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@joelklein3501 Жыл бұрын
Is his solution related to the stationary action principle from analytical mechanics?
@axiomfiremind8431 Жыл бұрын
But your hallway has no height. All you have solved is the limit of the base that will navigate the base of the hallway. A bigger sofa can simply be stood on its end. And because your hall has no celling then we know the largest sofa that can fit around the hall is one with infinite height. Like wise why limit yourself to 3 dimensions? An nth dimensional Sofa will peek at around 5 dimensions before becoming smaller again. You know because you live in a mathematical world with mathematical objects and not the the real world with real objects.
@lyrimetacurl0 Жыл бұрын
Could you have a slight extra spike on the corner of the phone shape? (along the length of it)? Since the bottom edge is slightly less length than the full width?
@olli3686 Жыл бұрын
12:14 & 12:21 these are just two 90 degree angles, so we can use shape, but we rotate it about it’s longest axis in the hall way between corners! As for the 45 degree, we could use the same shape, just cut the couch in half and move it in two pieces 😂
@fredashay Жыл бұрын
I bet'cha that Presh Talwalker from _Mind Your Decisions_ can solve it!
@guidoferri8683 Жыл бұрын
I tried to explain this problem to my friend, but he continued to scream things like "I'm not interested!", "I don't care about math!" or "Nobody asked you to cut off the edges of my sofa!"
@SaHaRaSquad Жыл бұрын
When you just want to move sofas around corners to further humanity's understanding and then people ask "who are you" or "how did you get in here, I'm calling the police"
@beyondobscure Жыл бұрын
@@SaHaRaSquad hate when that happens
@jackhandma1011 Жыл бұрын
Most people don't care about math. We just have to deal with it.
@kidredglow2060 Жыл бұрын
Ur friend is mean
@MandleRoss Жыл бұрын
HAHAHAHA!
@SgtSupaman Жыл бұрын
Seems like the problem now is less "can you find a bigger sofa?" and more "can you finalize the proof for Gerver's sofa?"
@amegatron07 Жыл бұрын
Not necessarily. The fact that it hasn't been proved yet can mean two things: either it's just hard to prove, or it can't be proved, if it's not the biggest possible sofa.
@GIRGHGH Жыл бұрын
@@amegatron07 That's the same as finding the null proof. I feel it'd be more productive to try and prove or disprove it as a launching off point as opposed to starting from scratch.
@Christian-mf4jt Жыл бұрын
It seems more likely that Gerver's sofa is really the biggest possible one, because it is locally optimal. Any better solution would need to have a significantly different shape, and that probably would have been found already.
@error.418 Жыл бұрын
@@GIRGHGH Usually you'd start with trying ti disprove.
@error.418 Жыл бұрын
@@Christian-mf4jt "probably would have been found already" is the same trap other problems have fallen into. this happens in a lot of fields, and a fun one is speedrunning where "this run is optimal, no run will be faster" and then it's trounced by a logical leap a decade later. it's just not a good way of thinking about a problem.
@blodpudding Жыл бұрын
I'm Swedish, so my solution is of course to disassemble the sofa and bring it through in pieces. IKEA beats math every time.
@R24_--___--- Жыл бұрын
Right😂
@stevenarvizu36029 ай бұрын
I know it’s a hypothetical but the whole time I was thinking just disassemble the sofa lol
@samueldeandrade85359 ай бұрын
By writing "IKEA beats math every time" you probably lost a thousand likes.
@noxlusus9 ай бұрын
IKEA 13B yearly income, Google 280B, math makes the difference 267B (subtraction) Sorry I was using math to explain that.
@michaelmichalski45887 ай бұрын
@@samueldeandrade8535I can just imagine a serious of solutions. The simple cube. The half circle. Gerbers etc. and the swedish solution where the whole sofa is broken down into a flat box.
@b0nes95 Жыл бұрын
4:02 sofa we've just been guessing at shapes
@remi177110 ай бұрын
Yes
@Bunny1sAw3somesauce Жыл бұрын
I gotta say as someone who worked for a moving company as a grunt for years, I find this fascinating. But it's not really the problem in the real world as we have 3 dimensions and most places have upwards of 12 foot ceilings. So you flip whatever your moving up on a side and then rotate it around, of course this breaks down and becomes complicated when the 90° turn is in the middle of a stairwell but there's ways to work it out. Even without touching the walls ( we put that to the test moving one family out and another into a place that was freshly painted so we couldn't touch a single wall) it's difficult but do able. The real problem is doorways.. like moving a L shaped couch that isn't sectional through a doorway into a hallway. Fun stuff Lol
@mrdraw2087 Жыл бұрын
True, this problem only considers 2 dimensions. It would be interesting to see what happens once you consider a third dimension, although that will be even harder to solve.
@benjaminpedersen9548 Жыл бұрын
@@mrdraw2087 What is required to be a sofa? The largest volume may simply be the largest in 2d filling the entire height.
@jamielondon6436 Жыл бұрын
Meh, all you have to do is pivot. Piiivoooot! ;-)
@doncarlodivargas5497 Жыл бұрын
Mathematicians: struggle moving a sofa for decades A random moving grunt:instantly move the sofa on the side
@Malekariel Жыл бұрын
Mover bro is right. Stand er' up take the legs off and spin the much easier to manuever L shape around the corner. Sofa's as big your ceiling minus like 5 inches or so depending on the shape. Don't scrape the fabric on the ceiling or you own it. Jordans Furniture customer service will replace anything damaged during delivery at the mover's expense so you learn to not touch the sides faster than a game of operation.
@YoungGandalf2325 Жыл бұрын
I didn't think a degree in mathematics was needed to to become a furniture mover. This is why sectional sofas exist.
@sicfxmusic Жыл бұрын
Exactly, I'm not good at math so guess that's the easy way out! 😂😂
@wearwolf2500 Жыл бұрын
I bought a large chair and was worried about then carrying it downstairs. It came in 5 parts...
@axiomfiremind8431 Жыл бұрын
What is the largest a section of a sectional sofa can be before it gets stuck?
@EaglePicking Жыл бұрын
@@axiomfiremind8431 The answer is: 2.
@BobBeatski71 Жыл бұрын
I'm not a furniture mover, I'm a corridor arranger.
@duvasrealm Жыл бұрын
On a fun note: Yes if you give the property of disassembly, there do exist a plethora of larger objects/sofa that can move over the hallway. Ikea still lurks around because of this.
@DevtheViolinist6 ай бұрын
The size possible is only limited by the parts allowed. IKEA teaches this the hard way.
@Kaanin Жыл бұрын
I thoroughly enjoyed the Numberphile video on this problem. When I saw you had posted one on the same topic I was skeptical you could add anything worthwhile to the discussion. I was wrong to doubt you! Your explanation of how a balanced shape has no space to gain through small movements was really intuitive! Your ability to turn a complex and difficult to explain concept into something easy is on another level. You are a terrific science educator!
@MedlifeCrisis Жыл бұрын
Shout out to the Douglas Adams fans who remember Richard Macduff’s staircase sofa. Stuck ever since delivery men couldn’t get it round a corner but then couldn’t get it back out the way it came either
@RussellChapman99 Жыл бұрын
Dirk Gently detective. Read it years ago and this video immediately reminded me of the story.
@MonkeyJedi99 Жыл бұрын
Yep, and it was solved in another book when a character opened a door that was accidentally on the landing of the stair, and let the movers turn the couch around before closing the door (making it disappear forever).
@bpj1805 Жыл бұрын
But can you get a swallowed toy sofa around the first corner of a person's small intestine?
@quantisedspace7047 Жыл бұрын
@@MonkeyJedi99 Was the resolution of the sofa thing done across two books ?
@MonkeyJedi99 Жыл бұрын
@@quantisedspace7047 IIRC, it was across two different book series.
@JosephBlanch Жыл бұрын
What makes the sofa problem even more complex is that you can rotate the sofa in a 3rd dimension (pitch, yaw, and roll as they name them in aviation). Additionally, real life sofas can also squish at the edges and corners. Sofas are so complicated 😂
@testales Жыл бұрын
I've a better idea: Move it in the 4th dimension! Go back in time to it's disassembled state, move it to the target destination and then bring it back to the assembled state. ;-)
@curtisowens750 Жыл бұрын
They never mentioned that the sofa could be stood on it's end .... I've had to do that before
@-YELDAH Жыл бұрын
@@testales as the proposed problem is in 2d, extending it to solve in 3d makes as much sense as 4d so you're not wrong lol
@error.418 Жыл бұрын
The original sofa problem is strictly a 2-dimensional question. Extending to the 3rd-dimension is an extension of the problem, but not the original.
@testales Жыл бұрын
@@error.418 Chopping out a part of the sofa or turning it into a weird object that you can't buy anyway and many people won't even identify as a sofa, is more of a cheat then just using the 3rd dimension with a sofa you can actually buy. I guess the problem is solved for regular rectangular sofas, so in fact having some online tool that calculates this for 2D or even 3D would probably be actually useful.
@huzzzzzzahh Жыл бұрын
This is such an incredibly elegant example of how math is actually done in real life. I wish all the students who “hate math” could see and really internalize this. Math isn’t about solving equations (although you gotta get your hands dirty sometimes) it’s about finding new perspectives and massaging hard problems into successively more tractable ones
@chekhov-and-his-gun Жыл бұрын
No school will tell you that though. That's why people tend to dislike math because it's shown as only equations.
@emissarygw226411 ай бұрын
My teachers did try to frame math concepts in terms of applications. I didn't give a shit at the time though, because none of those applications mattered to me. Luckily I paid enough attention anyway, but honestly the biggest motivator to learn anything is when you need it to solve an actual problem. Unfortunately in today's environment, often (but jot always!) that's too late to start learning something.
@GamezGuru110 ай бұрын
except the reason this problem is considered 'unsolved', is because it lacks a proof by the very sorts of equations you disdain... proving - in fact - that maths is about equations...
@emissarygw226410 ай бұрын
@@GamezGuru1 Of course equations are important. They're how you calculate numbers like the actual size of the sofa. Being able to calculate and/or prove things exactly is really important and useful. But there's a big component of just problem-solving and coming up with ideas.
@julien1426 Жыл бұрын
6:24 "sofa we've been..."
@Shamazya Жыл бұрын
Fun topic! I've seen Numberphile tackle this topic but the part where you showed how lateral movement of the hall allows for an increase in area was really cool!
@alanhilder1883 Жыл бұрын
Douglas Adams brought up a similar problem in his story " Dirk Gently's Holistic Detective Agency ". In this case it was a corner half way up some stairs, the movers got it to the corner, rotated it all over and then couldn't get it out in any direction. It was stuck. ( The use of a time and space machine finally solved it but that part is different to this puzzle...
@bjorntantau194 Жыл бұрын
Yeah, I thought that was going to be the reason why this is unsolved. But it also explains why Gently had to let his computer run so long to calculate every possibility.
@alanhilder1883 Жыл бұрын
@@bjorntantau194 It wasn't Gently's computer, it was " The Client " and old school friend whose name eludes me at the moment.
@bjorntantau194 Жыл бұрын
@@alanhilder1883 Ah, been too long since I've last read the books.
@alanhilder1883 Жыл бұрын
@@bjorntantau194 I will have to re find them, it was last century that I got to read them...
@babelchips Жыл бұрын
Dirk Gently’s “interconnectedness of all things” applies here! This video came out on Towel Day 😊
@kbrown4ou Жыл бұрын
We moved a large oak desk (with no real effort) into our home office. When it came time to move the desk out we found it impossible to get back out as the doorway was narrow and led to a 90 degree hallway. Ended up sawing the legs off the desk to get it out. Still confounds me how we managed to get it in with no real problem.
@MateusSFigueiredo9 ай бұрын
This is some Douglas Adams plot
@MohsinExperiments9 ай бұрын
You should rotate its legs towards the inner corner. That's how you can easily get it out from your home.
@SaiGanesh314 Жыл бұрын
Always a pleasure to be an audience in your family, Jade! I have been studying optimization in CS for my degree for 3 years now (about to graduate in the next summer!), and your content like this manages to tickle that little tone of fancy in my heart for math and provokes me to admire the hidden beauty that most often goes rather disappointingly unnoticed. But, I believe content creators like you, Derek, Diana, Henry, Brady, Grant (just to name a few) are always there to keep igniting those burning little sparks of curiosity ... Keep going and never forget that enthusiasts like me are always watching (in awe) the essense and value you bring upon in our community. Cheers :)
@DeclanMBrennan Жыл бұрын
That was very enjoyable with great graphics. A stuck sofa also plays an important part in Douglas Adams "Holistic Detection agency". There, a computer simulation proved it could not be freed by going backwards or forwards. For the resolution of this paradox, read the novel. 🙂
@bjornmu Жыл бұрын
-""Eddies in the space-time continuum!" -"And this is his sofa, is it?" 😄
@iriswaters Жыл бұрын
This was the FIRST thought I had when I saw the episode.
@renedekker9806 Жыл бұрын
Yeah, I immediately thought of "Dirk Gently's Holistic Detective Agency" as well. Excellent novel!
@vylbird8014 Жыл бұрын
The specific situation is this: During the attempt to move the sofa around a corner, it got stuck. It could not be advanced, or withdrawn. This eventually lead to such frustration that one character turned to computer modeling to try to calculate the solution - only for the program to calculate that not only is it geometrically impossible to get the sofa past the bend, but equally impossible for it ever to have been placed in the current position. The answer to this problem is part of the resolution of the novel's several interconnected mysteries.
@I.____.....__...__ Жыл бұрын
@@vylbird8014 Interestingly enough, this plays out in the real world with things other than sofas like kids sticking one's head between the balustrades of a staircase or sticking one's finger in a hole (I mean like rings and stuff that are just barely big enough).
@softerseltzer Жыл бұрын
I can already hear Ross yelling "Pivot! Pivot!"
@JMannus65 Жыл бұрын
My first thought
@gladitsnotme Жыл бұрын
It's in the first 30 seconds of the video, so yeah, I'd hope you could hear it lol
@softerseltzer Жыл бұрын
@@gladitsnotme I commented a minute after the vid was uploaded, hadn't seen it yet 🙂
@daveslamjam5 ай бұрын
i feel really proud that i had the idea of moving the hallway to make a shape before you mentioned how gerver approached the problem 😊
@oliverwilson11 Жыл бұрын
When I saw the thumbnail I thought it must mean that mathematicians hadn't solved it for an arbitrary number of dimensions. I definitely didn't expect the 2D case to be unsolved.
@randysmith9715 Жыл бұрын
At a music store I worked at we had pieces of plywood that had the same dimensions as our most common pianos and organs. We carried the plywood into the delivery location. Assuming plywood fit around corners, up stairs and through landings. Then the instrument would be delivered. Remember a baby grand that needed to be swung onto a 3rd floor balcony and rolled into the apartment.
@leftmono1016 Жыл бұрын
Great comment. There’s a Laurel and Hardy scene similar to this. Hilarious 😂
@nightpups5835 Жыл бұрын
I do love how the couch created so far is actually a reasonable enough shape. giving this a mathematicians favorite accomplishment, practical application.
@jamielondon6436 Жыл бұрын
You're thinking of engineers. Mathematicians scoff at applicability. ;-)
@nightpups5835 Жыл бұрын
@@jamielondon6436 Indeed
@Sef_Era Жыл бұрын
I feel the need to mention (even though this is more of a hypothetical), that in practice you’d just take your sectional sofa apart, and stand the pieces on one end to fit them through the corner space. That’s why they make sectionals to begin with, as well as the weight to volume restriction of two people being able to reasonably carry each piece. If it’s not a sectional, it’s probably shorter end-to-end than the standard hight from floor-to-ceiling in your country. So when standing it on one end, you just have to fit its hight and depth through the corner; and it’s a sofa. You need to be able to sit on it once you put it back down, so the hight can’t be *that* extreme.
@esbenthomas943011 ай бұрын
I spotted the engineer.
@karthik999x-narrowone86 ай бұрын
You come up with the weirdest complicated problems that are completely random and I absolutely love it.
@wetterschneider Жыл бұрын
OMG. When I was introduced to the puzzle, that's the first thing I did (similar to Gerver's model) - I built a 3d version of the hall in software, duplicated it and rotated it, using the stacked series of clones to Boolean carve a chunk from a much bigger solid. I failed, it didn't work, but animating the hall around a static chunk to carve the chunk was my first idea. Again, it failed. But thank you for elaborating on the history.
@matthewthompson6455 Жыл бұрын
I’m glad it failed
@buzbuz33-99 Жыл бұрын
When confronted with a narrow hallway, we generally solved this problem by tipping the sofa on it's side.
@boggers Жыл бұрын
Yeah, I think this problem would be a lot more interesting in 3D with design constraints so that it remains a functional sofa (eg. max heights for seat, arms and back) while using things like standard roof height and door frame sizes etc.
@secondarycontainment4727 Жыл бұрын
Wrong approach. Just cut the sofa to fit around the corner.
@LineOfThy10 ай бұрын
Issue is you can’t do that in a 2D world
@LineOfThy10 ай бұрын
@@boggersbeauty of most math problems lie in their simplicity. Being more complicated does not automatically make it a better problem
@boggers10 ай бұрын
@@LineOfThy Even so, it would be more interesting to me. I used to move furniture for a living, there is an art to getting long sofas up winding stairwells, around corners, and through doorways, to me the 2D math problem is an over simplification of a real world problem. :)
@LeoAngora Жыл бұрын
Great video, thanks! The visualizations helped a lot. Adding to the joke answers: - Sofa? In this economy? I can fit a larger bean bag for less money - "As big as the apartment" (Ant-Man)
@Its_just_me_again Жыл бұрын
lover the intentional or unintentional pun of "what is the biggest sofa....so far"
@devluz Жыл бұрын
This was a great explanation and the animation show the problem in a really intuitive way. Amazing that there isn't a proof for this yet!
@gamechep Жыл бұрын
"Some serious math lover has probably already made/ has had this Sofa made", is what I was thinking until that furniture thing popped up 😂
@danielyuan9862 Жыл бұрын
The problem is more applicable than other math problems I see. I would be surprised if absolutely no one had this sofa made.
@RHLW Жыл бұрын
As someone who once spent a few years moving furniture for a living, I can promise you that myself, and plenty of guys can do this in their heads. You can look at a given piece of furniture, in the back of the van, walk into the house (keeping a "picture" of the item in your head), look at a given hall/stairway, and be able to tell if something will go or not, and figure out the set and order of rotations needed to make it go. Ive seen guys who can do this, and be correct to the mm. So there must be a method or model, even if we don't have an exact analytical solution.
@davidshelton1898 Жыл бұрын
This problem also looks like minkowski sums and differences! Very useful for checking for intersections and getting resulting shapes efficiently. And the intuition of "draw a vector along another vectors path." Looks similar if not the same to drawing the shape of no collisions when drawn along a path! 😀
@johnchessant3012 Жыл бұрын
Modern math has become so specialized, so it's always neat when something discovered 'recently' (the Gerver sofa was found in 1992) is not just vaguely accessible, its main insight can be understood clearly
@keithmichael112 Жыл бұрын
In my experience it can be much larger than the corner, as long as you're willing to break it
@EaglePicking Жыл бұрын
This is math, though, not engineering.
@vigilantcosmicpenguin8721 Жыл бұрын
Ross, is that you?
@keithmichael112 Жыл бұрын
@@vigilantcosmicpenguin8721 pivot!
@alextaunton30998 ай бұрын
i think I realized one reason why I like your videos. You are very expressive and you naturally emote well, which makes your videos more engaging and fun to watch. Love your content!
@stacksmasherninja7266 Жыл бұрын
This is the best mathematical puzzle I've ever seen ! Such a simple puzzle yet difficult and quite an elegant solution !
@saschaschneider9157 Жыл бұрын
Am I the only one who was immediately reminded to Dirk Gently's Holistic Detective Agency by Douglas Adams. Where in the staircase MacDuff's sofa is stuck since about 3 week. And when he wrote a program to get the answer it can get out, the result is that the sofa never could have get there in the first place. Definitely one of my favorite books.
@grandetaco4416 Жыл бұрын
she had me at sofa and small hallway.
@DeclanMBrennan Жыл бұрын
@@grandetaco4416 Not entirely. There appears to be a countably infinite number of comments on "Dirk Gently", including my own. 🙂It's nice to know that Douglas Adams is still so fondly remembered.
@kanjakan Жыл бұрын
That's an insanely creative solution. Never would have thought to rotate the hallway, but it makes sense since, if you think about it, the sofa's shape is naturally dictated by the hallway's shape.
@techman2553 Жыл бұрын
Moving the hallway was the first thing that I thought of when she started describing the problem, because I suck at math and if I had to brute force a solution, I would do it graphically. Just create a big blob much larger than the hallway, then use the hallway as the clipping boundary and let it subtract from the blob as the hallway moves and rotates. Whatever doesn't get clipped away is the shape of the sofa. The hard part is figuring out the optimal combination of translation and rotation. When all you learned in math class was geometry and trig, then everything becomes a polygon nail.
@Mueller3D Жыл бұрын
The solution wasn't so much about the frame of reference as it was about considering the interaction between the sofa and the hallway. Another way to look at it is to consider at any point what is stopping a large shape from moving further. In order to allow the shape the move further, you must trim a bit off. Do you trim away where the hallway corner is bumping into the sofa, or do you trim away from where the outer walls are bumping into the sofa? It just so happens that these interactions are easier to consider if the sofa is stationary and the hallway isn't.
@milesgould8288 Жыл бұрын
@@techman2553based on that comment, you do not suck at math!
@koopalad4 Жыл бұрын
step one: create a machine that can determine if a given program will stop depending on it's instructions, step two: create a program that searches for a better sofa, step three: analyze the given program using the machine defined earlier, If the machine says the program will stop, it means it's not the optimal sofa, if it says the program will loop, congrats, you found the optimal sofa
@mathewmunro377011 ай бұрын
I remember trying to solve this problem in year 10 (final year of high-school), some 30-years ago. I thought the optimal solution was a little more like the bottom one at 4:24, but symmetrical and more optimised, although with two curves that meet at 90-degrees in the middle on the edge of the couch that pivots around the hallway corner. My highschool maths teacher thought it looked a bit like a butt crack, and joked 'ah, so that's how you get around a corner' and motioned like he was moving his butt around the corner of a desk LOL. The cutting bits off & adding bits on wasn't as genius as cutting out a semi-circle and elongating the sofa while simultaneously using rotational and translational motion in my opionion. I too was able to increase the size by cutting bits off & adding more in other areas. I started to try to define the shape algebraically, but the math became horrendus.
@me0101001000 Жыл бұрын
In ChemE, we learned two ways to think of movement. Eulerian, which has particles move through a slice of space, and Lagrangian, which models an object moving throughout space. I feel like a part of the problem would be trying to determine which process is less computationally taxing.
@BrickTsar Жыл бұрын
We put a sofa upstairs and it had to include 3 dimensions - hitting the ceiling happened.
@b1ff Жыл бұрын
“Let’s watch a movie” “Sure thing, just let me move my hallway real quick”
@kasperspookypookie10 ай бұрын
My friend: trying to explain the masterpiece that is the sofa problem Me: why don’t you assemble it inside the room?
@MathOrient Жыл бұрын
Impressive! This mathematical problem is truly captivating. While it may appear simple at first glance, the solutions prove to be more challenging than anticipated. The explanation and visualizations provided are truly exceptional, making the learning experience even more enjoyable. Mathematics never ceases to amaze, showcasing its inherent beauty and complexity.
@SmrutiDashiamironman Жыл бұрын
Pivot!!!!!!!😂😂😂
@stevendeans4211 Жыл бұрын
I was looking for this comment.
@solenya7723 Жыл бұрын
Mathematicians: *working on it for decades* Engineers: make it modular and join it in the room Ahahahah just joking. Great video, really enjoyed the subject,your presentation and passion about it. Keep it up
@jcbradley1386 Жыл бұрын
To prove the strength of flex-tape clear, I sawed this couch in half!
@Tiqerboy Жыл бұрын
Really enjoyed this one! You should make a follow up video, solving the problem with doorways at either end which are NOT as wide as the hallway because that is a more realistic problem to solve in the real world. At least the front entrance should be like that.
@bunchofenergy418810 ай бұрын
Ikea has entered the chat.
@usvalve Жыл бұрын
My first thought was a sectional sofa too. Then I asked myself whether I really want the biggest possible sofa cluttering up my room, especially when houses in the UK tend to be fairly small. I'm now working on finding out what shape and size of sofa combines minimum size with maximum comfort and intimacy.. 🙂
@svz59909 ай бұрын
Minimum size can just be a size of a person for you to fit
@RyanStonedonCanadianGaming Жыл бұрын
As a old furniture mover, Whatever ceiling height and width of the thinnest hallway is basically the limit of what you can fit around a corner as you have to tilt the couch up on an angle and hug it around the corner.
@TheRAYviewYT Жыл бұрын
I can’t believe math geniuses didn’t understand this😂
@LineOfThy10 ай бұрын
Try tilting your sofa upwards in a 2D world
@flarenaster Жыл бұрын
I think Gerver already proved his solution, but then he realized that the real solution was the friends we made along the way, and then decided to leave the problem unsolved.
@x7heDeviLx Жыл бұрын
u missed a chance at a good pun. and i quote " Sofa weve just been guessing at shapes" lol love your content. keep up the good work
@Szymmon614 Жыл бұрын
Love the altitude of Michał Batsch at the end, like everyone tried to make ideal shape, but he just made an actual sofa. And in looks really nice, especially wit that coffee table.
@dhy5342Ай бұрын
I recently ran into this conundrum when I had to move a rolltop desk from one room, into a hallway and then into another room. The solution was easy - set it on its end to move it. Sometimes a 2-D problem is not longer a problem in 3-D.
@TheSamuelCish Жыл бұрын
This is why no one wants to help mathematicians move. "How big is your sofa?" "1.67225472m^2." "Alright, do it yourself then."
@bwillan Жыл бұрын
This is similar to the firefighter's problem of what is the longest ladder that you can get through a 90 degree corner of a hallway.
@pranavid Жыл бұрын
A collapsible one. 🤯
@DaP84 Жыл бұрын
@@pranavid a rope ladder rofl
@pingnick Жыл бұрын
Yeah also is both the area and volume in the 3 dimensional thought about this identical almost challenge essential to consider-probably but maybe not!? I’m confused just thinking about volume but yeah probably volume doesn’t matter yeah just huge couch reaching ceiling of hallway!?!?🤯
@jeffwhite1334 Жыл бұрын
Jade, this probably isn’t what you intended for your videos… but they help me fall asleep. For me they’re like little scientific bed time stories to combat my insomnia. Your accent and voice are so calming. Thank you so much!! ❤
@leftmono1016 Жыл бұрын
I think you’re probably right 😂💤
@matteofalduto7669 ай бұрын
I’m sure there must be an IKEA engineer out there that after watching this was like: “Hold my SÄLLSKAPLIG of beer!” And we’ll see the most optimal solution on their next year’s catalog
@withershin Жыл бұрын
There's nothing like a perfect 90° trench you need to furnish with a couch. It is very satisfying to think so mathematically that you're trying find the ideal couch for a trench. The Polish dude added a coffee table. Big trench design wins again.
@Frightning Жыл бұрын
I have an idea for how to go about proving that Gerver's sofa is optimal. Observations: 1: Balanced solution is at least a local maximum (same perturbations of the hallway path will lower sofa area, as long as they are *small enough*) 2: Original search space at the beginning of the problem was *any* hallway path (so we didn't, at the outset potentially exclude a better solution). 3: Any hallway path must be continuous (note, sharp turns are fine here, but what's important to observe is the continuity of motion, this is a consequence of the motion being from the Special Euclidean group) 4: 3 implies that continuous perturbations of a hallway path can transform any hallway path into any other. I would argue that 4 can be used to show that the local maximum observation #1 actually implies global maximum (this is probably not easy, but I think, at least tractable).
@SAOS451316 Жыл бұрын
I think of gear geometry with this problem. Optimal force transfer requires sliding planes and said planes can't be interrupted without losing efficiency. The slight corner rounding is also involved in optimized gears.
@vylbird8014 Жыл бұрын
Then you learn that the involute gear pretty much perfected the practical engineering of gears.
@clockworkkirlia7475 Жыл бұрын
I'd call this a bizarrely fascinating video, but honestly it's not that bizarre for me to be fascinated by something like this. Thank you for the really interesting watch!
@MongrelShark Жыл бұрын
As an engineer I love the way of thinking presented here. As a removalist I'd like to point out 2 things I've noticed. 1.The biggest sofas I've moved into tight spaces, are always asymetrical. This makes sense somehow, but I can't explain the maths. its got to do with the big end usually going in first. 2. You can't ignore the 3rd dimension. In practice, Most sofas go in standing on their end. As this gives the smallest birds eye view for better cornering. Gervers solution can't be proved because it only looks at 66.6% of the solution. Unless you want to change the problem to: Whats the largest 2d shape that can fit around a 2d 90deg corner? 3. Gervers couch touched the walls so you lost money on that job due to patching the walls. In practive you need at least a few mm clearance from walls, or its a failed run.
@LineOfThy10 ай бұрын
Yes. That’s the literal problem. It’s meant to be 2D. Why are you changing the problem?
@diskritis2076 Жыл бұрын
We were giving a very hard applied calculus test and had similar questions like this and my friend just blurted out "sofa problem is still unsolved", I was confused but that day I got the taste of optimization problems for the first time
@leonardharris9930 Жыл бұрын
In the real world we operate in three dimensions and anyone who has had practical experience of moving large sofas ( or even beds ) around confined corners knows that the only way to do it is by tipping the sofa on its end and moving it vertically around the tight corner. That is by making use of the third dimednsion.
@AdmiralZhao007 Жыл бұрын
i can imagine some quirky math teacher taking a class on a field trip to ikea in order to tackle this problem and introduce it to his students
@Turbobuttes Жыл бұрын
Mathematician approach: What's the largest sofa I can fit through this 90 degree hallway? Engineer approach: Mate just buy Ikea, you can take it apart into a hundred pieces.
@andrewharrison8436 Жыл бұрын
Watching real furniture movers putting a large sofa from a narrow hallway through a doorway using 3 dimensions is impressive. Glad I saw it because it turns out the manover is reversible to get it out again.
@Blacksoul444 Жыл бұрын
well, every combination of translation and rotation can be reversed of course.
@husaynbootwala1729 Жыл бұрын
12:29 I think the bigger question is whether the largest sofa is waiting to be discovered or invented 🤔
@WaffleRune Жыл бұрын
I think the beauty of mathematics advancing through time was that I too, thought of a hallway moving around a sofa when I heard about this. It's intuitive to think this way because that's similar to the passage of a fluid around a given solid, and we already know that, we used it to make plane wings.
@jjwubs1638 Жыл бұрын
Michael Batch's comments on Gerver's findings boil down to "So-fa, so good!"
@markchapman6800 Жыл бұрын
"What's the biggest sofa we've come up with so far?" That pun was the inspiration for the video, wasn't it? Also, did you have a fit of giggles immediately after you cut there?😊
@Flying0Dismount Жыл бұрын
As a mathematician, I'm surprised that you didn't come up with the answer of the infinitely thin sectional, where you can literally make any size sofa you want by moving these thin slices and integrating them back into a whole sofa in the destination room...
@erikburzinski8248 Жыл бұрын
I was thinking the ikea sofa
@joachimfrank4134 Жыл бұрын
As soon as you split in into infinitely many parts and combine it back again, interesting things can happen. Theres the Banach-Tarski-Paradoxon, where a ball is doubled by splitting and re-assembling.
@SmallSpoonBrigade Жыл бұрын
The correct answer to this is the size of the room that it's going into and using an inflatable couch. Using an inflatable couch, you could even get a couch much larger than the final room to fit around the corner in most cases.
@PJ-oe6eu Жыл бұрын
@@SmallSpoonBrigade What if the hallway is much much smaller than the room. Maybe we should inflate the couch and then cut it up into infinitely thin pieces.
@davemarm Жыл бұрын
Do you have any infinitely thin friends/relatives that could sit on it though?
@icekweebec512 Жыл бұрын
Jack where's the cure for cancer I asked you? Jack: idk but look at this big sofa I found that can fit perfec...
@tomdekler9280 Жыл бұрын
I think what makes this problem fun is that unlike most unproven mathematics questions, this one had Gerver optimizing what was conjectured to be the best solution. With most unproven mathematics, it's a boring "yeah this is very likely the real answer but proving it is turning out to be annoying as hell". Now though? I don't see this sofa problem going anywhere anytime soon.
@b2gills Жыл бұрын
Before I got to the part of moving the hallway instead of the sofa, I thought about using the hallway to sand down the sofa until it fit. Which may be sort of a precursor way of thinking towards moving the hallway instead of the sofa.
@MikesTropicalTech Жыл бұрын
The movers told me my desk is too big to make this exact turn in the hallway. I will have to prove them wrong with Math! P.S. Within 5 seconds of the start of the video I was shouting "Pivot!"
@jamesphillips2285 Жыл бұрын
I have a large metal desk I have moved several times by taking it apart. May not work for cheap idea style furniture though (designed to be assembled once). Cleaning out of my grandma's house we found a bed frame that could not fit in the opening in the attic. Reasoned it was either assembled in place or the be frame was moved in during construction.
@peetiegonzalez1845 Жыл бұрын
Came here just for this comment. PIVOT!
@ChrisWilhelmaddafewcharacters Жыл бұрын
Mathematicians solution: What this video explained. Engineers solutions: "Uhhh, idk cut it into pieces and call it a sectional."
@stephenho527211 ай бұрын
The largest sofa that can fit around a corner is always infinitesimally smaller than the new sofa you just bought :)
@blue_champignon5738 Жыл бұрын
What if we could send blueprints to where we live and get AI generated furniture that can move through any hallway and designed optimally for the space we're in lol
@BruceAFairchild Жыл бұрын
End up the couch and it will fit around the corner. Usually the ceiling is high enough. Even if the ceiling is not high enough to allow for complete vertical position, it will most likely be close enough.
@BrainWeevil Жыл бұрын
Thank you for this interesting insight, and for the history! I immediately thought of Douglas Adams' book _Dirk Gently's Holistic Detective Agency_ when I saw the title. I'd had no idea this was a problem entertained by real mathematicians before Adams (Requiescat in pace) used it. I know his sofa was on a staircase, adding the z axis, but the principle clearly relates to your problem here.
@swr1240 Жыл бұрын
What if we pushed a large, completely rectangular, plastic substance that's rigid enough to keep its shape, but plastic enough to deform when pushed through? Then see what shape comes out on the other side.
@wilgarcia1 Жыл бұрын
Has anyone reimagined this in three dimensions? I bet it would be much more fun =D
@karabenomar Жыл бұрын
For a suitable definition of "fun".
@tarmaque Жыл бұрын
I tried to imagine this in four dimensions. There was a strange snapping sound, and now I can't remember my 7 multiplication tables and my Grandmother's maiden name.
@AlexandHuman Жыл бұрын
This reminds me a lot of the perfect wheel problem that "Morphocular" showed off. Is there a way to solve this problem for less complex hallways? Is there a way to transform the shape of the hallway into purely an equation and then use that to find the biggest optimal shape that matches up?
@lithothiryvi4143 Жыл бұрын
Tord: "hold my vodka" Tord again: "No really, my only arm is getting tired"
@King_Of_Midgard Жыл бұрын
I propose that is is the sectional sofa with infinite middle sections that is the largest. Just cuz the hall puts constraints for moving any part of my furniture doesn't mean the size of my furniture is constrained by the hall; its confined by my willingness to move multiple pieces of sofa.
@bsjeffrey Жыл бұрын
what if it's a gigantic plyable sofa, like a bean bag sofa?
@jeffbguarino6 ай бұрын
The answer is an infinitely long rectangle. There is no mention about the speed of the shape moving to the right and then down. So take an infinitely , or at least extremely long rectangle of height 1 and move it close to the speed of light. The length contraction will turn it into a flat vertical line. When it reaches the corner , it can easily rotate because it is only "1" in height while the corner is 1.414. As long as you maintain the speed as C the speed of light , you can fit an extremely long rectangle. After you make the turn, then you can slow down again and let the rectangle expand its length. This is the problem with mathematicians , they are divorced from reality. You can't state the question without the fact that the object has to move. Moving involves speed. If the object moves too slow then the contraction is not enough for it to rotate at the corner. You can calculate the slowest speed that still allows the rectangle to rotate.
@user-fx5hp4ru1l Жыл бұрын
Thank you for 0:43, as soon as I saw your thumbnail I had to think of this.
@anthonynorman7545 Жыл бұрын
Your prop making and work made this so much more digestible!
@olemanshavadoo7893 Жыл бұрын
The bigger sofa is a giant beanbag sofa. It’s amorphous, so you just push it through the hallway.
@stevestann595 Жыл бұрын
I was gonna comment "PIVOT" , you did it before i reached for the keyboard 😂.
@seedmole Жыл бұрын
If only this video came out before I tried to get my old desk into my attic.
@BreadApologist Жыл бұрын
Unpopular solution….just bring in more and more square cushions and turn the entire room into one massive sofa.
@kurzackd Жыл бұрын
The video is incomplete -- there's been a new development *since 2018:* The *maximum THEORETICAL area* of the sofa has now been determined to be able to reach *2.37 m^2...* (up from Gerver's 2.22) ...now what's left is *to find the actual SHAPE that fills this area... :P* .
@jimhutton2390 Жыл бұрын
This is only considering two dimensions, when you add a third dimension, and flexible sections and latches to lock sections together you can get even more solutions.
@willcool713 Жыл бұрын
As a nerd, geek, and former furniture mover, I can tell you with certainty that if the sofa fits in the hall, it will go around the corner, but you may need to stand it up, or be open to electric monks.