On 2nd thought, it's easier to think of the ends as you put them together. Think "am i separating the two halves, or simply joining them back together?" iow, think of each end as both ends of the two [already] cut final result, still held together and it all makes more sense. I just tested my theory and yes, multiple odd-numbered twists results in a single *very* twisted and messy result. Even-numbered twists will always result in two separate loops. Thanks 4 the vid - thought provoking.
The twists (# of times you flip the ends before taping) dictate the continuity of 'halving' the plane in the result. Simply put, you're forcing a linear idea (picture a line) into planar (two dimensional) physics. The result is three-dimensional. For this reason, i would think odd-numbered twists should give you a single loop with the twists multiplying and forming loops within the loop when cut along the center. Even-numbered twists should result in two separate loops. Right?
I don't know. I don't write movies :p The closest thing I can come up with is The Fountain that might be like this. It's more like three pieces of paper turning into one big triangle tho.
Oh snap. I've seen that illustrated before, by Escher I think, but I've never really seen how easy it is to make one. And I had no idea there was only one edge. That's crazyness, boundless insanity! Plus the suprise ending. Whew, I need a breather. That was a good video. Maybe I can bust that out at a party and get some tail. (joking)
Yeah, sorry if I came off condescending. I really did think it was a cool trick. Especially the one edge part. That's still blowing my mind. And it turns out I actually did use that at a party. I'm still waiting on the tail, but I did get a date later, so I guess it kind of worked. Either that or my insanely good looks. (sike)
Wow, this was interesting. It is like what we call "Art class" in our grade school's (kendguarden through 12th grade) here in the U.S.
There are plenty of paper here cause we have to write down a lot of phone numbers and my neice & nephew (sister Lori's kids) live here (it's her house I'm currently living in). I'll have to try this later on.
While you're at it... be sure to pick up some origami skills. It's especially useful when you're stuck on the phone in a conversation that's not of overly much interest to you. You can fold some stuff at the side if you're surrounded by paper. Certainly pwns doodling!
Very cool! I just tried it at work. (Had to see it for myself.) And though my Mobius Strip didn't turn out quite as well as yours, the general idea was the same... (c:
So, when Mr. Winter presents a non-orientable topological space with Euler characteristic 0, embedded in IR^3, and everyone is stunned by the mathemagic, what will the crowd say to MergeSorting a card game? ^^
I think I first heard of this in college. Great, fascinating, I -love- stuff like this!! Btw, was "Möbius" likely a German that described/discovered this??
Oh yes, August Ferdinand Möbius was a 19th century German mathematician who was huge in the field of topology. Both he and a guy called Listing discovered and explored this twisted strip shape independently of one another. They were both students of that heavyweight of mathematics, Carl Friedrich Gauß.
(Damn, my high school math teacher would be so surprised. He never thought I paid much attention in class except to anything directly relevant for exams.)
*sigh* I love this Möbius stuff, but at least for me it's "pretty old hat" - I was way younger when I got into that stuff. I recommend reading Ian Stewart's "Flacherland" / "Flatterland" for the funny theory and Douglas R. Hofstadter's "Gödel Escher Bach" for the philosophical background of stuff like that. - Besides: Someone once told me, the "Renault" car company's logo is a Möbius strip, but obviouly it is not, it's just inspired by it.
I hadn't heard that, though the logo is slightly reminiscent of a doubly twisted Möbius strip. You're right, the thing is rather old school, though people never cease to be fascinated by it.
Thanks for the reading recommendations. Is "Gödel Escher Bach" very difficult to read, because the philosophical implications interest me.
"GEB" goes _FAR_ beyond Möbius strips, as well as it obviously about Gödel (Kurt Gödel, the famous mathematician), M.C. Escher (the one with the drawings) and J.S. Bach (the composer). There's a whole lot of metaphysics and maths in this book. - "Flacherland" / "Flatterland" is somewhat of a children's book telling about dimensionality, one (of many) successors of the one and only, but rather old "Flatland" / "Flächenland" by Edwin A. Abbott.
Fascinating... geometry was glossed over in high school for us. Or at least I thought so. My math teacher was always annoyed at me for purposefully doing poorly in his class... I didn't help his annoyance by turning in my tests with all the bonus questions correct...LOL
I have always been a rebel. Strangely enough, it is a common personality trait amongst police officers. It comes from having a highly tuned sense of justice I think. "Law" and "Codes of Morality" mean nothing unless they are protecting individuals rights. I was also highly gifted in math...
You're way to clever for your own good. . . is this how math geeks get girlfriends!? ;) lol! Just kidding-although I am going to use that trick! LOL! (even though I know it's not a trick-you know what I mean, I've had wine-forgive me!)
In my experience, girls tend to appreciate craftiness more than I'd originally thought. You'd think you need to be supremo rich or über good-looking or totally self-confident... when really, simply using origami to fold a quick present from a napkin will make you look like a super hero.
While we're on the subject, what is it about girls needing something to toy around with? A glass, a cigarette, jewelry, salt shakers, their hair. Inquiring minds want to know.
hmm, not sure-flirting with inanimate objects is something women do though-at least I'm pretty sure that playing with stuff like that is some sort of flirting ritual!
Came across that old skool game soundtrack when I was surfing for free music. That game was so über-cool, wasn't it? I remember kicking so much ass with Blaze!
absolutely wonderful...I was thinking about putting the two sides together into a circle...but twisting it...wow...that's just really neat! Thanks for sharing.
Physics and geometry annoy me, it's major grey cell masturbation. It only works as a whole, when you take a precise point it actually has two sides and two edges. Why am I pissed at the dude who discovered this????Then again, why am I pissed at everything? Cuz I quit smoking, I'M sour.
Hi there. A sheet of paper?!?! O o o o o o o h. :) Really? 1 side and 1 edge? H m m m m. Man, you cut better than me. Very very cool, dude. Paper that has 1 side. Awesome. Take care.
I read about the Möbius Strip in an old science fiction novel and then just tried it out. I think I was ten at the time. When we covered this topic as well as the <i>Kleinsche Flasche</i> in high school math class much later, I was just like "Yeah, whatever. That is <b>so</b> old school." I was such a smartass in school, I'm surprised anyone hung out with me at all.
As for my English, I spent three years in the U.S. and one year in England.
Was the sci-fi novel by Arthur C Clarke by any chance, if you remember? I know it came up several times in one of his novels but I don't remember which one. I loved his writing!
Really cool. Your pronounciation definately sounds too clear for any U.S. dialect.
I'm gonna leave for England in september and I was thinking about starting some kind of vlog, too. Maybe u could give me any tips, any support? MSN or ICQ would be appreciate I think.
It leaks through.
MrChiefBlackhawk 9 months ago
you remind me of Dan Brown.
ICorruptYou 10 months ago
why did you send me to a german video?
pokeplatinum62 10 months ago
@pokeplatinum62 I didn't send you anywhere. And this video is in English.
AericWinter 10 months ago
@AericWinter the video this is a response to
pokeplatinum62 10 months ago
learning is not boring
amitscorpian25 1 year ago
@amitscorpian25 I agree.
But it depends on whom you ask, I suppose.
AericWinter 1 year ago
Sorry man, but after you cut it, it's no more a Moebius Band (because you obtain two faces and two edges again by the cutting)..!
cesup1 1 year ago
@cesup1 My point exactly. ^^
AericWinter 1 year ago
This is the internet for me in a nutshell: some guy in Germany has me cutting up pieces of paper xD Who'd have ever thought it?
Your videos are great. I see some of them are already years old. It'll be good to look back on these vids, Andreas, as you grow older.
Best wishes from London.
UtterObliteration 2 years ago 4
Thanks, man. Looking back, it's almost like a time capsule to me.
AericWinter 2 years ago
Someone should design a möbius strip rollercoaster!
CricketboyStudios 2 years ago 14
wicked idea!
Alacrates 2 years ago
One of the better mobius videos and I loved your character in the series "House".
JimminyPricket 2 years ago
Super Idee, ein Video fürs Möbiusband zu machen!
"I hope you can sleep on that." - Hey, ich find ja immer coolere Videos von dir! Hiermit abonniere ich deinen Kanal. :)
fluorisch 3 years ago
Im Nachhinein gefällt's mir nicht mehr so sehr. Ich hätte das ganze Thema schneller darstellen können. Aber man lernt ja nie aus.
Vielen Dank für's Abo!
AericWinter 3 years ago
I'd ask you to do a piece on the Klein bottle, but heads would explode.
merloon 3 years ago 9
Mine being one of the first, actually. *g*
AericWinter 3 years ago
On 2nd thought, it's easier to think of the ends as you put them together. Think "am i separating the two halves, or simply joining them back together?" iow, think of each end as both ends of the two [already] cut final result, still held together and it all makes more sense. I just tested my theory and yes, multiple odd-numbered twists results in a single *very* twisted and messy result. Even-numbered twists will always result in two separate loops. Thanks 4 the vid - thought provoking.
zihyer 3 years ago
The twists (# of times you flip the ends before taping) dictate the continuity of 'halving' the plane in the result. Simply put, you're forcing a linear idea (picture a line) into planar (two dimensional) physics. The result is three-dimensional. For this reason, i would think odd-numbered twists should give you a single loop with the twists multiplying and forming loops within the loop when cut along the center. Even-numbered twists should result in two separate loops. Right?
zihyer 3 years ago
voll cool!!!!
stormbreezemidnight 4 years ago
The mobius strip is probally one of the most ming boggling things for me
AehBeeSea 4 years ago 2
i just wanna ask a question how is a mobius strip related to real life??????? can somone plz tell me :)
pinkpunk9b 4 years ago
Is this a riddle?
AericWinter 4 years ago
Sweet and refreshing video
guacamolecestsibon 4 years ago
can you post that video of the cube that collapses in on itself? that sounds really interesting.
Ctall1990 4 years ago
It should be on the channel I posted this video as a response to.
AericWinter 4 years ago
its not geometry its topology
tekhiun 4 years ago
If your H O T W E T AND H O R N Y like me come check out my Breasttastic Videos at
boobs(dot)eastsidejvrback(dot)net
tdqjxg
oskpjrkgaymel 4 years ago
such bad lightning
nickodemo1 4 years ago
In fact, there wasn't a single streak of lightning in the video at all.
AericWinter 4 years ago
lol
wickedobseser 4 years ago
he used a lazer
dom5555 4 years ago
WOW maGIC awesome....
nctrls2 4 years ago
ZOMG GUYS ITS MAGIC!!!!
TheFungusAmungus 4 years ago
For me? Heh heh. Sorry it took me so long to get around to actually watching it...I've been away from the 'Tube for a while, enjoying "real" life.
Great presentation of a fun concept. =)
Prepoceros 4 years ago
Don't worry, dear. My mother always told me that patience pays. I'm glad you enjoyed it. (=
And where is this mystical place you call "real life"? I think I have heard of it, somewhere.
AericWinter 4 years ago
your cool...thanks...
konohafung 4 years ago
he was in the matrix
that s real life for these people
nickodemo1 4 years ago
I've seen this before and never knew that that's what it was called. I'd like to see a movie like this, other than what comes up from your tags.
dove95 4 years ago
What kind of movie?
AericWinter 4 years ago
I don't know. I don't write movies :p The closest thing I can come up with is The Fountain that might be like this. It's more like three pieces of paper turning into one big triangle tho.
dove95 4 years ago
I'd like to see that, actually.
AericWinter 4 years ago
Very interesting.
TheRealMojoMan 4 years ago
Oh snap. I've seen that illustrated before, by Escher I think, but I've never really seen how easy it is to make one. And I had no idea there was only one edge. That's crazyness, boundless insanity! Plus the suprise ending. Whew, I need a breather. That was a good video. Maybe I can bust that out at a party and get some tail. (joking)
onceyougoatee 4 years ago
You might be surprised by how many girls actually dig guys who can illustrate intellectual topics in this manner.
AericWinter 4 years ago
Yeah, sorry if I came off condescending. I really did think it was a cool trick. Especially the one edge part. That's still blowing my mind. And it turns out I actually did use that at a party. I'm still waiting on the tail, but I did get a date later, so I guess it kind of worked. Either that or my insanely good looks. (sike)
onceyougoatee 4 years ago
i'm not impressed mr. mobius ;)
SavannahLioness 4 years ago
Well, one cold shoulder and a ton of impressed females is a pretty good quota for Mr. Möbius. I'll take it. (c;
AericWinter 4 years ago
thats pretty cool
Ulgrim 4 years ago
I am going to show this to all of my friends to wow and amaze them. Hah hah hah.
celestialsam 4 years ago
Or better yet. Amaze and impress them with your own Möbius strip.
AericWinter 4 years ago
Mmmm. Aeric has a good idea!:P
celestialsam 4 years ago
Let me know how it went. (=
AericWinter 4 years ago
They weren't amused. Hah hah.
celestialsam 4 years ago
Ah, you're just ahead of your time. (c;
AericWinter 4 years ago
Koontug Aeric my friend ;)
Wow, this was interesting. It is like what we call "Art class" in our grade school's (kendguarden through 12th grade) here in the U.S.
There are plenty of paper here cause we have to write down a lot of phone numbers and my neice & nephew (sister Lori's kids) live here (it's her house I'm currently living in). I'll have to try this later on.
Stay cool! ...
- Brandon
brandonthyname 4 years ago
While you're at it... be sure to pick up some origami skills. It's especially useful when you're stuck on the phone in a conversation that's not of overly much interest to you. You can fold some stuff at the side if you're surrounded by paper. Certainly pwns doodling!
AericWinter 4 years ago
Clever!
Gigolo8 4 years ago
Smartie Pants! ;)
Bree5 4 years ago
Ah shucks, I bet you say that to all the geeks. (c;
AericWinter 4 years ago
Aeric, you forgot to say to cut along it again for the win! Topology is for 3-year-olds who don't want to grow up xD
CrowbarUpsideTheHead 4 years ago
DOUBLE MÖBIUS CUT MANOEVRE <b>FTW</b>!!!
Didn't I tell you? I never grew up on the inside.
AericWinter 4 years ago
Hahaha! xD
CrowbarUpsideTheHead 4 years ago
Heh, knew about mobius rings, never thought to cut 'em... ^_^
nonigold 4 years ago
Very cool! I just tried it at work. (Had to see it for myself.) And though my Mobius Strip didn't turn out quite as well as yours, the general idea was the same... (c:
<i><b>*Nick*</b></i>
DallasGuyZ 4 years ago
Weren't your colleages giving you slight WTF-side glances?
AericWinter 4 years ago
LOL!! I've got my own office so there's no one to give me those looks... (Lucky me, LOL!!)
DallasGuyZ 4 years ago
I can just hear your secretary on the phone:
"No, I am sorry, Ma'am. Mr. Z is in a very very important meeting involving the topology of paper right now. Can he call you back?"
AericWinter 4 years ago
OMG, LOL!! Ok, now I literally "LOL'D" at that one!! <b>I knew there was a reason I watched you... (c;</b>
DallasGuyZ 4 years ago
thx 4 confusing me, just kiddin.
ehrlich gesagt war das irgendwie cool, auf eine sehr physikalische art und weise
AlexMinden 4 years ago
Wer hätte gedacht, dass "cool" und "physikalisch" in einen Satz passen?
AericWinter 4 years ago
I was edutained by this.
usenetposts 4 years ago
So, when Mr. Winter presents a non-orientable topological space with Euler characteristic 0, embedded in IR^3, and everyone is stunned by the mathemagic, what will the crowd say to MergeSorting a card game? ^^
Redfrettchen 4 years ago
Who knows? Why don't you show us and we'll find out, Redfrettchen? ^^
AericWinter 4 years ago
I think I first heard of this in college. Great, fascinating, I -love- stuff like this!! Btw, was "Möbius" likely a German that described/discovered this??
Squawk7600 4 years ago
Sorry, "...a German mathematician"!! **Heard that the second time through the video, don't know how but missed it the first!** |c:
Squawk7600 4 years ago
Oh yes, August Ferdinand Möbius was a 19th century German mathematician who was huge in the field of topology. Both he and a guy called Listing discovered and explored this twisted strip shape independently of one another. They were both students of that heavyweight of mathematics, Carl Friedrich Gauß.
(Damn, my high school math teacher would be so surprised. He never thought I paid much attention in class except to anything directly relevant for exams.)
AericWinter 4 years ago
*sigh* I love this Möbius stuff, but at least for me it's "pretty old hat" - I was way younger when I got into that stuff. I recommend reading Ian Stewart's "Flacherland" / "Flatterland" for the funny theory and Douglas R. Hofstadter's "Gödel Escher Bach" for the philosophical background of stuff like that. - Besides: Someone once told me, the "Renault" car company's logo is a Möbius strip, but obviouly it is not, it's just inspired by it.
xOREGx 4 years ago
I hadn't heard that, though the logo is slightly reminiscent of a doubly twisted Möbius strip. You're right, the thing is rather old school, though people never cease to be fascinated by it.
Thanks for the reading recommendations. Is "Gödel Escher Bach" very difficult to read, because the philosophical implications interest me.
AericWinter 4 years ago
"GEB" goes _FAR_ beyond Möbius strips, as well as it obviously about Gödel (Kurt Gödel, the famous mathematician), M.C. Escher (the one with the drawings) and J.S. Bach (the composer). There's a whole lot of metaphysics and maths in this book. - "Flacherland" / "Flatterland" is somewhat of a children's book telling about dimensionality, one (of many) successors of the one and only, but rather old "Flatland" / "Flächenland" by Edwin A. Abbott.
xOREGx 4 years ago
A doubly twisted sheet of paper is no Möbios strip anymore: It's twisted, but it has again two surfaces. :)
xOREGx 4 years ago
Yep, that comment was actually a jab aimed at our neighbourly <i>créateurs d'automobiles</i>.
AericWinter 4 years ago
The reason is for the fun of it. :)
monicavm 4 years ago
this was obvious camera trickery. ;)
Paperlilies 4 years ago
You can see right through me, Bryony.
P.S. So... do you miss Diana?
AericWinter 4 years ago
LMAO- and who is the $martas$?
BlackenedRoseThorn 4 years ago
Fascinating... geometry was glossed over in high school for us. Or at least I thought so. My math teacher was always annoyed at me for purposefully doing poorly in his class... I didn't help his annoyance by turning in my tests with all the bonus questions correct...LOL
BlackenedRoseThorn 4 years ago
SmartassRoseThorn, eh? So why were you such a rebel in math class? Didn't like the teacher? Weren't fond of authority? Or just because you could?
AericWinter 4 years ago
I have always been a rebel. Strangely enough, it is a common personality trait amongst police officers. It comes from having a highly tuned sense of justice I think. "Law" and "Codes of Morality" mean nothing unless they are protecting individuals rights. I was also highly gifted in math...
BlackenedRoseThorn 4 years ago
Like a geek version of James Dean, eh?
AericWinter 4 years ago
Pretty cool!
Ilutvar 4 years ago
interesting
clearysteve 4 years ago
Well, I actually learned about the Mobius strip in high school, but that doesn't mean you don't still fascinate and baffle me.
rhythm7a 4 years ago
Jeff, you're back! Does this mean IRL's toll on your online time is lessening?
AericWinter 4 years ago
You're way to clever for your own good. . . is this how math geeks get girlfriends!? ;) lol! Just kidding-although I am going to use that trick! LOL! (even though I know it's not a trick-you know what I mean, I've had wine-forgive me!)
samsarajade 4 years ago
In my experience, girls tend to appreciate craftiness more than I'd originally thought. You'd think you need to be supremo rich or über good-looking or totally self-confident... when really, simply using origami to fold a quick present from a napkin will make you look like a super hero.
While we're on the subject, what is it about girls needing something to toy around with? A glass, a cigarette, jewelry, salt shakers, their hair. Inquiring minds want to know.
AericWinter 4 years ago
hmm, not sure-flirting with inanimate objects is something women do though-at least I'm pretty sure that playing with stuff like that is some sort of flirting ritual!
samsarajade 4 years ago
You're pretty sure?
I thought I could get a female opinion here...
AericWinter 4 years ago
female opinions can be elusive and mysterious-I'm not going to give a man any kind of clarity concerning females, I'd be thrown out of 'the club' :P
samsarajade 4 years ago
First rule: Don't talk about the Female Club.
AericWinter 4 years ago
Streets of Rage! I recognised it as soon as it came up! More of that please :D And also more weird geometry, if you can handle it!
FoxDougan 4 years ago
Came across that old skool game soundtrack when I was surfing for free music. That game was so über-cool, wasn't it? I remember kicking so much ass with Blaze!
AericWinter 4 years ago
now that I calmed down, I appreciate this symbol of infinity. how amazaging!yes amazaging, that is what I meant to say.
shebitch 4 years ago
Sometimes, talking to you makes me think I'm talking to two people. At least. No wonder I like you.
AericWinter 4 years ago
absolutely wonderful...I was thinking about putting the two sides together into a circle...but twisting it...wow...that's just really neat! Thanks for sharing.
zemilla 4 years ago
Great job with the Mobius strip demonstration :) Hehe... Good cure for boredom.
MichaelFrankel 4 years ago
Physics and geometry annoy me, it's major grey cell masturbation. It only works as a whole, when you take a precise point it actually has two sides and two edges. Why am I pissed at the dude who discovered this????Then again, why am I pissed at everything? Cuz I quit smoking, I'M sour.
shebitch 4 years ago
Holy crap, Gen. When'd you quit smoking?
GaeriSummer 4 years ago
like a week ago and I'm turning into a potential mass murderer. for realz.
shebitch 4 years ago
Ducks.
rhythm7a 4 years ago
You hear that, Gaeri? It's high time you quit smoking, too!
AericWinter 4 years ago
spiffy!
meredithrose 4 years ago
Hi there. A sheet of paper?!?! O o o o o o o h. :) Really? 1 side and 1 edge? H m m m m. Man, you cut better than me. Very very cool, dude. Paper that has 1 side. Awesome. Take care.
ROMEDAWG
Roamdawg 4 years ago
Hi Andreas,
This was really amazing. Where do u know this string (and the theory that comes along with) from? Are u any kind of physics student or sth?
And a last question: Watching a lot of ur videos (commented on one of them before)I wondered where u learned to speak english like that?!
Regards, Burkhard
Quiz4fun 4 years ago
I read about the Möbius Strip in an old science fiction novel and then just tried it out. I think I was ten at the time. When we covered this topic as well as the <i>Kleinsche Flasche</i> in high school math class much later, I was just like "Yeah, whatever. That is <b>so</b> old school." I was such a smartass in school, I'm surprised anyone hung out with me at all.
As for my English, I spent three years in the U.S. and one year in England.
AericWinter 4 years ago
Was the sci-fi novel by Arthur C Clarke by any chance, if you remember? I know it came up several times in one of his novels but I don't remember which one. I loved his writing!
Squawk7600 4 years ago
Really cool. Your pronounciation definately sounds too clear for any U.S. dialect.
I'm gonna leave for England in september and I was thinking about starting some kind of vlog, too. Maybe u could give me any tips, any support? MSN or ICQ would be appreciate I think.
Regards, Burkhard
Quiz4fun 4 years ago
I don't chat much. But if you have any questions, feel free to pm me. (=
AericWinter 4 years ago
FIRST COMMENT (I hope!)
TipoBarra 4 years ago