Cutting a Möbius strip in half (and more) | Animated Topology |
ฝัง
- เผยแพร่เมื่อ 9 ก.ย. 2024
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About the video:
Exploring the properties and other unexpected shapes that we get by cutting up some Mobius strips.
This video is a lot more text heavy compared to most of my previous ones, however it's quite difficult to explain something in more depth without using a lot of words.
Thanks for watching:)
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Support my animations on:
/ think_twice
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Any further questions or ideas:
Email - thinktwiceask@gmail.com
Twitter - / thinktwice2580
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More in depth info:
Tadashi Tokieda lecture:
• Topology & Geometry - ...
en.wikipedia.o...
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Programs used:
- Cinema 4D
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Music:
Tom Day - Foreword:
• Tom Day - Foreword
Sound Cloud:
/ tomday
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![ตีสิบเดย์ [FULL] | นางเอกหมอลำเงินล้าน "อุ๋งอิ๋ง เพชรบ้านแพง" & ไฮโซสาวสุดฮอต "ลิลลี่ เหงียน"](http://i.ytimg.com/vi/jPxQS_EgrJ4/mqdefault.jpg)
When I was little, I knew something happened when you cut a Möbius strip in half, but I didn’t know what, so as a child my brain defaulted to physics breaking.
i had the same thoughts too
Soul Knight!
THIS NEEDS TO BE A MARIO KART TRACK
DynestiGTI I love it
They already did:
th-cam.com/video/u4cBijsCvyI/w-d-xo.html
Lego Luigi lol I recently got Mario kart and I found that lol
HAHAH
sooo rainbow road?
After 10 years of public education ....finally found my will to learn again
How did you do?
What did you do?
why did you do?
When did you do?
Uhm, just asking. Aren’t there 12 grades..?
The education system is made to adapt to an extensive work schedule in an unpleasant activity and that you memorize things, you can learn on your own or study at home :)
The best thing is that you can actually make a Möbius strip easily
Yesss, it’s such a simple but fascinating shape
ye
I've done it way too many times in accident
Ikr
Its basically a 3d representation of a 1 dimensional loop
One word : underrated
Ya
yeah?
@@friasluca Yeah.
yes?
One word: underwear
Me, not understanding this at all: "Haha, circle strip go brrrrr"
I would encourage you to rewatch the video, perhaps pausing at the questions and try to figure it out yourself. It really is quite intuitive, and very satisfying once you get it. You can do it!
Haha same. Nice Rantaro pfp
I have been fascinated by the " basic" mobius strip for a long time and I never imagined the result of cutting one in half or more counterintuitively at the 1/3 point. My mind, brain and imagination are in ecstatic mode! Thank You!
Everything is on point, that's interesing! what if we cut in 4 pieces? would we have 2 Möbius strips, but each one "inside" the other?
if we cut in 4 pieces, I think we would get 2 linked loops but i don't think that they would be mobius loops anymore because they would have an even number of turns on them therefore they would have 2 separate faces. correct me if i'm wrong
I'm not a topologist and not even close to be a mathematician(still in high school), but I did it myselft with paper and adhesive tape haahaha, and at the end you are completely right, I just didn't understand how did you know that they'd have an even number of turns.
It's nice to know that you're recovering and not at the hospital anymore, get better!!!
For 4, the middle 1/2 is identical to a Möbius cut down the middle: double long, double twisted loop. The outer half is 1 piece due to the outer edge, but now has an inner edge, so it's the same: double long, double twisted loop. So the result is 2 pieces just like a Möbius cut down the middle, but half as wide.
In fact, cutting any distance from the edge will yield a double long, double twisted loop. So for 1/N being the distance between cuts, you'll get int(N/2) double long, double twisted loops. If N is odd, you will also get a narrow Möbius down the centerline.
@@vpambs1pt what happened?😰
@@hoodedR What do you mean?
Thumbnail, title, and concept made me think of that “Outside in” video, the one so many including myself got recommended where there’s a Female and Male voice explaining a concept like this, and the comment’s on it of course are a laugh 😂, thank you for making this!
Update: Thank you all so much for the likes!, 😃☺️including the person who uploaded this video!, I hope for the best for you all in life,
🗺🌄🕊May God Bless you all and himself greatly!
Update 2: I don’t deserve a thousand likes, I just said that because I didn’t see anyone else say how it reminded them of the inside out loop educational video, I still wish you all the very best and that God Blesses you all greatly in life, take care, and please spread love as much as you can and then some 😇☺️🌄
Thats the next recommended video for me-
eyy, outside in!
Yeah true. Saw the same thing
YESSSSSS
YES FINALLY SOMEONE KNOWS!
Jolyne pulled some +1000 IQ move on her behalf to counter C-Moon on that particular scene.
finally this comment
I liked the part when the Möbius strip said "It’s möbin time" and möbed all over the bad guys,… truly the best moment in cinematic history…
went straight to the comments to look for one like this
Beautifully animated! Well done.
...accompanied by a soul-soothing music........mmmmmm~, learning can never be too mundane.
Hello there, you don't look hollow far from it. I am solaire of Astora an adherent of the lord of sunlight.......
I deeply enjoy Think Twice's video's. They are calming, soothing, yet mathematically delightful. They are clear and simple, yet they speak of great effort to create. I hope this creative genius gives us many more moments of joy.
A perfect counter to an ability that turns you inside out.
juju
So this is the Sacred Timeline!
yeee
Jolyne:Good thing that i watched this video before fighting Pucci
Ah, I was looking for a jojo reference
*Jolyne
Yeah, I remember that, I like how it is confirmed now.
I was looking for this comment
Why did the chicken cross the Möbius strip?
...to get to the same side
TRUE THOUGH
Its Möbin time!
never been genuinely angry at a strip of paper before. what business does it have breaking physics like this 😠😠😠
Just so beautiful!
You couldn't have picked a better background music for something simple yet fascinating thing.
Thank you so much
1:53 wonderful explanation...
I never was big in science especially in math & physics…but then from time to time I stumble over such gems and I don’t know why…but it just overflows my heart with joy! 🤷🏻♀️
Everything- from the background music to the graphic- is perfect & beautifully made….thanks for sharing! 🤩
Thank you! Glad you enjoyed it :)
goddamnit i'm here for loona HAHAHHS
2:29 this reminds me of something...
@@insertnamehere4833 yyxy 🥰😍
I would love to see a part 2 with an animation of two Möbius strips with ’opposite’ twists getting their edges glued together to form a Klein bottle, as well as an animation of a mobius stip getting its edge glued to the edge of a unit disk to form a real projective plane, if possible. This was a wonderful video with smooth animations and tips/explanations. Thank you.
i love when the möbius strip said its möbin time and möbed everywhere
Nicely done; however, visualization would be helped if when the ball rolls it would leave a visible trail - likewise with the cuts - make the "cutting" that we might do with scissors visible. Thanks!
I've always watched these videos just for the joy of visualizing math, but today this video made me realize just how much work you put in to just make all the 3D animations so freaking smooth. Really, really great work
Hope you get better soon!
thanks a lot!
This is the random science shit that I live for
Damn, that Morbius strip is really a thing
I CAME HERE BECAUSE OF LOONA'S STORYLINE
STAN LOONA PLS
Yes
This is rather soothing and informative. This popped up in my recommended probably because of the song Möbius by Hiiragi
So glad to have discovered your channel (thanks to 3b1b). Beautiful animations, very insightful, love it.
1:53 "To understand this..."
That was more confusing than watching the first part. The "helpful explanation" was more confusing than the original @ 1:38 lmao
This was... surprisingly comforting to watch
This is so frickin cool! I just googled the Möbius Strip after watching Avengers Endgame for probably the 5th time
Love the simplistic and elegant take on the challenging subject.
It's both refreshing and intellectually stimulating.
That video was outstanding! I have always had a hard time figuring out how the mobius strip makes one large loop when it is cut in half, so the animation with the strips already cut in half, but then formed into a mobius strip were super helpful! Great job!!
Excellent detailed accurate imaging. Thank you. I was surprised at the ⅓ cut. Shouldn’t have been. Quite beautiful. Thanks!
Wondering about why do not have any orbits in the comments because of LOONA? lol
And the animation it's really pleasing to see, makes the understanding of the thing really more easy!
Hello 👋 finally 😌 introducing 💫 LOONA 🌙 are ⭐ you 😍 girls 👭 ready 🙈? okay 👌 lets 🌚 go 🤩
@@ichliebebaeumeweilbaum lmaooo streams in love4eva
Ikr lol
Circle: Im better than you! I have only 1 face and 1 side!
Sphere: but what about m-
Mobius Strip: WELL IM A 3D SHAPE WITH ONE CONTINUOUS FACE AND I CAN DO SOME CRAZY STUFF
Where are my orbits!!! stan loona
Stan loona
stan loona
Stan loona
This the best random video to ever appear in my recommend
I remember back when I first played on the Mario circuit shaped like a mobius strip in Mario kart 8, I was so confused on how the track worked at first, like it was in a shape of an 8 and you drive on both sides, it blew my mind on how it would work, then I tried to figure it out using my own pieces of paper and my mind blew up even more when I found out how it worked, and that’s when I learned about the mobius strip
So I both understood and learned nothing, yet this was an amazing way to spend my time.
mobius strip more like morbius strip
I never anticipated this being THIS cool.
I'm glad there was no commentary. These kinds of videos that show me something really weird and really real I just want to get to the point and don't want to hear it explained for 40 minutes. Great job 👍✅
When I see so many people know what this disability is it makes me happy because when I tell me freinds at school about this disability they are always like what and even when I tell doctor's they always have to look it up and see what it is but seeing so many of you knowing what it is makes me happy and makes me feel like I'm not alone and also happy Mobius awareness day !!!!
what?
I'm sorry but I think your lost
Mind. Blown.
Mobius strip be like:
You'll never be able to cut me horizontally
THIS IS SO CALMING
Bro, What in the world? Idk why this got recommended but I’m glad.. idek why I watched it
These things are also great for giving you the world's nastiest paper cuts as I recently found out, the twist in them makes them really really sharp & they don't fold up easily like a flat sheet of paper does when you run your finger along it more than once.
Ive heard several explanations, and seen several videos on how this happens, and this 4 minutes long video does a better job then any half an hour proof I’ve seen.
Wow this is just mindblowing!
That was the most relaxing video I’ve ever seen
Mind boggling, never thought I'd say that
You should do a video on the properties of the theodorus spiral, love your videos by the way
Garrett Dennis thank you! i dont really know a lot about teodorus spiral but I'll read more about it and will put it on my 'future videos' list.
This is the third video I’ve watched on your channel, and now I’m subscribed
Elegant. simple. but most of all silent. All math videos should be this way. The creator with the least questions gave the most answers
i'm pretty sure my brain has turned into a mobius strip after this video
That's mind bending but the muted green and brown are such a nice color combination
Cut it in four! Cut it in four! Cut it in four! Cut it in four!
This video made me think twice :>
when you attach two Möbius strips to one another, they form a Klein Bottle, a shape that is 4th dimensional in nature, but can be represented in the 3rd dimension with intersecting parts
Nobody:
My earbuds tangling at 3 AM: 2:39
This music is so calming
I am emotional.
Thank you
This is one of the most beautiful things I saw
Such a strangely nostalgic video.
We did this in middle school with a piece of paper( cut in half and taped together to have a 4.25x22 piece) and had a competition, continuously cutting the mobius strip in half, to see who could get the longest piece without breaking or doubling the strip, over a week of time. It was a lot of fun!
I might just be dumb but the Möbius strip just blows my mind
Awww. Mobius strip! The video is so soothing and relaxing. I enjoyed the video 😍
This _broke_ my mind. Holy heck. Thank you so much for making this video, available for free, on TH-cam.
I learned more from this one video than my entire 17 years of life
Great video!! love the animations
Thanks for the support:)
Makes me think of the Banach Tarski Paradox
Bruh, i got recommended this and now im happy because its cool lol
Amazing video; very clear!
This channel is persistent. Such beautifully crafted videos, had to subscribe.
not to be dramatic but the möbius strip cut in half is the prettiest thing i have ever seen
I'm feeling so realized rn
My respect for mobiius strips has increased tenfold
This video is currently helping me with an assignment. Thank you!
Very thought provoking
I find this oddly calming
This gave me a really cool idea for a loop antenna.
This channel is awesome!
I didn't even know this was a thing until today and I had Mobius for 15 years well i still do have it
That makes so much sense! Now all I need is tape, scissors and some strips of paper!
Omg I saw this on a kids arts and crafts show from my country years ago! Totally forgot this was a thing until now
Soothing video.
I somehow was interested in this, and it indeed was very interesting
awesome!
s t o n e free
I don't know why, but this was really satisfyng to watch
I admired the first person to eat mushrooms
This is very well done.
Thank you for putting the effort I recently discovered your videos and watching them . Love learning from your content. Kudos