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How to knit a klein bottle hat Videos

A mirror paradox, Klein bottles and Rubik's cubes

The Mathologer puts the latest $2000 addition to his Klein bottle collection to work. A couple of first-ever fun mathematical stunts in this video. This video finishes ...

User Comments

https://lh3.googleusercontent.com/-Tv6oaBvQvI0/AAAAAAAAAAI/AAAAAAAAAEU/cIzJzMEgj4U/photo.jpg?sz=64
Every time I see something interesting that is related to math (I know everything in the universe relates to math but still), it always has someone wearing glasses. Just an observation I had
https://lh3.googleusercontent.com/-Tv6oaBvQvI0/AAAAAAAAAAI/AAAAAAAAAEU/cIzJzMEgj4U/photo.jpg?sz=64
Ah, gotta love it when you comment on a video and the youtuber who did it, replies ^-^
https://lh6.googleusercontent.com/-DS-q02P8PoE/AAAAAAAAAAI/AAAAAAAAAJE/Pc40V0POuuA/photo.jpg?sz=64
+Bigfunnyhah I also own contact lenses but for math videos it's strictly glasses :)
https://lh6.googleusercontent.com/-5qN4uAJLu6E/AAAAAAAAAAI/AAAAAAAAAIU/lwkkGn04YYM/photo.jpg?sz=64
Question. How do you create a Mobius loop in two dimensions? A Mobius loop is a Three- Dimensional object like the Klein bottle is a four dimensional one. If that is true how does one walk over a Three dimensional object in a two dimensional universe.
https://lh6.googleusercontent.com/-DS-q02P8PoE/AAAAAAAAAAI/AAAAAAAAAJE/Pc40V0POuuA/photo.jpg?sz=64
Yes, it is possible that our universe is curved and that the angles in triangles actually don't add up to 180 degrees :)
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Aah I get it. So even though the object itself is 3D, its surface can be used as a 2D plain. So the 2D universe can be bent an manipulated in our 3D world. If our 3D universe is susceptible to the same rule, wouldn't that leave us open to the same type of phenomena that enables us to draw a triangle on a ball with three 90° angles?
https://lh6.googleusercontent.com/-DS-q02P8PoE/AAAAAAAAAAI/AAAAAAAAAJE/Pc40V0POuuA/photo.jpg?sz=64
+Adriaan de Clercq Let's start with your last question. >If that is true how does one walk over a Three dimensional object in a two dimensional universe.It's important to realise that there is not just one infinitely many 2-dimensional universe. In fact any surface in space is a possible candidate. So, in particular the surface of a ball is a possible 2d universe and so if you are a flatlander who lives in this surface then in some sense you are constantly walking over the 3d ball.>How do you create a Mobius loop in two dimensions? If your 2d universe contains Mobius strips, for example, if your 2d universe is a Klein bottle, then this is clearly not a problem. I guess what you are really asking here is to what extent it is possible to squash a Mobius loop into the x-y-plane. In that case the sort of pictures of Mobius loops as on some of my t-shirts are pretty much the best you can do. Or you go for setups like in the game packman where the two sides of a rectangle get identified with a twist (by definition or teleportation :)
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I have a question/observation that I might just be overthinking. in the segment around 6:50 where the man is walking around the mobius strip, you show him walking around to end up upside down. however, in 3D, when he reaches the left side where it flips, he would actually begin walking on the "back side" of the strip where he started (still upside down) and continue around until he comes around the left side, right side up again. is it portrayed the way it is in this video because we're viewing it in 2D? and do the laws of the 3-dimensional world not apply to the 2-dimensional one? I was under the impression from the bit at 5:10 (about the bridge) that even if it doesn't necessarily make sense in 2D, it still is possible because of the 3D laws.. so I would think he would still end up right side up going around the mobius strip in 2D because that is the way it actually is, whether or not it "makes sense" in that dimension. does that make sense?
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
+Mathologer ah, I didn't see that video! thanks, that makes perfect sense now :)
https://lh6.googleusercontent.com/-DS-q02P8PoE/AAAAAAAAAAI/AAAAAAAAAJE/Pc40V0POuuA/photo.jpg?sz=64
+Ashley Seeling Actually, quite a few people who watched the video left similar comments. The important thing to keep in mind here is that a mathematically perfect Mobius strip does not have any thinkness and in this scenario the little man is supposed to be part of the strip and not sliding around on it. I also talk about this at the beginning of a follow-up video: https://youtu.be/G2hsSMhCgAY Hope this helps :)
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
Is this guy working for Tim Heidecker?
https://lh6.googleusercontent.com/-DS-q02P8PoE/AAAAAAAAAAI/AAAAAAAAAJE/Pc40V0POuuA/photo.jpg?sz=64
+HillDueceua No, I don't :)

Top N Facts About The Klein Bottle

In honour of Felix Klein's 163rd birthday, Matt Parker (@standupmaths) and Katie Steckles (@stecks) have put together a rundown of N interesting facts about ...

User Comments

https://lh3.googleusercontent.com/-48wj45Rf_uA/AAAAAAAAAAI/AAAAAAAAABA/DH2eNPxqHiE/photo.jpg?sz=64
The Klein stein is a perfect way to limit how much someone drinks!
https://lh5.googleusercontent.com/-V-DrGbKnR3Y/AAAAAAAAAAI/AAAAAAAAAKY/706psiJXreU/photo.jpg?sz=64
Now tell me how to wash it

Demonstrating the Crochet Klein Bottle Hat

I demonstrate the crochet klein bottle hat that doubles as a neckwarmer and vice versa. Each direction creates a whole new look. Really! Visit the link here ...

User Comments

https://gp6.googleusercontent.com/-7vafQf6IfZU/AAAAAAAAAAI/AAAAAAAAAAA/lS2enxaQIQg/s48-c-k-no/photo.jpg?sz=64
@jgilferez Thank you. You just gave me a new idea. Somehow I can come up with one.
https://gp6.googleusercontent.com/-7vafQf6IfZU/AAAAAAAAAAI/AAAAAAAAAAA/lS2enxaQIQg/s48-c-k-no/photo.jpg?sz=64
Thank you. You just gave me a new idea. Somehow I can come up with one.
https://gp4.googleusercontent.com/-UI_o-1onvhc/AAAAAAAAAAI/AAAAAAAAAAA/hIdhyQsAuDU/s48-c-k-no/photo.jpg?sz=64
Is next level a "projective plane hat"?
https://gp6.googleusercontent.com/-7vafQf6IfZU/AAAAAAAAAAI/AAAAAAAAAAA/lS2enxaQIQg/s48-c-k-no/photo.jpg?sz=64
Thank you. Good to see you here too!
https://gp4.googleusercontent.com/-UI_o-1onvhc/AAAAAAAAAAI/AAAAAAAAAAA/hIdhyQsAuDU/s48-c-k-no/photo.jpg?sz=64
@strawberrycouture Nice!
https://gp5.googleusercontent.com/-LwlrGDvggrg/AAAAAAAAAAI/AAAAAAAAAAA/iw9CceoMtB8/s48-c-k-no/photo.jpg?sz=64
brilliant and beautiful

Klein Bottles - Numberphile

Cliff Stoll is passionate about Klein Bottles. Don't miss the video about how he uses a robot to store 1000 bottles UNDER his house...

User Comments

https://lh3.googleusercontent.com/-j4gBUec-mGc/AAAAAAAAAAI/AAAAAAAAABc/dpvDWTqVWvI/photo.jpg?sz=64
So what happens if you fill it up with water?
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+Ross Kopynets you get a badass water bottle
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This guy was so fascinated about klein bottles. I wish his wish about living in 4 dimensional world comes true.
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+Shivanshu Siyanwal his internal organs would fall out of his body if he did lol
https://lh6.googleusercontent.com/-r-z8frgVfvs/AAAAAAAAAAI/AAAAAAAAABE/xNJ7KlgGftQ/photo.jpg?sz=64
Admit it. Nobody is here for Klein Bottles, everyone is here for the guy.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
+ArtificialPenguins nope, I was actually here for the Klein Bottles but I decided to stay for him
https://lh3.googleusercontent.com/-dBXrJoE3wjU/AAAAAAAAAAI/AAAAAAAAAI4/MGBMBUoywtg/photo.jpg?sz=64
+Nicholas Keough Klein bottles are the complete opposite to "2edgy4me"
https://lh3.googleusercontent.com/-B1qVoTKyZ8Y/AAAAAAAAAAI/AAAAAAAAAMI/CRPUB84uUY4/photo.jpg?sz=64
Actually, im here for the lack of edges.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
I bet he snorts 20 pounds of 'math' a day. No? I'll just show myself out.
https://lh6.googleusercontent.com/-YG9gf2geqDw/AAAAAAAAAAI/AAAAAAAADPM/ny7FkF3E3r0/photo.jpg?sz=64
+Stijn S. Sch. he uses Klein bottles as a bong, so he can smoke an infinite amount of weed through it
https://lh6.googleusercontent.com/-RuFDXmYxxnY/AAAAAAAAAAI/AAAAAAAAAK0/eyxnRAtYZoE/photo.jpg?sz=64
+Henry Davies he's high on klein bottles
https://lh3.googleusercontent.com/-kf7TJbE6peQ/AAAAAAAAAAI/AAAAAAAAAFc/Rcv8rkpWdR0/photo.jpg?sz=64
That joke was so good I kept a straight face

How to make a Klein Bottle (in three dimensions) - Numberphile

Cliff Stoll on how he makes Klein Bottles from glass. More videos on Klein Bottles: //bit.ly/KleinBottles ACME Klein Bottles: //bit.ly/ACME_Klein ...

User Comments

https://lh4.googleusercontent.com/-0tI4-MeBW9U/AAAAAAAAAAI/AAAAAAAAAGw/doXoUKAy9_0/photo.jpg?sz=64
I, Joshua Allan Rivera, have cracked PI. With each step subtract the whole number and reciprocate the decimal. On the 81st step the reciprocal collapses into the whole number of 158. So I have cracked the chief of all irrational numbers. Bow down Numberphile. Bow. 1))) 3.1415926535897932384626433832795 2))) 7.0625133059310457697930051525706 3))) 15.996594406685719888923060404755 4))) 1.003417231013372603464147175288 5))) 292.63459101439547237854369576041 6))) 1.5758180896283656987656107376674 7))) 1.7366595770643507716201135470073 8))) 1.3574791275843891875198494723762 9))) 2.7973661196874565661571990519128 10))) 1.2541290322091560577073406952356 11))) 3.9350088862612480037552103620699 12))) 1.0695085519439577024570816127689 13))) 14.386718929294697189230321745787 14))) 2.5858573869756323624588253438221 15))) 1.7069000446717813965322191935073 16))) 1.4146271563249185387681830023868 17))) 2.4118053647609123920687426940947 18))) 2.4283316478418973607745191530978 19))) 2.3346395369998732207614847989982 20))) 2.9882900537254175472322442805887 21))) 1.0118486938429068680936409510052 22))) 84.397488301939923706531979292942 23))) 2.5157973080454070252970422376889 24))) 1.9387460624590295622430464768696 25))) 1.0652508063581292431332464677943 26))) 15.32548110611073602394571507566 27))) 3.0723749588702006345779533262055 28))) 13.816933586013212270601475523479 29))) 1.2240897144163038431531065726785 30))) 4.4624984355250002738912720570324 31))) 2.1621694760218170962874670785563 32))) 6.1663885493806942267743835589265 33))) 6.0100289576539108654303488981844 34))) 99.711259585390978480295927044239 35))) 1.4059564476031648624515259404503 36))) 2.4633184320736083216927294940426 37))) 2.1583427957408092263593030738788 38))) 6.3154120484072829854947248906933 39))) 3.1704559323261083625529774566443 40))) 5.8666189340177759592735616018578 41))) 1.1539097067310188125289471205896 42))) 6.4973159993583495866318524023333 43))) 2.0107939444743920679611387898079 44))) 92.644538090077731563507603032398 45))) 1.5514986862597982088801514015294 46))) 1.8132409467407566040304245314636 47))) 1.2296478725127180423650761132995 48))) 4.354492767811813177152563505038 49))) 2.8209320211882636616609813228906 50))) 1.21812765757698569150349009692 51))) 4.5844713646505890790782709179143 52))) 1.7109478076788652411227806185597 53))) 1.4065730130947945554442173469925 54))) 2.4595828247135648906265336814837 55))) 2.1758863609040443314429418578343 56))) 5.6854891695982891723066415781112 57))) 1.4588122531330738276365477663438 58))) 2.1795407449808455106267313513363 59))) 5.5697663508452414541270533175533 60))) 1.7551054015676990370397834525909 61))) 1.3243184301474565965543281323395 62))) 3.0833893699637541340260888081143 63))) 11.991936147672756256297986350554 64))) 1.0081294066620748265867079846381 65))) 123.01020745649045328147095449501 66))) 97.967598582004154377626904541468 67))) 1.0334864256712051559367436133124 68))) 29.862846808995085347371877455577 69))) 1.1589542773701048220312197387701 70))) 6.2911172731239384093636709959355 71))) 3.4350417935326921807618971873766 72))) 2.2986297290649910429645572793229 73))) 3.3486284273538256668528458594063 74))) 2.8683834178131788559015206372194 75))) 1.1515650569632787500390873367452 76))) 6.5978268344680558421016436283612 77))) 1.672725181180259979293684573795 78))) 1.4864911080711354309165526675787 79))) 2.0555360281195079086115992970123 80))) 18.006329113924050632911392405063 81))) 158 note: this must be calculated consecutively on a scientific cpu calculator with no break, as a break will cause the infinitude of the decimals to stop and round off to the 32nd numerical position. For example if you start at step 79 with just the published number, you'll get 157.99999999999999999999999998151, the only way to get 158 is to start from the beginning and do the subtraction to reciprocal calculations without breaking.
https://lh4.googleusercontent.com/-0tI4-MeBW9U/AAAAAAAAAAI/AAAAAAAAAGw/doXoUKAy9_0/photo.jpg?sz=64
+Derp Taderp so actually I cracked it to 51, but also explained is a process on the second to last step where two brief calculations do collapse PI into 13..... First multiply Pi to 7.06251330593104576979300515257063.1415926535897932384626433832795 (7.0625133059310457697930051525706) =22.187539917793137309379015457712then follow the same process of subtraction of the whole, then reciprocation of the decimal. 1))) 5.33219813556190662964102013491842))) 3.01025169304011781039244152586393))) 97.5448636714651574595145652534684))) 1.83532148016212026530077937001085))) 1.19714388262339275190899016392316))) 5.07243738275316756255954841740327))) 13.8050266587837440112656310338678))) 1.24219488769580248601361434600469))) 4.1289063097648990630767725383510))) 7.757572160926897087376558893952211))) 1.320006266830726773216949434842712))) 3.124938801679682337158350535063613))) 8.003918610999619662194131407035114))) 255.192464905819777001717548750115))) 5.195752419074228936567047129163716))) 5.108493702041055978153887836920217))) 9.217124876258549297531324609956218))) 4.605644536138797106335851756435819))) 1.651133528546895771983958567228920))) 1.535783301209589388376433354570321))) 1.866426216984349183239120711582522))) 1.154166368003686165393579340753423))) 6.486499052608476134475642934302624))) 2.055502461183163431969233162908125))) 18.0172190328624225761724464784926))) 58.07527100911219425159706931427527))) 13.28532740287117228377837015273928))) 3.504745740988321369710883633550129))) 1.981195518444478860873374449490330))) 1.019164866942454542377203933372131))) 52.17881256377378706549142487333932))) 5.592448197684163389577740500222233))) 1.687911287280350846249174863261634))) 1.453675813277447729354831801668835))) 2.204217131999595847358282172772536))) 4.896748819300718775989612061025137))) 1.115139466567456527150581675256438))) 8.685119271541283509883513899990639))) 1.459599870472688337334801073077640))) 2.175805661066705784113322587984741))) 5.68809897208356048303235177528442))) 1.453279310928200716448557932332743))) 2.206145252807268868624751641792644))) 4.850948476290787001913454273117945))) 1.17515928151010514972578375594546))) 5.709089414952348937695427390037847))) 1.410259381840018522444968068441548))) 2.43748234474245863078446856897649))) 2.285806529149627154163207512738450))) 3.498870382616325681850277751165951))) 2.004528700933296700722622613773752))) 220.8138746031177510392152318508753))) 1.228690508549165792982047399008554))) 4.372721921622784179665391320096955))) 2.68296534758708658547696419351956))) 1.464203130558520099608680184987557))) 2.154229332311524092346010154229358))) 6.483850931677018633540372670807559))) 2.066752246469833119383825417201560))) 14.980769230769230769230769230769 Special note on this one....if you subtract 14.98 and multiply by 100, then reciprocate, you get the whole number 13.61))) 1.019607843137254901960784313725562))) 51There you have it... I cracked PI twice in one day!!!!
https://lh4.googleusercontent.com/-s0cCFfbXUos/AAAAAAAAAAI/AAAAAAAAAAs/HxMVGX97gGI/photo.jpg?sz=64
This is pretty cool... but 3D printing will make this MUCH easier
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Haha I like to think of myself as a polymath, +RedsBoneStuff (or, at least, an aspiring polymath =p).I'm mostly interested in the idea of dimensions (but I also really like numbers... even though I struggle to count haha)
https://lh6.googleusercontent.com/-iJX-SHgoWxE/AAAAAAAAAAI/AAAAAAAAACY/-ImcaJTtwWY/photo.jpg?sz=64
Hey, Static, I had no idea you were into math :P
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Cool guy! I read his book back in the early 90s: "The Cuckoo's Egg". Also saw a talk he did on it.
https://lh6.googleusercontent.com/-obFa8lJgbFU/AAAAAAAAAAI/AAAAAAAAAI8/sLN71w3pIDc/photo.jpg?sz=64
Wow this guy wrote the Cuckoo's Egg? He's a legend
https://lh4.googleusercontent.com/-41MW73526Mg/AAAAAAAAAAI/AAAAAAAAABQ/XlbLlVRtuXI/photo.jpg?sz=64
Feel like I'm the only one here that finds this guy extreamly annoying... ._.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
+Jakob Öhrnell Yep.
https://lh4.googleusercontent.com/-41MW73526Mg/AAAAAAAAAAI/AAAAAAAAABQ/XlbLlVRtuXI/photo.jpg?sz=64
+Sherlock Combs Could ask you the same considering I think the way you're feeling about him is weird. So, what the hell is wrong with you?
https://lh6.googleusercontent.com/-3Y5EFdQ99JQ/AAAAAAAAAAI/AAAAAAAAABM/iUmNFqW3jJQ/photo.jpg?sz=64
What the hell is wrong with you?
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
what is the purpose of such a contraption?
https://lh4.googleusercontent.com/-s0cCFfbXUos/AAAAAAAAAAI/AAAAAAAAAAs/HxMVGX97gGI/photo.jpg?sz=64
+Carlos Eddy Absolutely my pleasure. One of the best ways to learn something is to attempt to help someone else understand it.
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
+777static777 excellent summary. thank you
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Yeah, very cool concept indeed.I just watched the rest of the other videos in the playlist the other day and would highly recommend.Essentially, a Klein Bottle is two Möbius strips sewn together, creating a shape with only one side, and no edges.
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
oh yeah! im familiar with the Möbius strip. i remember constructing these in art class as an exercise where "art meets science", it was pretty mind-blowing
https://lh4.googleusercontent.com/-s0cCFfbXUos/AAAAAAAAAAI/AAAAAAAAAAs/HxMVGX97gGI/photo.jpg?sz=64
+Carlos Eddy I'm not sure what everyone else is on about but, from my understanding of Klein bottles:They are similar to the mobius strip - the inside of the bottle is simultaneously the outside.
https://lh3.googleusercontent.com/-PmlkEl9MhaU/AAAAAAAAAAI/AAAAAAAAAE0/B6CU_9jsHvs/photo.jpg?sz=64
To allow humans to think beyond the natural, no offence to the natural world, still awesome just not enough.
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
+Jorge Salas in all honesty i clicked thinking it was a rather interesting-looking BONG, but was blown away by the presenter's colorful "mad scientist" personality. needless to say, im now a fan
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
+Carlos Eddy With simple philosophical thinking you could have came up with the purposes yourself since the purpose is what the possessor makes of it.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
+Carlos Eddy a tool to understand the 4th dimensional manifolds. A tool to study glass engineering. A tool to study the forms of art. A tool to study theoretical physics. A tool to demonstrate to math novices that mathematics is not about numbers.
https://lh6.googleusercontent.com/-xDsC-d8MhY4/AAAAAAAAAAI/AAAAAAAAACE/MTYaC0lMHA4/photo.jpg?sz=64
+Carlos Eddy I'm not sure about ordinary Klein bottles, but you can use a KleinStein to drink beer without your boss noticing.
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
+CastelDawn by asking a question?? i think you're just too accustomed to YT confrontations
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+Carlos Eddy you failed pretty hard there
https://lh4.googleusercontent.com/-5FqoFrSp-9A/AAAAAAAAAAI/AAAAAAAAABM/5WzZPiWRoas/photo.jpg?sz=64
+Carlos Eddy Did you guys not see the other videos? Klein bottle
https://lh3.googleusercontent.com/-kRItXIZw9Dw/AAAAAAAAAAI/AAAAAAAAABU/UKBf0z_zljo/photo.jpg?sz=64
+Carlos Eddy It contains the whole universe :)
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
+ACoolStupidDog thank you! that's what i was wondering, if perhaps it's a useful teaching tool. I was genuinely curious. Now i want to know more and will be researching Klein Bottles. 
https://lh6.googleusercontent.com/-l3LI_XT0hFk/AAAAAAAAAAI/AAAAAAAAAnE/bzKzRSLmK_Q/photo.jpg?sz=64
+Carlos Eddy Math is an art in its own right, despite it's many applications.
https://lh3.googleusercontent.com/-SN_zL5aYLmI/AAAAAAAAAAI/AAAAAAAAAIk/AbpzNR6WGGo/photo.jpg?sz=64
+Carlos Eddy Well, I think it can be many things.For someone who teaches maths, that can be an useful contraption to show what it would look in 3D.It can help learning the concept of a fourth dimension.And it looks cool...
https://lh3.googleusercontent.com/-GeleraWCSwM/AAAAAAAAAAI/AAAAAAAAAMI/a2FA05-WEKs/photo.jpg?sz=64
+Carlos EddyYeah! Science, bitch!
https://lh6.googleusercontent.com/-ykwJ0vNC1og/AAAAAAAAAAI/AAAAAAAAIes/iRILg1kADdg/photo.jpg?sz=64
well, no. i'm all for "art for art's sake," but i thought this was science.
https://lh3.googleusercontent.com/-GeleraWCSwM/AAAAAAAAAAI/AAAAAAAAAMI/a2FA05-WEKs/photo.jpg?sz=64
+Carlos Eddy Does everything needs a purpose?It looks cool. It's decorative.

Paper Klein Bottle

A flat folded paper Klein bottle to use as a pattern for a knitted Klein bottle. This could be done with a square and then you could call it Origami.

Bizarre Nested Klein Bottles Will Blow Your Mind - ...

Astronomer and the OG 1337 hax0r Clifford Stoll now makes the theoretically impossible Klein Bottles. If you don't know what they are, look it up. They'll either ...

User Comments

https://lh4.googleusercontent.com/-n5ywOM1DWhA/AAAAAAAAAAI/AAAAAAAAC30/g77C1EbE8pc/photo.jpg?sz=64
actually it has one side, not no sides...
https://lh4.googleusercontent.com/-n5ywOM1DWhA/AAAAAAAAAAI/AAAAAAAAC30/g77C1EbE8pc/photo.jpg?sz=64
+Linj Karma oh whats the difference?
https://lh3.googleusercontent.com/-dHAPVcl4gN0/AAAAAAAAAAI/AAAAAAAAACk/JNbkJV9WEQI/photo.jpg?sz=64
+stuffandpoop side and surface are two different things in mathemathics, so nope
https://lh5.googleusercontent.com/-ZKkUHbxWERo/AAAAAAAAAAI/AAAAAAAAAHc/QB_WLjn1es8/photo.jpg?sz=64
+stuffandpoop youre right, it has one side but no edges
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
It is a side..wait, no its not. Where
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
no sides and no edges...but, one surface?
https://lh4.googleusercontent.com/-OgD1ILIsh14/AAAAAAAAAAI/AAAAAAAAA-c/08csLoPB4Jg/photo.jpg?sz=64
+Bart NikkelenDoesn't every surface have an outside where the observer is? That outside could hold the inside, like watching the inside of a bowl with zero thickness (pretty much imaginary). Adding thickness to a surface would make the official inside inside that thickness, methinks.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
One surface, no in- or  outside. The bottles are therefore not REALLY nested; there is no 'inside' to be in.
https://lh6.googleusercontent.com/-A0YdhfxUpUA/AAAAAAAAAAI/AAAAAAAAACk/yr2OK_8nMUw/photo.jpg?sz=64
spiky hair guy is obnoxious 
https://lh3.googleusercontent.com/-z4YqzHLZdZE/AAAAAAAAAAI/AAAAAAAAAZk/nZPqvO5VJEA/photo.jpg?sz=64
His voice is high as fuck.

Hunt for the Elusive 4th Klein Bottle - Numberphile

Carlo Séquin on his search for the elusive "fourth type of Klein bottle". More videos on Klein Bottles: //bit.ly/KleinBottles Carlo's paper: //bit.ly/Carlo_Klein ...

User Comments

https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
Where can I buy one of those Klein Steins?
https://lh4.googleusercontent.com/-OLbdvwkaf6Q/AAAAAAAAAAI/AAAAAAAAABE/ECg9DbIZKKo/photo.jpg?sz=64
+TheTslat Link is in the description of the blein bottle videos featuring the eccentric seller of them (cliff).
https://lh5.googleusercontent.com/-3V39unEwpNs/AAAAAAAAAAI/AAAAAAAAAUc/d6j6cWgko8A/photo.jpg?sz=64
Doesn't the Klein bottle that he starts talking about at 11:00 technically have both an inside and an outside? I'm confused about how it is a Klein bottle and not some sort of mobius tube.
https://lh5.googleusercontent.com/-3V39unEwpNs/AAAAAAAAAAI/AAAAAAAAAUc/d6j6cWgko8A/photo.jpg?sz=64
Ahh, that actually makes sense. Thank you. I guess I've never really studied 4 dimensional geometry so the concept of surfaces passing through each other is new to me. I'm curious why this works if anyone has any insights or helpful video links on the subject. I'm familiar with the concept of the fourth dimension being time, so perhaps it has something to do with only acknowledging the existence of certain parts of the surfaces at certain points in time. Then again, maybe its a different fourth dimension that I don't yet understand.
https://lh5.googleusercontent.com/-w2ztLO7RR90/AAAAAAAAAAI/AAAAAAAAAEU/YpBN7tkl7l0/photo.jpg?sz=64
+Robert Barga The Klein Bottle Ring has a figure-8 cross section. Remember, in topology, surfaces pass through each other as if they existed in four dimensions instead of just three dimensions. With a figure-8 cross section tube, bringing the ends together so that they form one continuous "tunnel" yields a Klein Bottle that composes two Mobius strips that twist in the same direction.
https://lh3.googleusercontent.com/-XdUIqdMkCWA/AAAAAAAAAAI/AAAAAAAAAAA/4252rscbv5M/photo.jpg?sz=64
Should be called a Klein Noodle not a Klein Noddle :P
https://lh6.googleusercontent.com/-U7-Vk10ZDFs/AAAAAAAAAAI/AAAAAAAAACw/0f4hkJE2cEc/photo.jpg?sz=64
+n0lsk1 Klein Knottle*
https://lh5.googleusercontent.com/-bifYwQ9BDJE/AAAAAAAAAAI/AAAAAAAAAQg/7AUDPd0pq1Y/photo.jpg?sz=64
So what would the 4th dimension do? if it could cross the interception without moving over an edge?. how?.
https://lh4.googleusercontent.com/-MhKTJ9hde20/AAAAAAAAAAI/AAAAAAAAAM0/si1h00L8vi4/photo.jpg?sz=64
Do you not understand the concept of dimension or?
https://lh6.googleusercontent.com/-f1q5a8pvjas/AAAAAAAAAAI/AAAAAAAAAA8/Xwv_WoCflUU/photo.jpg?sz=64
Wouldn't it be better if the Klein Stein's handle went the other way (i.e. the bottom end of the handle to the inside and the top end to the space between inside and the outside)? I'm quite certain that much less air would be stuck in between the walls...
https://lh5.googleusercontent.com/-w2ztLO7RR90/AAAAAAAAAAI/AAAAAAAAAEU/YpBN7tkl7l0/photo.jpg?sz=64
+KasabianFan44 You'll probably need a piece of polyurethane tubing to bypass the trapped air, either through providing an exit for the air or an entrance for the liquid.
https://lh6.googleusercontent.com/-f1q5a8pvjas/AAAAAAAAAAI/AAAAAAAAAA8/Xwv_WoCflUU/photo.jpg?sz=64
+E1craZ4life Oh yeah, I haven't thought about that... lol
https://lh5.googleusercontent.com/-w2ztLO7RR90/AAAAAAAAAAI/AAAAAAAAAEU/YpBN7tkl7l0/photo.jpg?sz=64
+KasabianFan44 Because there would still be air in the outer chamber, and the liquid would have to flow against gravity to get there.
https://lh6.googleusercontent.com/-f1q5a8pvjas/AAAAAAAAAAI/AAAAAAAAAA8/Xwv_WoCflUU/photo.jpg?sz=64
+E1craZ4life Yeah I'm sure it would
https://lh5.googleusercontent.com/-w2ztLO7RR90/AAAAAAAAAAI/AAAAAAAAAEU/YpBN7tkl7l0/photo.jpg?sz=64
+KasabianFan44 But then the liquid couldn't pass up the handle.

The man with 1,000 Klein Bottles UNDER his house - Numberphile

Thanks Squarespace: //squarespace.com/numberphile More Numberphile on Klein Bottles: //bit.ly/KleinBottles This video features Cliff Stoll, the man ...

User Comments

https://lh3.googleusercontent.com/-Q6buaI_kfgY/AAAAAAAAAAI/AAAAAAAAAGc/agOPR2qPHC0/photo.jpg?sz=64
Is it's possible to fill a Klein Bottle?
https://lh3.googleusercontent.com/-Q6buaI_kfgY/AAAAAAAAAAI/AAAAAAAAAGc/agOPR2qPHC0/photo.jpg?sz=64
 Or just flipping it over and over.
https://lh4.googleusercontent.com/-EeCbHOl9YTg/AAAAAAAAAAI/AAAAAAAAAJM/b0XuqdTSNQQ/photo.jpg?sz=64
+Diego Hernández You can. I'd consider it a bit difficult to do it under a tap because of air pressure. I'd recommend putting a flexible straw that can hit the... erm, "floor" of it, if you know what I mean. It has an opening that meets with the floor, and you can fill it as such.
https://lh4.googleusercontent.com/-EeCbHOl9YTg/AAAAAAAAAAI/AAAAAAAAAJM/b0XuqdTSNQQ/photo.jpg?sz=64
+Diego Hernández You can. I'd consider it a bit difficult to do it under a tap because of air pressure. I'd recommend putting a flexible straw that can hit the... erm, "floor" of it, if you know what I mean. It has an opening that meets with the floor, and you can fill it as such.
https://lh5.googleusercontent.com/-uzmM_fbm9pw/AAAAAAAAAAI/AAAAAAAAAOE/QyaBqGSBOEg/photo.jpg?sz=64
But how did he get all those bottles down in there in the first place?
https://lh5.googleusercontent.com/-uzmM_fbm9pw/AAAAAAAAAAI/AAAAAAAAAOE/QyaBqGSBOEg/photo.jpg?sz=64
+Super Comet That old man? Crawling down there?
https://lh4.googleusercontent.com/-1A_TZvQLKkk/AAAAAAAAAAI/AAAAAAAAAFM/2cX5rjZcLxo/photo.jpg?sz=64
+Logan Finn crawl space
https://lh5.googleusercontent.com/-uzmM_fbm9pw/AAAAAAAAAAI/AAAAAAAAAOE/QyaBqGSBOEg/photo.jpg?sz=64
+Super Comet Yeah but how did he set up the space
https://lh4.googleusercontent.com/-1A_TZvQLKkk/AAAAAAAAAAI/AAAAAAAAAFM/2cX5rjZcLxo/photo.jpg?sz=64
with a robot , duh
https://lh4.googleusercontent.com/-x6XaqlrWRdw/AAAAAAAAAAI/AAAAAAAAFpg/ZoynksUXR8k/photo.jpg?sz=64
I'm not understanding why these bottles are "so amazing" :/
https://lh4.googleusercontent.com/-NBP-QFBKMoQ/AAAAAAAAAAI/AAAAAAAAAJ4/X9xBAJ6ZHHc/photo.jpg?sz=64
+teca luca also a 3 möbius loop
https://lh4.googleusercontent.com/-NBP-QFBKMoQ/AAAAAAAAAAI/AAAAAAAAAJ4/X9xBAJ6ZHHc/photo.jpg?sz=64
they are a 4D object with no inside or outside (of course they have been made in 3D)
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