Are odd-numbered mobius-loop cogs possible?
Вставка
- Опубліковано 12 чер 2024
- 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/ - Розваги
So this is what the gear wars were fought over.
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.
@@Lattamonsteri legend man comment
I dont get it
@@lkjsdf1 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
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.
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.”
Yea being intertwined is not really necessary here, is it?
@Boco Corwin Fun this thread.
@@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
what an unexpected twist
@@CM-mo7mv no it just makes it easier/more compact
You looked very proud of that triple negative
I wasn’t unproud.
*visible sigh*
*sighs echo throughout the world*
Given that 3 negatives makes a full circle to renavigste itself as a single negative... Could one argue that he made a möbeus negative?
Looking In With Victor B I suppose one couldn’t not
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...
Likewise, the mechanism in the video does not block itself if it is well designed.
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.
where can i buy my own mobius cog strip?
reddit.com/user/elmins
but it costs alot of Reddit karma
@@aniofri I up doot.
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.
@@elminz let me know when you can make one :)
@@elminz You should start a kickstarter to sell them as a desk toy
The solution is easy: parents move in a clockwise and anticlockwise way at the same time. I know that from experience.
So the system works, provided we never try to measure the parents' spin?
exactly, most people have two parents
Everyone's entitled to own a pinion.
best pun I've seen in a while
I must askew, ... was this pun a spur of the moment thing?
Get out
God what a mesh
I just learned a new word with this pun.
All the school needs is another cog with "Admin" on it and the ring should be fixed.
Actually, it needs the parents out of the school, they're the ones who ruin their children's learning in school
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
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.
The reality is Admin would be a ring gear that surrounds the whole mechanism and simply makes it not work even worse.
@@renerpho HOT TAKE
Do we need a 10 hour video of mobius cogs spinning?
Yes. Yes we do!
With Matt in the background
@@andrerenault if that ever happens I will have a new animated desktop background.
@@andrerenault Not even on loop. Just sitting there for 10 hours straight.
Confirmed.
ua-cam.com/video/baWpiyMX9g8/v-deo.html at least a start!
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.
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
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
George W. It would be much bigger though
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.
Deepfriedpillows just use less or smaller gears lol
You definitely said that date wrong and then re-dubbed it. What a parker line read.
Aziraphale686 haha, nice catch. 9:00 if anyone is looking for it
its a parker sqript
Ah yes, teachers think that parents jam the system, parents think teachers jam it, but students know that they themselves are the problem.
So take all of them out so there is no problem
People who aren’t in the system realize that they’re all technically at fault. The school system itself is a fail.
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).
@@fumiko___ yup. The three cogs aren't the problem. It's how the idiot decided to place them thats the problem.
Administrators are the problem
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
I live their stuff! I must have missed that.
I first came across Oskar via the “Magic Gears”, which are incredible. ua-cam.com/video/qGAnmRb66s0/v-deo.html
@@fanrco766 I assume because he tends to partner with lots of other people to make stuff
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.
standupmaths Another name for those are paradoxical gears. They can even be made in different sizes! ua-cam.com/video/-1Gfc1Iq0GY/v-deo.html
Watched the videos, and those gears are pretty neat!
Intellectual proves his worth by saying “ain’t *not* goin’ nowhere” to negate the contraction :-)
It's an odd number of negatives, so it works!
Now if only we could find 12 more things to put on that school poster, it can finally make sense.
Homework
Homework
Homework
Homework
Homework
Homework
Homework
Homework
Homework
Homework
Homework
Homework
perferction
7:52 "some people just want to watch the cogs spin"
-Joker, 2019
I think the USA Today one is probably deliberate, as you suspected.
3:30 "You CAN'T use the you are NOT looking at it from the WRONG angle argument"
Boole has left the chat
I could not fail to disagree less.
9:01 When you “say” 22nd but mouth 18th
I love the triple negative to illustrate the silliness of the three cogs.
Top notch.
@@aknopf8173 ow. My head hurts.
Its incredible what people are making with 3d printing and simple part accessibility
Absolutely fantastic! The only way to make this better is to make that loop with a prime number.
Absolutely incredible ingenuity, creativity and engineering proficiency on the redditor’s side. Matt is as awesome as ever. One of my favorite videos ever.
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.
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.
So they have finally leaked all that Alien Technology from the Area 51 raid
dude the raid is 20 of september.
tho they might have found some time machines in there so maybe.
Since you own the license to the triple gears then we shall call it the Parker Gears
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.
"making cogs grate again" absolute legend, gutted it missed that, given I listened to the audiobook. still brilliant
I'd kickstarter that as a desk curiosity.
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?
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.
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.
@@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.
I'll wager it's not possible to have a working Mobius loop of gears using 4.
@@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.
This is not a "Parker" results, it is a huge success!
7:49 - This moment of satisfaction. I must admit that this construction is brilliant
Your presentation and the music make maths so much fun!
Thank you for the close up of the gears
Props to Elmins for the print, Super cool.
I hate that when you said “ain’t not going nowhere”, it was in fact a true statement
You mean you didn't not dislike it?
andymcl92 You’re not incorrect
This is freaking mind blowing!
Nice video, well done man
At 6:15: "You spin me right round, baby
, right round like a mobius strip. Right round round round."
It makes me happy seeing you so happy about this.
Love how he was so proud of the triple negative at 1:50 but missed the double at 3:31 😂
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
What is the minimum amount of gears you can use in this system with it still working?
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.
1
Gold161803 oh yeah
Wow. That's really neat! So simple, yet awesome at the same time.
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.
Very nice video Matt!
You got me! I just wanted to watch it spin, and then you said it. Thanks for the COGS
This was fun. I like it whenever Matt has toys with him
I would absolutely love to buy one of those mobius cog cycle thingamajiggies :D
I want one too!
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.
@@elminz If you ever get more free time, hit me up with estimated cost ;)
Awesome work though!
@@elminz
@@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
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
This is immensly satisfying to watch
Once again Matt, ... mind blown!!
Something works best when all its parts are working. Thanks poster, I never would have guessed...
this just simultaneously mad both cogs and mobius loops great again
Thanks Matt, I want to start my bachelor study in math next year so I will remember WiSE!
A massive thumbs up for the person that built that.
5:15 It's not a humblebrag when you have that good a grasp on your target audience. :-)
I've not watched this yet, but just the name makes me excited.
It is my birthday today and I got a copy of humble pi! All ready read the first 2 chapters!
HAH! I'm way ahead of you! I'm already at chapter 5!
This is absolutely incredible!!!
Matt gets working odd number cog set. Immediatly adds another to make it even 👌👌😂
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.
That snicker after reading the caption really made it :D
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.
So beautifully nerdy
Correct me if im wrong but you could make the odd number of cogs work without intertwining them like in the one in the video right? Of course the intertwining is very nice and flashy though
It's possible, but the circumference would be near double of what it currently is. These are designed to be as compact as possible within the limits of a standard 3d printer could do.
I read the title as "morbius-loop" I think the internet has done something to me.
morbius moment.
Really loved it!!!! Brilliant!!!! 👏🏻👏🏻👏🏻
The longer I look at the gears turning the more satisfying they get
This is beautiful. How did I not see this before today??
I totally want one of these as a desk "toy."
Elmins, you absolute madlad.
Why do I feel like I have seen this entire video before
Well, the mobius loop is the key to time travel.
@@standupmaths is that an endgame reference?
May be on his Twitter?
Deja vu, I've just been in this place before
The video loops back itself in the temporal dimension.
We love you, Matt!
6:18 I love that you can hear the pure excitement
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.
I was watching a short video of a working mobius-loop cog on Facebook, next morning UA-cam recommends this video to me...
"Making cogs grate again." Now that's clever!
Ohohoho yes please I remember the tweet and I've been looking forward to this for a while
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.
The moment i read the title, it was like a light bulb moment and it just made sense
Great bit of engineering and math
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.
That thing looks amazing! I want!
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)
That "ain't not going nowhere" comment made me stop and try to figure out the sentence. Perfect choice of words Matt.
me waiting for the pizza rolls @ 7:50
Mesmerisingly beautiful.
I noticed at 9:00 your voice doesn't line up with your mouth, is that a Parker deadline then? :P
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.
I got goose bumps watching this video...
Angled view looks pretty.
Just amazing!
Cool! I saw that gif too, but didn’t think anything of it. Do the gears have to be slightly helical?
unusually mesmerizing
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… :)
Absolutly amazing 😀
Now i need a Mobius-Cog-Loop animated Wallpaper :D
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.
Now I want one of those mobius cog rings...