Are odd-numbered mobius-loop cogs possible?

Подписаться 1,2 млн

Просмотров 239 тыс.

50% 1

More details about WiSE and WiTT
www.janestreet.com/witt-wise-...
Apply for WiSE: Women in STEM Education
www.janestreet.com/apply-wise/
Apply for WiTT: Women in Trading and Technology
www.janestreet.com/apply-witt/
Here is the reddit post I first saw:
"I designed an Intertwined Mobius strip of Gears. 60parts, 285 balls"
/ i_designed_an_intertwi...
Just the gif:
i.redd.it/wi38hd95ebb11.gif
Thanks to ElminsCosplay for making the cogs for me! Check out their other stuff.
/ elminscosplay
If you really want to, you can buy my book:
mathsgear.co.uk/products/humb...
These are the lectures I mention:
What Happens When Maths Goes Wrong? - with Matt Parker
• What Happens When Math...
Matt Parker: "The Greatest Maths Mistakes" | Talks at Google
• The Greatest Maths Mis...
This is my previous video with Sabetta:
Exploring Hyperbolic Space with VR (and crochet)
• Exploring Hyperbolic S...
And check out Henry's crazy gears:
Three Gears are Possible - Numberphile
• Three Gears are Possib...
CORRECTIONS
- When I read the poster I say that education works best when all the parts are “moving” instead of “working”. The first person to complain about this was Steven Brace.
- Let me know if you spot anything else!
Thanks as always for Jane Street being my principal sponsor.
www.janestreet.com/
Thanks to my Patreon supporters who help make these videos possible. Here is a random subset:
Andy
Fernando Gaete Ferrari
Daniel Brockwell
Matt Langford
Markus Herrmann
Erin Eldridge
Support my channel and I can make more maths videos:
/ standupmaths
Music by Howard Carter
Filming and editing by Matt Parker
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: wwwh.umble-pi.com
Nerdy maths toys: mathsgear.co.uk/

Развлечения

Опубликовано:

7 июл 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 865

@Pining_for_the_fjords 5 лет назад

So this is what the gear wars were fought over.

@Lattamonsteri 5 лет назад

I wish they made a rick and morty game about the gear wars. An fps maybe? :D it should be called the gears of war! They might have to negotiate with epic games though.

@Nielsquake0 5 лет назад

@@Lattamonsteri legend man comment

@jake_a_g 5 лет назад

I dont get it

@Lattamonsteri 5 лет назад

@@jake_a_g i think conway79 was making a reference to an animates series called rick and morty where there's a continuous joke about "gear people" (robotic people with lots of gears in/on them) having gear wars. It might be a reference to something else too :P

@standupmaths 5 лет назад

It’s a reference to TV show Rick and Morty which talks about the “Gear Wars” but never explains it. To be fair, you have to have a very high amount of free time to understand Rick and Morty references.

@outside8312 5 лет назад

You looked very proud of that triple negative

@standupmaths 5 лет назад

I wasn’t unproud.

@nutmeggaming11261 5 лет назад

*visible sigh*

@CriticalMonkey623 5 лет назад

*sighs echo throughout the world*

@Maninawig 5 лет назад

Given that 3 negatives makes a full circle to renavigste itself as a single negative... Could one argue that he made a möbeus negative?

@CriticalMonkey623 5 лет назад

Looking In With Victor B I suppose one couldn’t not

@spinter1310 5 лет назад

This solution was so elusively simple. “How can we make a loop of an odd number of cogs work?” “Oh, just give it a twist.”

@CM-mo7mv 4 года назад

Yea being intertwined is not really necessary here, is it?

@blueredbrick 3 года назад

@Boco Corwin Fun this thread.

@magicstew45 3 года назад

@@CM-mo7mv while them being intertwined is fun and saves space the principle would work in a large circle and be more true to a mobius strip

@giansieger8687 3 года назад

what an unexpected twist

@tyronium2 2 года назад

@@CM-mo7mv no it just makes it easier/more compact

@witerabid 3 года назад

Well, there is also a solution for an odd nnumber of cogs in 2D: Just use only one cog (after all, one cog is usually enough). I know this is a bit of a Parker solution but it certainly doesn't block itself...

@Qeswara 4 месяца назад

Likewise, the mechanism in the video does not block itself if it is well designed.

@andrewince8824 4 года назад

As an engineer, the extra effort that went into the base, that beautiful extra design to improve the aesthetic really pleases me. I love good looking technical works.

@massimookissed1023 5 лет назад

Everyone's entitled to own a pinion.

@zackhjorth487 5 лет назад

best pun I've seen in a while

@JNCressey 5 лет назад

I must askew, ... was this pun a spur of the moment thing?

@旭球 5 лет назад

Get out

@ntlespino 5 лет назад

God what a mesh

@jimi02468 5 лет назад

I just learned a new word with this pun.

@Cyranek 5 лет назад

where can i buy my own mobius cog strip?

@aniofri 5 лет назад

reddit.com/user/elmins but it costs alot of Reddit karma

@wobblysauce 5 лет назад

@@aniofri I up doot.

@elminz 5 лет назад

Hi, elmins here. Currently they take a surprising amount of time to build. I'd build more, but I have limited free time at the moment so it's hard to justify right now.

@geraldyoules5618 5 лет назад

@@elminz let me know when you can make one :)

@iSmartMan1 5 лет назад

@@elminz You should start a kickstarter to sell them as a desk toy

@yriafehtivan 5 лет назад

All the school needs is another cog with "Admin" on it and the ring should be fixed.

@yashvangala 5 лет назад

Actually, it needs the parents out of the school, they're the ones who ruin their children's learning in school

@azialifaziz6652 5 лет назад

Ugh admin messes up teacher imo. They serve to introduce unnecessary crap which prevents teachers from doing what they are their to do. Two of the best teachers I had decided to retire due to excess admin in school. It has definitely made my school worse

@renerpho 5 лет назад

Forget the admins. It would all be fine if there were no children. Teachers and parents could just enjoy their free time, maybe even leave school early to, like, get to know each other and see the real world.

@z-beeblebrox 5 лет назад

The reality is Admin would be a ring gear that surrounds the whole mechanism and simply makes it not work even worse.

@8BitEggplant3 5 лет назад

@@renerpho HOT TAKE

@NanakiPL 5 лет назад

Do we need a 10 hour video of mobius cogs spinning? Yes. Yes we do!

@andrerenault 5 лет назад

With Matt in the background

@eyondev 5 лет назад

@@andrerenault if that ever happens I will have a new animated desktop background.

@Marconius6 5 лет назад

@@andrerenault Not even on loop. Just sitting there for 10 hours straight.

@logosimian 5 лет назад

Confirmed.

@LyriMetacurl 5 лет назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-baWpiyMX9g8.html at least a start!

@feliciabarker9210 5 лет назад

There's a nice kind of intuition here because you go around the mobius loop twice to get back to your starting 'parity' (that is to say, if you're drawing a line around it, your first lap will bring you back to the opposite side of the paper, and your second lap back to your original start point), so in a sense it's a loop of 30 cogs: An even number. It's just that half of those cogs are the first 15 cogs, but upside down.

@shoto5892 Год назад

That Intuition does break down however when using 16 cogs instead of 15, because if we Stipulate that a loop of an even number of cogs always works and this works because when Accounting for the Twist we actually have an even number of cogs, it should still work when usign 16/32 cogs, however it doesnt

@Huntracony 5 лет назад

Ah yes, teachers think that parents jam the system, parents think teachers jam it, but students know that they themselves are the problem.

@somedude4087 4 года назад

So take all of them out so there is no problem

@fumiko___ 4 года назад

People who aren’t in the system realize that they’re all technically at fault. The school system itself is a fail.

@soriso717 4 года назад

Diavolo The Boss Thank you Italian Mafia leader Diavolo on your opinion about the education system! (In all seriousnesses, the teachers are either causing a lot of the parts, or are the only saving graces of school, while students can’t really effect the system too much, they can only really effect themselves, and Parents usually ruin everything or point out bad teachers).

@wolflordy3193 4 года назад

@@fumiko___ yup. The three cogs aren't the problem. It's how the idiot decided to place them thats the problem.

@davidwillis7991 4 года назад

Administrators are the problem

@georgew.9663 5 лет назад

So since it works off of the string of gears gradually making one 180° turn, I feel like there could be a design where it does this without the gears going through each other, and have it be a more simple mobius loop of gears that looks much more like a traditional mobius loop than this thing, even though the interlocking gears are very cool regardless

@iain3713 5 лет назад

George W. It would be much bigger though

@elminz 5 лет назад

Yes it's possible, but it would be larger overall. Also interlocking is definitely cooler, just a bit harder to wrap your head around. It's still a mobius loop though, as that's about how it twists/connects, not the exact shape, despite this not being classical loop shape.

@georgew.9663 5 лет назад

Deepfriedpillows just use less or smaller gears lol

@nschnitz1954 4 года назад

Intellectual proves his worth by saying “ain’t *not* goin’ nowhere” to negate the contraction :-)

@txikitofandango 4 года назад

It's an odd number of negatives, so it works!

@Aziraphale686 5 лет назад

You definitely said that date wrong and then re-dubbed it. What a parker line read.

@gojoubabee 5 лет назад

Aziraphale686 haha, nice catch. 9:00 if anyone is looking for it

@soslunnaak 5 лет назад

its a parker sqript

@GuanoLad 5 лет назад

I think the USA Today one is probably deliberate, as you suspected.

@sinom 5 лет назад

You not talking about Oskar Van Deventer in this video is a sin. He made a 7 gear loop over a year ago and a lot more weird gear stuff

@standupmaths 5 лет назад

I live their stuff! I must have missed that. I first came across Oskar via the “Magic Gears”, which are incredible. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qGAnmRb66s0.html

@z-beeblebrox 5 лет назад

@@fanrco766 I assume because he tends to partner with lots of other people to make stuff

@user-vn7ce5ig1z 5 лет назад

zaphod> I assume because he tends to partner with lots of other people to make stuff Indeed. Oskar is one of the holy-quintology of puzzle designers.

@xenontesla122 5 лет назад

standupmaths Another name for those are paradoxical gears. They can even be made in different sizes! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE--1Gfc1Iq0GY.html

@jacksonpercy8044 5 лет назад

Watched the videos, and those gears are pretty neat!

@JohnSmith-kc6ov 4 года назад

7:52 "some people just want to watch the cogs spin" -Joker, 2019

@MaturedSinner 5 лет назад

Now if only we could find 12 more things to put on that school poster, it can finally make sense.

@Zitronenscheibe 5 лет назад

Homework Homework Homework Homework Homework Homework Homework Homework Homework Homework Homework Homework perferction

@ilrompiscatole5414 5 лет назад

3:30 "You CAN'T use the you are NOT looking at it from the WRONG angle argument" Boole has left the chat

@aknopf8173 5 лет назад

I could not fail to disagree less.

@montano0222 5 лет назад

9:01 When you “say” 22nd but mouth 18th

@Verlisify Год назад

Its incredible what people are making with 3d printing and simple part accessibility

@MichaelFrancisRay 5 лет назад

Absolutely fantastic! The only way to make this better is to make that loop with a prime number.

@RyanSteenvlogs 5 лет назад

Since you own the license to the triple gears then we shall call it the Parker Gears

@woolfoma 5 лет назад

I'd kickstarter that as a desk curiosity.

@Maninawig 5 лет назад

I won't lie, that möbeus cog is quite relaxing to watch... If it was solar powered, I could definitely see myself buying one for my desk. That said, I am amazed at all the technology möbeus loops can achieve.

@SarmonOflynn 5 лет назад

I love the triple negative to illustrate the silliness of the three cogs. Top notch.

@SarmonOflynn 5 лет назад

@@aknopf8173 ow. My head hurts.

@satyris410 Год назад

"making cogs grate again" absolute legend, gutted it missed that, given I listened to the audiobook. still brilliant

@user-kh8ez5si8p 5 лет назад

Absolutely incredible ingenuity, creativity and engineering proficiency on the redditor’s side. Matt is as awesome as ever. One of my favorite videos ever.

@ahobimo732 5 лет назад

I completely agree. This is mechanism reveals a level of ingenuity that is just staggering. It looks so simple, yet it's achieving the supposedly impossible.

@PhilippeAllardRousse 5 лет назад

This is not a "Parker" results, it is a huge success!

@Varun2799 5 лет назад

So they have finally leaked all that Alien Technology from the Area 51 raid

@MouseGoat 5 лет назад

dude the raid is 20 of september. tho they might have found some time machines in there so maybe.

@LittleCazzy 5 лет назад

I now want to find a practical use for a mobius loop of cogs, it is a beautiful piece of engineering. Also I just want to thank you for all the great videos you make on Maths. I've been watching you for a fair while and you actually encouraged me to train as a Maths teacher (I start my PGCE in September). Without your videos I wouldn't have thought that I could actually succeed in finding an alternative way to teach Maths.

@CriticalMonkey623 5 лет назад

I hate that when you said “ain’t not going nowhere”, it was in fact a true statement

@andymcl92 5 лет назад

You mean you didn't not dislike it?

@CriticalMonkey623 5 лет назад

andymcl92 You’re not incorrect

@mathensorcellment8113 2 года назад

I read the title as "morbius-loop" I think the internet has done something to me.

@glowstonelovepad9294 2 года назад

morbius moment.

@80cardcolumn 5 лет назад

At 6:15: "You spin me right round, baby , right round like a mobius strip. Right round round round."

@hotdogskid 4 года назад

Love how he was so proud of the triple negative at 1:50 but missed the double at 3:31 😂

@_neopolis_ 4 года назад

7:49 - This moment of satisfaction. I must admit that this construction is brilliant

@mojann1 5 лет назад

It makes me happy seeing you so happy about this.

@claymeistereu 4 года назад

Your presentation and the music make maths so much fun!

@andie_pants 5 лет назад

5:15 It's not a humblebrag when you have that good a grasp on your target audience. :-)

@andrewseburn 5 лет назад

Wow. That's really neat! So simple, yet awesome at the same time.

@treschlet 4 года назад

oh man that is delightfully, satisfyingly elegant. at first your brain is going "wait wtf... why does a mobius strip magically work? what weird confusing geometry is at play?" But then when it dawns on you that the end kf the strip is just flipped... it just puts a smile on your face

@totsuka2213 5 лет назад

This is freaking mind blowing! Nice video, well done man

@HellbladesFFXI 10 месяцев назад

I paused the video and was counting them like "Clockwise, counter clock, clock, counter clock..." and when I looped back around I hit the final 'Counter clock' when it was spinning clockwise and froze, thinking to myself what trickery is this? Then, it dawned on me, the slow turning of the gears! So it's technically just twisting 180 degrees and thus turning the previous "clockwise" into counter, and boom, it meshed perfectly. That moment was worth the entire video alone, thank you =3

@simonbillson9648 4 года назад

You got me! I just wanted to watch it spin, and then you said it. Thanks for the COGS

@Slikx666 4 года назад

A massive thumbs up for the person that built that.

@BeaDSM 3 года назад

This is amazing. I also think it might be a little easier to see how cool it is/prettier if instead of the repeated purple cog the last one was a third colour to maintain the pattern and draw sharp attention to the fact that with an equal number of purple and yellow cogs there is one left.

@linuxgaminginfullhd60fps10 5 лет назад

There is yet another elegant solution. It is possible to make cogs that would rotate in the same direction when joined. Any number of those cogs(either odd or even) joined in a loop would work just fine with each other and no mebius strip needed.

@stevemason4753 5 лет назад

I would absolutely love to buy one of those mobius cog cycle thingamajiggies :D

@billschlafly4107 5 лет назад

I want one too!

@elminz 5 лет назад

Hi, elmins here. Currently they take a surprising amount of time to build. I'd build more, but I have limited free time at the moment so it's hard to justify right now. Glad you liked them though.

@stevemason4753 5 лет назад

@@elminz If you ever get more free time, hit me up with estimated cost ;) Awesome work though!

@andrewseburn 5 лет назад

@@elminz

@elminz 5 лет назад

@@andrewseburn Currently i mostly post updates on my facebook/iG as elminscosplay . Although I'm close to moving house, so I'm not sure when it will be

@n8style 4 года назад

That snicker after reading the caption really made it :D

@lara.0783 5 лет назад

Thanks Matt, I want to start my bachelor study in math next year so I will remember WiSE!

@soft8oiled 5 лет назад

This was fun. I like it whenever Matt has toys with him

@daviddechamplain5718 5 лет назад

Something works best when all its parts are working. Thanks poster, I never would have guessed...

@imagesbyraphael 3 года назад

I was watching a short video of a working mobius-loop cog on Facebook, next morning RU-vid recommends this video to me...

@munjee2 5 лет назад

Why do I feel like I have seen this entire video before

@standupmaths 5 лет назад

Well, the mobius loop is the key to time travel.

@yashvangala 5 лет назад

@@standupmaths is that an endgame reference?

@sarunint 5 лет назад

May be on his Twitter?

@ailkoclaeys182 5 лет назад

Deja vu, I've just been in this place before

@ahobimo732 5 лет назад

The video loops back itself in the temporal dimension.

@varunachar87 3 года назад

To be fair, whether the mechanism "works" depends on what its intended purpose was. It could be intended to keep things from moving, for example (in which case you want to achieve a jam). Or it could be educational.

@PaulMenden5659 5 лет назад

The longer I look at the gears turning the more satisfying they get

@nekogod 3 года назад

This is immensly satisfying to watch

@timothytraver5918 3 года назад

When the music swelled (6:19), I realized how much of a Stand-up Maths fan I am. The music gets me jazzed. It's not quite as salivating as hearing the Avengers theme, but it's like a Parkenger's square of a theme.

@cushmanproductions 5 лет назад

I totally want one of these as a desk "toy."

@ChrisWalshZX 5 лет назад

Once again Matt, ... mind blown!!

@HPD1171 5 лет назад

this just simultaneously mad both cogs and mobius loops great again

@rq4740 5 лет назад

We love you, Matt!

@Typhaaris 5 лет назад

I've not watched this yet, but just the name makes me excited.

@genessab 5 лет назад

Very nice video Matt!

@ellismiles9109 5 лет назад

It is my birthday today and I got a copy of humble pi! All ready read the first 2 chapters!

@andrewhenshaw4067 3 года назад

HAH! I'm way ahead of you! I'm already at chapter 5!

@Infernoblade1010 2 года назад

This is absolutely incredible!!!

@pyromen321 5 лет назад

"Making cogs grate again." Now that's clever!

@vaalrus 4 года назад

I used to do layout and design for a monthly engineering association newspaper, and one of the things the editor was adamant about was to be careful when attempting to be clever, and *at* *all* *costs*, avoid any graphic with three interlocking cogs… :)

@kierancoburn4507 5 лет назад

Matt gets working odd number cog set. Immediatly adds another to make it even 👌👌😂

@skyepyro7104 5 лет назад

Elmins, you absolute madlad.

@tranced42 3 года назад

6:18 I love that you can hear the pure excitement

@marshmellominiapple 5 лет назад

me waiting for the pizza rolls @ 7:50

@jamesmacleod7407 5 лет назад

Ohohoho yes please I remember the tweet and I've been looking forward to this for a while

@Atlessa 2 года назад

This is beautiful. How did I not see this before today??

@td4972 5 лет назад

That "ain't not going nowhere" comment made me stop and try to figure out the sentence. Perfect choice of words Matt.

@FishManChannel 5 лет назад

What is the minimum amount of gears you can use in this system with it still working?

@MusicBent 5 лет назад

fish man three, as shown by the other 3D print shown in the beginning. The gear profiles would slowly angle from true involute shape to the more spiral auger type that one used.

@Gold161803 4 года назад

@FishManChannel 4 года назад

Gold161803 oh yeah

@idontwantahandlethough 2 года назад

LOL the parents gear is making the whole thing so much worse.. that's hilarious, so unintentionally spot on

@Intrebute 5 лет назад

I wish there was a version that didn't loop in on itself the way this one does, with cogs going through other cogs. I bet it would also work fine with a long ring of cogs at a slight angle from one another so that by the end it's done a half turn. Which makes me curious What's the smallest number of cogs you can use to do something like this? It feels like with 3 it's impossible but maybe it's possible with 5?

@PopeGoliath 5 лет назад

If you stretch your definition of a cog to something that is thicker than it is across, one of the 3D prints he dismisses at 4:15 could count as a 3-cog loop. There is a third of a twist between each cog, giving the flip required.

@Royvan7 5 лет назад

for 3, since both of the other 2 gears have to mesh inside the first. a gear can't mesh with one going through it. so, 3 is definitely impossible. well at for this system of mobius gears it might be possible with a different system of meshing the gears. for this system i think looking at the chain support to figure out how few interlocking rings must be made to complete the loop. i think in theory 5 should work. be a bit cluttered but that;s more an implementation detail.

@mythicalbeast6585 5 лет назад

@@Royvan7 If you read the comment he makes clear he's talking about just a long ring of slightly angle cogs that *doesn't* loop through itself, so 3 is definitely possible because the third isn't inside of the other two.

@massimookissed1023 5 лет назад

I'll wager it's not possible to have a working Mobius loop of gears using 4.

@Royvan7 5 лет назад

@@mythicalbeast6585 i see, you are right i missed that. well considering it. with higher number of gears it should be possible. probably want to use helical gears rather than spur gears. helical gears let you shift the axis angle more. for 3 gears you would probably have to use beveled gears to shift the axis quickly enough.

@agentdelta569 5 лет назад

The moment i read the title, it was like a light bulb moment and it just made sense Great bit of engineering and math

@grugs6801 5 лет назад

So beautifully nerdy

@s.vidhyardhsingh3881 5 лет назад

Really loved it!!!! Brilliant!!!! 👏🏻👏🏻👏🏻

@zimdalf 3 года назад

Very interesting timing for me cuz at work I have been spending a lot of time hand tightening bolts and realized that they turn clockwise looking at them but turn counterclockwise to tighten the nuts when you’re looking at the bolt heads.

@jake_a_g 5 лет назад

Shoutouts to Henry Segerman, the real champ

@sarahgargani5836 5 лет назад

this reminds me of the time had a lot of free time and stripes of paper at work. so i started weaving them into lanyard and since the paper was the perforated sides of triplicate forms it was bi-colored, and anyways i used a couple paperclips and a quarter turn to turn it into a mobius loop.

@IIIIIawesIIIII 5 лет назад

I saw the thumbnail, traced if it's indeed a moebius structure, stood naked and alone in my living room and silently said: "Coooooooooool!". I really need more friends. Friends who'd stand naked in the living room with me and be hyped about moebius gears. But all my friends are cool and I actually hate them.... :(

@ChrisWCorp 5 лет назад

That thing looks amazing! I want!

@HebaruSan 5 лет назад

The parents jamming up the system joke never gets old

@cortster12 5 лет назад

Plot twist: it's the teachers jamming it up. Further plot twist: every cog jams it up at different times.

@davidwillis7991 4 года назад

Who needs parents when you have administrators

@FinlayStafford 5 лет назад

To be fair, the mobius loop thing is exactly what the cogs in the top video at 4:18 do. It's just that for three cogs to flip around that quickly and still mesh they have to be longer.

@WhirligigGirl 5 лет назад

you edited a correction of anticlockwise vs clockwise in the explanation at around 7:30 and honestly I respect that and prefer it to youtubers who just pop a text on the screen with the correction.

@omikronweapon 5 лет назад

Grate stuff! Although somehow after seeing the base, I expected it to sit on there tilted at an angle, and am now slightly disappointed that it's just flat. I think a jaunty angle will make it more eye catching and keep interest for longer. Especially from a static point of view. The first few times you'll walk up and around, but after a bit it becomes just a symmetrical, predictable shape on your desk or shelf. An angle might counter that.

@rif6876 5 лет назад

We need a half hour show of hypnotoad staring at the mobius cogs.

@2inthemorning 5 лет назад

I can't believe you've left your 2x2x2 unsolved.

@onefellow8635 5 лет назад

Now I want one of those mobius cog rings...

@KlaasDeSmedt 5 лет назад

If you look at this from a 2D curved surface, it is still a loop of 30 gears, alternating rotation. It only happens that the 2D gears only have one side (like a mobius strip)

@eatingsfun 5 лет назад

The fact that its impossible to buy and looks really cool makes me want one bad.

@youtubeuniversity3638 5 лет назад

Angled view looks pretty.

@wizzletide9179 5 лет назад

Now i need a Mobius-Cog-Loop animated Wallpaper :D

@benthayermath 5 лет назад

Next step: a Klein bottle made of gears. A true marvel of 4D engineering.

@timh.6872 5 лет назад

actually, this "gears meshing inside other gears" thing the object of this video does, I bet you could actually get a klein bottle to work, though making one that has an equidistant tessalation could be problematic. For small enough neighborhoods, use a planar gear tiling, and globally link it up into a klein bottle.