^3 is enought to freak your mind.

( also remember that the video belongs to the R^2 world. in conclusion you are showing something from R^4 in a R^2)

[TheseEyesGod]

@gigioneumatica

Great comment! I like that. Showing a R^4 something in R^2, or 4D to 2D. Cool!

♥ ☼ ♥

[kcox669live]

@gigioneumatica your logic is flawless sir... except, of course, that he has mapped it to 4D, which i'm guessing is the purpose of this vid........ ding-a-ling

[gigioneumatica]

@kcox669live but you can't map a 4D... you can't draw 4 different orthogonal axis. the 4th axis you draw is a linear combination of the other three axis. And it's even harder to draw them in a paper/computer screen ( 2D)

nobody can draw them

[kcox669live]

@gigioneumatica you CAN map a 4D, he did it in this vid. the only thing this mapping doesn't show is that all 4 dimensions would be at a 90 degree angle from each other in a 4D universe. i'm just tired of people pointing out the obvious on every 4D mapping vid. everyone knows that they are looking at a 2D picture of a 3D shadow of a 4D map... sheeesh!!!

[Thehamez]

klein bottles destroy my eyes.

[gregjockca1001]

they also make you sterile.

[GR1o6180339887498948]

This video is driving my eyes crazy O.o

[stockshunter]

what bloody software are u using man

[CoauthoredStaircase]

does a Klein bottle have parallel and perpendicular lines similar to the euclidean plane, or locally, or not at all?

[stigomaster]

I thought a 4D klein bottle wouldnt self-intersect

[FluffyBunniesOnFire]

It doesn't self-intersect, only the projections do.

[sillygramcracker]

@stigomaster

It's a 3D representation of a Klein bottle. It's impossible for us to actually see a 4D object, so we use 3D models.

[begvend]

Hi,

In timing between 5 & 5:22 minute the torus with 2 pinches, is it same the Bohemian dome?

Your job is very VERY ... superb.