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 ...
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
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.
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?
+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 :)
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?
+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 :)
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 ...
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 ...
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.
+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!!!!
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)
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.
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
+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.
+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
+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.
+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.
+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...
+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 ...
+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.
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 ...
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.
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.
+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.
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...
+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.
+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 ...
+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.
+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.