Cutting a Möbius strip in half (and more) | Animated Topology |

________________________________________________________________
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:)
_________________________________________________________________
Support my animations on:
/ think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [e-mail]
Twitter - / thinktwice2580
_________________________________________________________________
More in depth info:
Tadashi Tokieda lecture:
• Topology & Geometry - ...
en.wikipedia.org/wiki/M%C3%B6...
_________________________________________________________________
Programs used:
- Cinema 4D
_________________________________________________________________
Music:
Tom Day - Foreword:
• Tom Day - Foreword
Sound Cloud:
/ tomday
________________________________________________________________

[@adibabrar1702]

After 10 years of public education ....finally found my will to learn again

[@abstractassassin8767]

How did you do?

[@Lulleebee]

What did you do?

[@BoyscoutWakitaOk]

why did you do?

[@JustAKomiFan]

When did you do? Uhm, just asking. Aren’t there 12 grades..?

[@chalealermancilla]

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 :)

[@officersoulknight6321]

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.

[@auriidraws5563]

i had the same thoughts too

[@anoNEMOs]

Soul Knight!

[@nilaksh007]

The best thing is that you can actually make a Möbius strip easily

[@OrigamiAhsoka]

Yesss, it’s such a simple but fascinating shape

[@miuiswaifu]

ye

[@TheBluePhoenix008]

I've done it way too many times in accident

[@haveagreatlife829]

Ikr

[@justinjennings3772]

Its basically a 3d representation of a 1 dimensional loop

[@ggarpett8063]

THIS NEEDS TO BE A MARIO KART TRACK

[@ggarpett8063]

DynestiGTI I love it

[@Mattstak]

They already did: kzbin.info/www/bejne/q2XGc5ygqKipr6s

[@ggarpett8063]

Lego Luigi lol I recently got Mario kart and I found that lol

[@johnsjunk9157]

HAHAH

[@thatplaneguy944]

sooo rainbow road?

[@ameremortal5715]

One word : underrated

[@Anonymous-8080]

Ya

[@lucafrias6616]

yeah?

[@themaverick1891]

@@lucafrias6616 Yeah.

[@NoName-jh7yj]

yes?

[@Ru4444]

One word: underwear

[@Imamotherfreakingavocado]

Me, not understanding this at all: "Haha, circle strip go brrrrr"

[@Sky_Guy]

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!

[@1Furina.de.Fontaine]

Haha same. Nice Rantaro pfp

[@vpambs1pt]

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?

[@ThinkTwiceLtu]

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

[@vpambs1pt]

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!!!

[@jursamaj]

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.

[@hoodedR]

@@vpambs1pt what happened?😰

[@vpambs1pt]

@@hoodedR What do you mean?

[@erikforrester9374]

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!

[@AccipiterSmith]

Jolyne pulled some +1000 IQ move on her behalf to counter C-Moon on that particular scene.

[@abiyyupanggalih854]

finally this comment

[@InnerBluePerson]

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 😇☺️🌄

[@mossthenon-binary7637]

Thats the next recommended video for me-

[@champagnesupernova1839]

eyy, outside in!

[@Maggie66112]

Yeah true. Saw the same thing

[@Icantdothisanymoreplskillme]

YESSSSSS

[@pikapikachu4495]

YES FINALLY SOMEONE KNOWS!

[@liminalreality9617]

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…

[@streetratcore]

went straight to the comments to look for one like this

[@oliot4814]

Beautifully animated! Well done.

[@SHabbIZZLEx]

...accompanied by a soul-soothing music........mmmmmm~, learning can never be too mundane.

[@gundhamtanaka8088]

Hello there, you don't look hollow far from it. I am solaire of Astora an adherent of the lord of sunlight.......

[@dubarnik]

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.

[@Fukuroul]

So this is the Sacred Timeline!

[@abiyyupanggalih854]

yeee

[@blakeamazing12]

Why did the chicken cross the Möbius strip? ...to get to the same side

[@VinVintheBinBin]

TRUE THOUGH

[@ruby_240]

Jolyne:Good thing that i watched this video before fighting Pucci

[@emeraldz6744]

Ah, I was looking for a jojo reference

[@pogkakuna3429]

*Jolyne

[@betr8]

Yeah, I remember that, I like how it is confirmed now.

[@cameron3786]

I was looking for this comment

[@DJBlueX]

Its Möbin time!

[@muhammadaryawicaksono4232]

A perfect counter to an ability that turns you inside out.

[@ej-jz5rc]

juju

[@rea9lizer]

1:53 wonderful explanation...

[@HuslWusl]

Just so beautiful! You couldn't have picked a better background music for something simple yet fascinating thing. Thank you so much

[@danielvieira8978]

i love when the möbius strip said its möbin time and möbed everywhere

[@probablyapproximatelyok8146]

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.

[@Siwdvi]

Damn, that Morbius strip is really a thing

[@jaysonlavern3453]

This is the random science shit that I live for

[@MrsMeOnYouTube]

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! 🤩

[@ThinkTwiceLtu]

Thank you! Glad you enjoyed it :)

[@derekhasabrain]

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

[@garryfay8000]

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!

[@aditya95sriram]

So glad to have discovered your channel (thanks to 3b1b). Beautiful animations, very insightful, love it.

[@briann363]

Hope you get better soon!

[@ThinkTwiceLtu]

thanks a lot!

[@oskernelrouter6091]

Love the simplistic and elegant take on the challenging subject. It's both refreshing and intellectually stimulating.

[@MersuneLiku]

This is rather soothing and informative. This popped up in my recommended probably because of the song Möbius by Hiiragi

[@ryveseul]

goddamnit i'm here for loona HAHAHHS

[@insertnamehere4833]

2:29 this reminds me of something...

[@ucanonlybribemewithkpopmer2019]

@@insertnamehere4833 yyxy 🥰😍

[@smithchasea]

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!!

[@25VolarSleet]

This was... surprisingly comforting to watch

[@wishingforhappiness7912]

This is the third video I’ve watched on your channel, and now I’m subscribed

[@alaeaaa]

This is so frickin cool! I just googled the Möbius Strip after watching Avengers Endgame for probably the 5th time

[@mayab8053]

So I both understood and learned nothing, yet this was an amazing way to spend my time.

[@modelstatus3456]

I CAME HERE BECAUSE OF LOONA'S STORYLINE STAN LOONA PLS

[@ucanonlybribemewithkpopmer2019]

Stan loona

[@diannecomandaoliver]

Awww. Mobius strip! The video is so soothing and relaxing. I enjoyed the video 😍

[@part3dio35]

This the best random video to ever appear in my recommend

[@DerekReznik]

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

[@margarett.newman7574]

Excellent detailed accurate imaging. Thank you. I was surprised at the ⅓ cut. Shouldn’t have been. Quite beautiful. Thanks!

[@KilsE90]

Bro, What in the world? Idk why this got recommended but I’m glad.. idek why I watched it

[@lapsemweaver4001]

I never anticipated this being THIS cool.

[@darshpatel8385]

This channel is persistent. Such beautifully crafted videos, had to subscribe.

[@peakinonolympus]

Thank you for putting the effort I recently discovered your videos and watching them . Love learning from your content. Kudos

[@anbu1325]

This is so cool! The animation made everything so clear!

This channel is awesome!

[@rahul7270]

This was fantabulous! I greatly appreciate your work and can never thank you enough for your videos.

[@ThinkTwiceLtu]

Thanks a lot~

[@goddessdeedeebubblesofimag7789]

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 👍✅

[@NikhilWolf]

This _broke_ my mind. Holy heck. Thank you so much for making this video, available for free, on KZbin.

[@jacobphillips7962]

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.

[@mikaelalerrandro1372]

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!

[@ichliebebaeumeweilbaum]

Hello 👋 finally 😌 introducing 💫 LOONA 🌙 are ⭐ you 😍 girls 👭 ready 🙈? okay 👌 lets 🌚 go 🤩

[@mikaelalerrandro1372]

@@ichliebebaeumeweilbaum lmaooo streams in love4eva

[@ucanonlybribemewithkpopmer2019]

Ikr lol

[@newhairnewteenewjeansdousee]

THIS IS SO CALMING

[@math4fun378]

Great video!! love the animations

[@ThinkTwiceLtu]

Thanks for the support:)

[@sarthaktharaney5125]

Mobius strip be like: You'll never be able to cut me horizontally

[@AshRavens]

Mind. Blown.

[@dyray732]

I really like this channel, subbed.

[@DanieleGiorgino]

This is very well done.

[@doctorsphoenix4681]

That was the most relaxing video I’ve ever seen

[@Anna-jy7cj]

This is one of the most beautiful things I saw

[@al7462]

This video is currently helping me with an assignment. Thank you!

[@AgrawalVivek]

Such an elegant video!

[@andrewhalloran280]

Amazing video; very clear!

[@user-ie2sv1ri8k]

Wonderful! Just a little paper amazingly has such a interesting nature.

[@quynhanhnguyenphuc2499]

This is brilliant !

[@magicmofy2871]

Wow this is just mindblowing!

[@isavenewspapers8890]

Such a strangely nostalgic video.

[@lightestseed]

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

[@nicholasauwaerts2280]

Extraordinairy how you visualize it!

[@pah4159]

I might just be dumb but the Möbius strip just blows my mind

[@Dani_matt]

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 !!!!

[@OwlyFisher]

what?

[@yumikodazaiswaifu]

I'm sorry but I think your lost

[@billejean1705]

I am emotional. Thank you

[@richardbrook1386]

This is AWESOME! 😵

[@gtzodiac274]

This video made me think twice :>

[@foreverkurome]

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.

[@porcelainbratz8670]

Where are my orbits!!! stan loona

[@muhammadalthaf4168]

Stan loona

[@stewedtea]

stan loona

[@ucanonlybribemewithkpopmer2019]

Stan loona

[@garrettdennis2365]

You should do a video on the properties of the theodorus spiral, love your videos by the way

[@ThinkTwiceLtu]

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.

[@transwithnoplans]

I learned more from this one video than my entire 17 years of life

[@jlpsinde]

Great video!

[@justinlowe2423]

This is incredible

[@evansmith7911]

That makes so much sense! Now all I need is tape, scissors and some strips of paper!

[@davidbluecame]

Beautiful!

[@nilaksh007]

Instantly Subscribed

[@deltaixe]

i'm pretty sure my brain has turned into a mobius strip after this video

[@rochelimit55555]

Very thought provoking

[@lucaslayton3974]

Soothing video.

[@wesKEVQJ]

This gave me a really cool idea for a loop antenna.

[@CHROMIUMHEROmusic]

Your videos are awesome :))

[@devamjain5932]

sincerely beautiful!

[@phillipa9290]

Makes me think of the Banach Tarski Paradox

[@mandarinsandclementines2997]

Mind boggling, never thought I'd say that

[@cathrynmartinez8431]

Elegant. simple. but most of all silent. All math videos should be this way. The creator with the least questions gave the most answers

[@sladewoomy_0387]

Bruh, i got recommended this and now im happy because its cool lol

[@soll8660]

I'm feeling so realized rn

[@ariannasv22]

That's mind bending but the muted green and brown are such a nice color combination

[@hanniffydinn6019]

Mind bending !

[@kulgydudemanyo]

Cut it in four! Cut it in four! Cut it in four! Cut it in four!

[@seecow5634]

this is super cool

[@DynestiGTI]

So if I'd always get a circle inside the loop only if I cut 1/n of the width where n=odd?