Using topology to close a rubber band bracelet

With Sabetta Matsumoto and Saul Schleimer.
It seems impossible, but you can make a giant loop out of lots of little (not very stretchy) loops. So you can wrap a broken suitcase using hair ties, without any cutting or knotting. Or you can finish off a rubber band bracelet without using a clip and, again, without any cutting or tying knots. We explain the problem, the solution, and some of the mathematics behind it all.
Links and references:
Snappy - computer program for analysing knots, links, and manifolds - snappy.computo...
Mathoverflow question (by Anton Petrunin) -
mathoverflow.n...
Anton Petrunin - anton-petrunin...
Michael Freedman - en.wikipedia.o...
Larsen Linov - math.berkeley....
Mathematics:
Hopf link - en.wikipedia.o...
Borromean rings - en.wikipedia.o...
Hyperbolic geometry - en.wikipedia.o...
Hyperbolic links - en.wikipedia.o...
bookstore.ams....
Linking number - en.wikipedia.o...
Milnor invariants -
J. Milnor. Link groups. Ann. of Math. (2), 59:177-195, 1954
For an introduction to hyperbolic geometry and its application to knot theory we recommend Jessica Purcell's book "Hyperbolic Knot Theory" - users.monash.e...
Loom bracelets:
• Fishtail Loom Bracelet... - Fishtail Loom Bracelet - Tutorial || Rainbow Loom
• How to Make a Boxed Bo... - How to Make a Boxed Bow Bracelet - EASY design on the Rainbow Loom
• Rainbow Loom! DIY 5 Ea... - Rainbow Loom! DIY 5 Easy Rainbow Loom Bracelets without a Loom (DIY Loom Bands)

[@paulathevalley]

Only in math does the phrase "once the human has been turned into a hair tie" appear completely casually. ❤

[@mskiptr]

Indeed. I didn't question it at all

[@electro-verload]

5:07

[@n7sArchive]

shape shifters are crying reading this comment

[@MattHudsonAtx]

Math is special that way. It's a felony in other venues.

[@felipems3624]

That's where I got lost

[@whydoihavetodothissomeonet4234]

If you’re ever out of hair ties, just turn yourself into one. Just make sure you aren’t wearing a bracelet also made from hair ties, or else you won’t be able to get back out.

[@charliepalmer484]

First you have to hold your own hand tho

[@echognomecal6742]

@@charliepalmer484 For pity's sake. I'm getting the steps all mixed up. Also, can I hold my ankle instead? Plus, what if I'm wearing a balaclava? Forget it. Just forget the whole thing.

[@fredk.4661]

​@@echognomecal6742, that simply turns you into a newt.

[@EricBridges]

And we know it's true, because math proved it.

[@whydoihavetodothissomeonet4234]

@@echognomecal6742 the balaclava turns into that metal thing some hair ties have.

[@custos3249]

This video is like if your dad got a blackboard and detailed the mechanics of gear ratios, inverted pendulum equations, and geometric functions rather than just giving you a bike.

[@quillclock]

yeah, what he said

[@saulschleimer2036]

@custos3249, I _am_ your father!

[@BinaryBolias]

@@saulschleimer2036 No. That's not true. That's impossible!

[@Samu2010lolcats]

@@saulschleimer2036 Noooooooooooooooooooooooooooooo....!

[@mmmteeth]

i still dunno how to ride a bike so id kinda like that

[@CrispyChicken38]

If removing the clasp makes it not a bracelet, you have several extremely expensive bracelet companies to argue with.

[@aguyontheinternet8436]

well they aren't bracelets >:( they are simply watches that don't tell time.

[@DiggleTime]

They said that cutting isn't allowed for the bracelet test, and opening a clasp is effectively the same as cutting the bracelet

[@jordancruz8069]

​@kingjnc2677 the difference with that 'cutting' is that it is a design flaw for this rule set. Using scissors or a knife is an outside component separate from the bracelet.

[@jessebeegee]

⁠@@jordancruz8069an outside component separate from what? you didn’t prove that was a bracelet yet…so how can you try to define bracelet with this example?

[@jordancruz8069]

@jessebeegee outside component of the potential bracelet. My point wasn't to define what the bracelet is, but that an outside tool or force essentially can't be used to break it. Otherwise, you could literally call nothing a bracelet. By opening a clasp on the supposed bracelet, nothing has been broken since it can be closed again. By cutting the supposed bracelet, you have broken it.

[@CarloRoosen]

I always wondered how topology would look like. Apparently it looks just like normal Math, but now I am even more curious because I understood none of it.

[@CarloRoosen]

'hyperbolic geometry', that is what I will need to learn, apparently.

[@williamcompitello2302]

Since I'm too dense to understand logic, try to hear me out. The surface of a Pringle is an example of hyperbolic space. The inner surface of a donut is hyperbolic space. Look up Hyperbolica, (if you can handle it) and compare it to flat geometry. Hope this helps you on your quest.

[@ccreutzig]

@@williamcompitello2302 To a topologist, a Pringle (not infinitely thin), a cube, and a sphere are the same thing. Just like donuts and coffee mugs are.

[@stickguy9109]

​@@ccreutzigExplain

[@ccreutzig]

@@stickguy9109 In topology, the shape of an object is irrelevant, the only thing relevant is “neighborhood,” which is enough to find such things as how many holes an object has. But you can take a donut made from clay, and, without tearing it or closing or creating holes, shape it into a coffee mug (the donut hole then is in the handle). Hence the old joke how a topologist can't distinguish the two. Same for a cube and a sphere, or any finite contiguous object without holes, really. And no, I have no idea what they were talking about in the video with hyperbolic topology. It just has to be something that remains there under deformation, like flattening a Pringle.

[@timseguine2]

Finally answering the question that 12 year old me thought should be doable but couldn't figure out how. It always seemed like since it wasn't actually a knot, it should be possible to do but I couldn't figure it out.

[@doridear1604]

This video was suggested to me by youtube and I have never before watched anything from this or similar channels, but I loved how it was talking casually about turning humans into hairties. Wouldn't that just solve a lot of problems (mathematical ones of course)

[@Frommerman]

I can think of six specific humans it would be extremely useful to turn into hairties right about now. For entirely mathematical reasons, I assure you.

[@echognomecal6742]

I think that's Exactly the line that got this recommended to me. Also, yes, being able to do so could solve a # of problems. But, how many would it Create?! This...this right here is where math will ultimately fail us.

[@agilbert9066]

Once my brain wrapped around the fact that you weren’t trying to join two loops but we’re joining three, I made myself a very cool bracelet

[@bottlekruiser]

finally someone who understands it! maybe sorting the comments by new is not a fruitless endeavor after all

[@thefourhorsemenofapocalypse]

This could be taken as a very sneaky joke

[@tafellappen8551]

My child self feels simultaneously upset that its not possible without cutting but also strangely comforted that it takes such high level math to actually have that answer

Did you watch the video? They show that it is possible, not that it isn't.

[@shanepurcell8116]

@ I wish they had actually shown it being done with real hair ties instead of a bunch of math and drawn circles. Seems like the obvious thing to do?

@@shanepurcell8116 Never mind the fact that that's what they do from 3:16 for a minute or so. Your ignorance is beyond staggering.

[@aidenlilley1319]

@ they quite literally showed that you cannot close the loop without cutting. The only way they could get the red hair tie / "human" on the bracelet was by cutting and melting it back together.

[@aidenlilley1319]

Of course for the purpose of getting the bracelet on your arm and taking it off, not being able to truly close the loop on its own is fine, but it isn't truly closed without cutting a loop (your arms).

[@91722854]

this video served as an advert for hair ties, so that hair tie companies can sell more hair ties, and even me as a guy with short hair wants to invest in this and buy some hair ties just to play with topologically, great video, thanks

[@danielleanderson6371]

It never hurts to carry some hair ties with you, in case something else needs one, or you have to tidy some cables, or you want to fidget with topology, or any of their other myriad uses. Hair ties are great!

[@livinginthenow]

I can confirm this is a valid impulse. Despite the fact that I have really, really short hair, after watching this video I literally dug around in the junk drawer of my bathroom and scraped together as many hair bands as I could find just so I could try it out. I succeeded in making a bracelet. I failed in making an attractive one.

[@tumblingartist]

:D

[@dolphin64575]

You don't have to pay a lot for hair ties, I got a pack of like 50 at the dollar store

[@Ltdo007]

Never has a video, where I understand absolutely nothing, kept me this interested

[@amazinggrace5692]

Perfect comment! 💕🐝💕

[@JobvanderZwan]

I actually regularly find myself in a situation where I want to close something with an elastic band, but only have a bunch of short and weak ones, so this non-destructive trick might actually prove useful to me in the future!

[@saulschleimer2036]

Very curious to know your application, if you can tell us? Or, if you don’t want to share on a public forum, you could email one of us? Thanks in any case for the comment.

[@nixand_brennt]

I'm only a minute in but I stumbled my ass in here with my crafting-brain active and am now giggling because I forgot how much I love the math-brain approach to solving problems. Defining the problem to a superficially silly level of specificity, and (naturally) testing some absurd potential solutions to make sure that the definition makes sense.

[@anthonycannet1305]

I like the inclusion of the trivial non-bracelet

[@dewinmoonl]

wow I've only had to wait 10 years for someone to tell me how to make larger loops out of smaller loops. really thanks for this ! (a former math major)

[@briansimon4363]

Jeez! Now I know why I flunked out of Uni after a year. It hurt my brain just to watch this!!!! Education is a wonderful thing and thinkers like this, with such a facility within their given specialist field, have me in awe!

[@AllenKnutson]

Hi Saul! While we were in the middle of the hyperbolic geometry I pointed out to my son, "Only moments ago she was threatening him with a saw". Interesting choice & mix of material. I hadn't seen Freedman's trick before.

[@saulschleimer2036]

Hi Allen! Glad you enjoyed the video. :)

[@Muhahahahaz]

It was just a little Hyperbolic Sawmetry…

[@justlola417]

Just went around the house to collect enough hair ties to try this and it works and I'm so disproportionately happy about it aaaaaa

[@echognomecal6742]

I am vicariously well pleased.

[@NonTwinBrothers]

Name a more iconic trio

[@Fanny-Fanny]

The Beatles?

[@IsaacMyers1]

@@Fanny-Fannythere was four of them

[@Fanny-Fanny]

@@IsaacMyers1 exactly! They needed one extra to be more iconic! #science

[@Magnogen]

Can't

[@connorhamilton5707]

Kushala Daora, Teostra, and Chameleos (Elder Dragon Trio in Monster Hunter).

[@donaldasayers]

I like the way it was, easy, easy, easy, easy, hyperbolic, wait what?

[@redfailhawk]

I didn't understand a word of it but didn't feel talked down to, either. impressive!

[@kemikao]

Believe it or not, but I have been wondering about this for several YEARS! Or at least a very similar problem. I had actually decided that it was impossible. Thank you for showing me a solution!

[@azy6868]

You were correct there is no solution. They cheated by cutting and rejoining the red hair tie. A shameful clickbait image for the topologically fascinated.

[@deborahbarry8458]

@@azy6868ah that explains a lot

Y'all failed to comprehend the video. It is possible.

sHaMeFuL cLiCkBaIt... watch how this person will continue to fail to understand that they are absolutely wrong and not apologize for their insinuation. It's just the same thing over and over again with most people. Most people are dumb, arrogant pricks who will never admit they were wrong.

[@Jooolse]

@@azy6868 LOL, the red hair tie represents the person's arms... The solution they presented is of course valid.

[@dangerouscommiesubversive7243]

Came to this video due to a slightly goofy DIY problem--"I've left all of my headbands upstairs, but I have the stuff for my son's potholder loom next to me, can I make a functional headband by stealing some of the loops from it?" This video absolutely did answer that question, but also ended up giving me several more that I hadn't even considered asking. Since I love questions, it was like getting a surprise present! Thank you very much, this was fascinating.

[@louiesumrall358]

before watching i just have to say thank you for answering a question i've had lurking in the back of my mind for decades

[@MrJesterboi]

This is the most beautiful visual drawing I’ve ever seen from a mathematician

[@saulschleimer2036]

Thank you!

[@adrianghandtchi1562]

It was randomly recommended to me, but I sincerely appreciate the solutions to join those loops

[@Frommerman]

Well of course humans are topologically similar to hair ties. We already knew humans were topological toruses, and so are hairties, so they are obviously identical.

[@JerusalemStrayCat]

I don't think the hair ties are going through the gastrointestinal tract though

[@matthewwhiteside4619]

5:08 "...once the human has been turned into a hairtie..."

[@AlphaPizzadog]

If you think about it, it makes sense. If you want to open something that's closed, you have to cut into it, and if it's closed, then it's not open. therefore, if you can't cut then you can't go from closed to open.

[@charlesmartin1972]

Careful making assertions about "open" and "closed" in a channel dedicated to math. An open set is a set which contains it's own boundary points; a closed set is a set whose complement is open. These properties are not mutually exclusive, and you'll find that many sets are clopen

[@AlphaPizzadog]

@@charlesmartin1972 CLOPEN?

[@charlesmartin1972]

@@AlphaPizzadog yes. For instance, the set of positive real numbers is ∀x:(x∊ℝ)∧(x≥0), which is open; the set of negative real numbers is ∀x:(x∊ℝ)∧(x≤0), which is also open. Since these two open sets are complements of each other, it follows that they're also both closed, ergo clopen

[@yaeldillies]

@@charlesmartin1972 Unless you're French, "positive" sadly means x > 0, not x ≥ 0 (that's "nonnegative"). In the order topology of the reals, nonnegative numbers form a closed set, and nonpositive numbers too. They are not complement to each other since they both contain 0. Positive numbers and negative numbers both form an open set, and they are not complement to each other since neither of them contain 0.

​@@AlphaPizzadogYou failed to grasp the essence of the video, it is possible without cutting.

[@rayrous8229]

If you started with a large block of rubber, and removed all the non rubber band bits, you could make a continuous loop of loops.

[@jennoq1311]

That I can understand, this video I just watched absolutely confused me.

[@rfresa]

I can't even guess how many times in my life I have wanted a way to close a chain of loops without using a non-loop object. One way I often end up using which you didn't cover is wrapping both ends around a rigid stick-like object. Thanks for presenting the solution!

[@heritagehuntress9553]

This showed up in my feed a couple days ago and i didn't take the time to watch it. Today one of my students had a string of bands that he was trying to.tie into a bracelet. So now I'm watching this.

[@MeUrWishGranted]

I didn't realize my level of nerdiness until I spent 11 minutes engrossed in the math behind a bracelet 😅

[@justme-qd6qb]

I don't know what topology is or how I got here lol but it's so interesting to see all the fidgeting and playing with hair ties I've done in the past turned into an educational video. I don't totally get what's going on but I feel like I'm learning

[@laymandigitization2598]

I have literally agonized about this problem while messing with my hair Ties. Thank you

[@josuevalar6465]

Awesome, I didn't get any of that, so basically you can't close it unless you join the last band as if it were a human's hands?

[@thebezierguy]

That's right, but there is another way. The only way without cutting or joining is this: 3:26

[@henryseg]

I’m not sure if it’s the *only* way. I bet there are other things you can do…

[@makingitthrough190]

I am glad someone else mentioned that. Everything else was way above my comprehension. However, it always was very annoying that you could make an elegant bracelet out of elastic bands until you come to join the loop. And it seems it remains so.

[@henryseg]

@@makingitthrough190 if you want the loop to close up in the same pattern as the rest of the bracelet then it is impossible. A bracelet like that would be a version of the link L_n (this time with all hair ties - no human loop), which we proved is not the unlink. So it cannot be made from hair ties without cutting and rejoining.

[@leif1075]

​@@henrysegThabks for sharing Henry..I really hope you can respond to my other comments whenever you have a chance. Thanks very much.

[@emilyblenn]

You have NO idea how long I have been asking this pointless question. THANK YOU

[@ironbacon]

Me just trying to learn how to close a rubber band chain and getting roped into high level mathematics

[@duncanhoward5045]

That last part was a lot of English-sounding words strung together that basically made almost continuous whooshing noises above my head.

[@tsloth1390]

I actually knew this solution from messing about with such things! I couldn’t come close to proving it like y’all did though.

[@Erhannis]

Oh, I was just trying to figure this out the other day. Ended up using an S-hook. A little disappointing I didn't figure it out, but "double the length" wasn't really in my space of actionable solutions, anyway.

[@officalJesusChrist]

When this had shown up on my recommendations page, the power I gained from this video was unstoppable

[@saulschleimer2036]

Please use your newfound understanding for good…

[@officalJesusChrist]

@@saulschleimer2036 I can't promise anything

[@ZippedUpKitz]

I just wanted to know how to connect the two ends together… didn’t know I was going to get a lesson in advance mathematics… by the end of this, I felt like I was sitting in the classroom with Charlie Brown!!!!

[@elijg6104]

Thanks, I’ve been wondering about this for ages

[@BrianSpurrier]

I love that you can tell that everyone here was just goofing around and having fun the whole time

[@sarahkudrick6567]

This video was great! I learned how to make a bracelet out of hair ties, which is exciting, and then I quickly and gently drifted off to sleep!

[@oresteszoupanos]

8:43 Surely you are talking about the Tau Theorem?!? Especially today (6.28) of all days! Happy Tau Day everyone ^_^

[@quillclock]

so you are telling me i spent $200 on a silver bracelet for my wife and it doesn't even pass the bracelet test? :(

[@saulschleimer2036]

It does if it is made only of links; it doesn't if it has a clasp. ;)

[@sammccardalkilby]

Saul taught my Cohomology and Galois theory courses and was awesome! Hope you're doing well Saul!

[@brendanbennett6770]

And me Foundations. I don't know if you can double take on audio but I did

[@WackoMcGoose]

4:48 "It looks like we're going to have to use..." _dramatic zoom in_ *"...topology."*

[@Tann114]

excellent, I enjoyed the live diagrams as you explained

[@elijahboyle4688]

So, it turns out to make a bracelet out of hair ties you must become one with the bracelet

[@nickalasmontano1496]

I was just thinking about this the other day! I'm glad to see that people have put some rigorous thought behind this

[@cuchareable]

Ive been waiting for this información for almost 34 years.

[@DavidLindes]

Not a complaint, nut just to let you know… it was at 5:43 that I lost track of what you were saying, and the rest degenerated into math babble. I think if you could find a way to make that transition smoother (or, obviously, if I had more and/or fresher mathematics background), I probably could have kept track until the end and it all made sense…. Alas, not today. 😅 Still, interesting video, and I love that there’s a whole theorem out there whose very name is supportive of the notion that we ought to switch to tau.

[@crackedemerald4930]

Finally, i can make custom sized rubber belts for my contraptions

[@stevebailey805]

Wow. I understood the pair of slip knots making a bracelet. I understood the individual words but being honest have absolutely no idea what was said. But presumably H & S & S understand it! The slip knots are the thing though.

[@JobvanderZwan]

10:52 "Which is due to Gauss" Dread it, run from it, Gauss still arrives

[@Hacker1o1]

thats cool how you showed some peoples unique designs

[@space8381]

*Brings the handsaw into the camera* "So, no cutting the arm either?"

[@bottlekruiser]

hey its called the *hand*saw for a reason

[@joehart3481]

I love all the comments on how ridiculous the whole thing is, from the human-hairtie transformation to the MAAAAATH. This video is delightful, thank you.

[@paratethys]

ok who gave calculus to the knitting community? (seriously though this is fantastic, more please? my only complaint is that you didn't re-seal the red hair tie in the arm position so i had to go find some string to replicate that step and prove to myself how the two loop thing reduces to the perfect ring)

[@wesleyooms]

I figured a lot of hair ties linked together can be seen as a long string with a loop on each end. Now the loop on each end can be wrapped around itself to create one big loop.

[@Theleaddog]

I just needed to see them make the bracelet and I am good. I can follow any direction if presented to me in reality. The math… you can leave that part out.

[@Rogueaviation]

What beautiful science you have shared with us. Thank you for posting this, it was entertaining and completely amazing.

[@possums154]

never in my life have I so thoroughly enjoyed what could be defined as a math class. the only reason i understand anything in this video is because in my geometry class we covered topology for exactly a week

[@Jooolse]

4:34 It is pretty satisfying to figure out the solution was just to assimilate the person's arms as a little loop... with a lock to close the pattern. 🤗🤓

[@ImAShrimpbruv]

Honestly laughed when you put just a band on the guys arm and having someone pick it up

[@adorablycutekitten5291]

i am almost embarrassed to say the amount of times ive wondered if this was possible. 😅

[@Kerygmachela]

I paused the video at the 3 minute mark, got out some rubber bands and stumbled upon the solution in about a minute. Judging by the other comments I must have been very lucky!

[@Kerygmachela]

Obviously the maths behind it is beyond me..

[@saintsatellite]

"pshh grad level topology... I'm sure my decade-old bachelor's in math will carry me through t- oh wow I really can't understand those propositions"

[@mrwhisper3837]

The epitome of being trolled, you are now a component.

[@yanikb.1312]

Thanks for the warning, it was necessary 😢

[@janaki3829]

* turns you into a hair tie for topological purposes *

[@tash17kids]

I was waiting for the guinea pig human to be cut and melted back together again so the theory worked in practice!! Lol

[@nathanhelmburger]

Boromian knot bracelet... Not exactly as tight as 1 hair tie! Tighter! It has to loop around the other and the hair ties have non-zero thickness! Such a mathematician-style oversight...

[@saulschleimer2036]

Yes, it is very very slightly tighter.... but I could not feel the difference... perhaps because of the lingering numbness from the first one. :P

[@idol_wannabe]

No music, no mr beast editing, no bs. Nice!

[@FelanLP]

And I thought I get to see a neat trick to close the loop without having to cut something.

[@SimonClarkstone]

You did.

[@FelanLP]

@@SimonClarkstone um, no. They closed the loop, by cutting another band and "reparing" it. And if you make a loop with your arms, it's also an open ring that got closed by holding the hands together. Btw are the arms not part of the loop because the loop is supposed to go around the arm.

[@angerock49]

​@@FelanLP3:49 did you miss this solution in the video?

[@FelanLP]

@@angerock49 this is not a loop ether. If you remove the arm, the bracelet falls apart and becomes a string/chain again. It may pass the bracelet test, but it fails the loop test. The video misses a true solution. The thumbnail implied that the question was how to join the lose ends together. How to bridge the gap between these to ends to form one continuous ring shaped loop.

[@Aquaticfireartglass]

Nice try KZbin suggested videos. Trying to sneak in Maths when I'm least expecting it!

[@Kram1032]

I realize it'd have been a lot of work, but I'm pretty sure you could've explained that proof in greater detail to make it more accessible to a wider audience. Either way, nice way to close up some hairties

[@henryseg]

There is a lot going on in hyperbolic knot theory - I think that we would just replace one set of unexplained things with another, unless we would go through an entire course on hyperbolic knot theory. If you're interested in how technical the details get, the 2\pi theorem is covered in Section 13 of Purcell's "Hyperbolic Knot Theory" (users.monash.edu/~jpurcell/hypknottheory.html).

[@SleepingUnderable]

@@henryseg Could it be proved using coloring or its generalizations? If it exists it will be much easier to explain to us the general audience

[@leif1075]

@@henryseg Is there even an entire course on such a thing? How would someone manage yo get through all that? Thanks for sharing Henry and hope you can respond when you can.

[@SleepingUnderable]

​@@henryseg I counted the number of tricolorings in L_n, note that each unit of two unknots combining (same unit as in Larsen Linov's answer on Mathoverflow with 2 inputs and 2 outputs) force a tricoloring to be the same in input and output therefore we can assume inputs are the same color for all units. When the inputs are different colors all colors are forced and when they are different we have 2 choices. So we have 6(different colors)+3(same color)*2^n(time choice for each unit). However n unknots have 3^n tricolorings, and the number of colorings is allegedly a knot invariant. So we need to find all n such 6+3*2^n=3^n, but that can't be since they are different mod 2. Thus L_n in not an unlink. Because I was confused I went and computed more tricolorings. In Larsen Linov's answer (what you seems to suggest as the solution for the bracelet) has no tricoloring when we remove the block in the middle. When we add a knot in the middle (like in Ian Agol's first picture in the same MO question), I counted 2*3!*2^n=12*2^n colorings and no coloring in his second picture who he claims to be equivalent to L_n and to the first picture. So I might have a mistake somewhere because 6+3*2^n!=12*2^n.

[@henryseg]

@@SleepingUnderable Saul looked into this - yes, looks like this is a simpler proof. There's a paper by Przytycki titled "3-coloring and other elementary invariants of knots" where Lemma 1.2 tells us that "the number of tricolourings is a link invariant". Also, Lemma 1.4 tells us that the set of tricolorings always has cardinality 3^k for some k. Saul checked that the number of tricolorings for L_n is 3^{n+2}, which is different from the (as you say) 3^n for the unlink. So they must be different.

[@1.4142]

I have been wondering this for ages

[@toinks302]

this has the same energy as that turning a sphere inside out vid omfg..

[@UnrelatedAntonym]

I was actually wondering a couple weeks ago how to do this with hair ties.

[@ImThistle]

Thought I was gonna learn how to improve the rubber band bracelets I don’t make, now I think I’ll just cry.

[@Atlass-Lark]

Literally thought this was going to be about crafting. Did not pay enough attention to the title

[@ivarangquist9184]

This video makes me want to learn topology.

[@saulschleimer2036]

My work here is done.

[@ZedaZ80]

This was fantastic and hilarious, definitely going to be implementing this!

[@ZedaZ80]

I had to rewatch this for my partner's sanity 😁 When I first watched, I told my partner because this is a combo of my favorite things! And then they kind of scoffed at it >:[ But no worries, today I had a bunch of rubber bands from our produce, and put them together. I told them it was possible, so they tried and tried and got invested. Secretly, I had already forgotten the solution so I had to come back to this to figure it out so they wouldn't lose sleep at night trying to figure it out >_> (It was not actually a secret, I told then I had forgotten and just remember that it had to be double the ending circumference.) Anyway, thanks for the couple's bonding exercise!

[@ZedaZ80]

Maybe I should have reworded that "couple's bonding exercise" in regards to restraints >_>

[@johnsullivan6560]

Ow! You gave fair warning, which I ignored to my peril. Thank you for the effort.

[@TheAceOfFire]

1:47, Damn. They were READY for violence!

[@stitchbritt]

Today I learned topology exists and that it’s different from topography.

[@TinTeddyVideos]

The word bracelet usually means a loop around the arm that can indeed be opened for removal. Usually via a catch of some type. A loop around the arm that can not be opened and must be slid on, over the hand, is called a bangle.

[@saulschleimer2036]

Good point. “Bangle” is a great word and we should have thought of that. Ah well!

[@laurenpinschannels]

we should make a list of videos that explain the prereqs of this that most people don't have. share a video if it helps explain something about the proof that confused you?

[@TheRealAmythyst]

Imagine me somebody who suffers insomnia at 6 in the morning decides that they are going to investigate as to how to link a whole bunch of cheap Dollar tree rubber bands so that they could wrap around a oddly-shaped trash can to hold the bag. I got my answer in the first 4 minutes thank you

[@harvieradish6945]

im so glad theres an actual math to this i did as a kid all the time

[@ArDeeMee]

Everything is maths. EVERYTHING.

[@cmilkau]

If a bracelet can be assembled, it can also be disassembled in reverse order. When you do this, some rings may end on your arm. These can't be removed.without opening your arms. So that is how you should start assembling a bracelet. One obvious solution is to just make any chain and pull both ends over your arm. Another way to see this is that your arms are the only ring that can open and close, and thus always the last ring closing and preventing the thing from being disassembled (which would mean it's off your arm then because your arm would be a ring on its own after disassembly).

[@AlexisTwoLastNames]

topology is so interesting to me. also i quite enjoy your handwriting in the ipad portion lol

[@purplelord8531]

"incidentally... these form the Borromean rings" W H A T

[@alexc8114]

1:55 "you have lost arm privileges"

[@GrowlyBear917]

Bought a package of 100 hair ties. Brought them home and stored them all in my Klein bottle.

[@SnowmanInABlizzard]

The Borrowmean rings bracelet is actually slightly tighter since they have to reach around each other (instead of fusing) and then backtrack, unlike the regular hairtie.

[@saulschleimer2036]

Yes.... it is tighter by perhaps "epsilon". :)

[@KKIcons]

I think it's also tighter because two strands of elastic are stiffer than one.