What's The Largest Sofa That Can Fit Around a Corner?

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  • Опубликовано: 6 июн 2024
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    Chapters
    0:00 The Moving Sofa Problem
    2:06 Hammersley's sofa
    3:15 Gerver's Sofa
    3:55 Why is it so hard?
    5:34 How Gerver came up with his sofa
    9:50 Thank you Brilliant!
    11:23 Will you find a bigger sofa?
    Creator - Jade Tan-Holmes
    Script - Alexander Berkes
    Animations - Daniel Kouts and Simon Mackenzie
    Music - epidemicsound.com
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Комментарии • 1,9 тыс.

  • @upandatom
    @upandatom  Год назад +75

    Sign up to Brilliant to receive a 20% discount with this link! brilliant.org/upandatom/
    Recommended course: Advanced Geometry Puzzles brilliant.org/courses/advanced-geometry-puzzles/

    • @joelklein3501
      @joelklein3501 Год назад +1

      Is his solution related to the stationary action principle from analytical mechanics?

    • @axiomfiremind8431
      @axiomfiremind8431 Год назад

      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
      @lyrimetacurl0 Год назад

      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
      @olli3686 Год назад

      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
      @fredashay Год назад

      I bet'cha that Presh Talwalker from _Mind Your Decisions_ can solve it!

  • @guidoferri8683
    @guidoferri8683 Год назад +3930

    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
      @SaHaRaSquad Год назад +397

      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
      @beyondobscure Год назад +118

      @@SaHaRaSquad hate when that happens

    • @jackhandma1011
      @jackhandma1011 Год назад +48

      Most people don't care about math. We just have to deal with it.

    • @kidredglow2060
      @kidredglow2060 Год назад +21

      Ur friend is mean

    • @MandleRoss
      @MandleRoss Год назад +8

      HAHAHAHA!

  • @SgtSupaman
    @SgtSupaman Год назад +1011

    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
      @amegatron07 Год назад +71

      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
      @GIRGHGH Год назад +22

      @@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
      @Christian-mf4jt Год назад +39

      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
      @error.418 Год назад +4

      @@GIRGHGH Usually you'd start with trying ti disprove.

    • @error.418
      @error.418 Год назад +58

      @@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
    @blodpudding Год назад +248

    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_--___---
      @R24_--___--- Год назад +4

      Right😂

    • @stevenarvizu3602
      @stevenarvizu3602 7 месяцев назад +12

      I know it’s a hypothetical but the whole time I was thinking just disassemble the sofa lol

    • @samueldeandrade8535
      @samueldeandrade8535 7 месяцев назад +7

      By writing "IKEA beats math every time" you probably lost a thousand likes.

    • @noxlusus
      @noxlusus 6 месяцев назад +2

      IKEA 13B yearly income, Google 280B, math makes the difference 267B (subtraction) Sorry I was using math to explain that.

    • @michaelmichalski4588
      @michaelmichalski4588 4 месяца назад +1

      ​@@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
    @b0nes95 10 месяцев назад +30

    4:02 sofa we've just been guessing at shapes

  • @YoungGandalf2325
    @YoungGandalf2325 Год назад +929

    I didn't think a degree in mathematics was needed to to become a furniture mover.
    This is why sectional sofas exist.

    • @sicfxmusic
      @sicfxmusic Год назад +12

      Exactly, I'm not good at math so guess that's the easy way out! 😂😂

    • @wearwolf2500
      @wearwolf2500 Год назад +12

      I bought a large chair and was worried about then carrying it downstairs. It came in 5 parts...

    • @axiomfiremind8431
      @axiomfiremind8431 Год назад +23

      What is the largest a section of a sectional sofa can be before it gets stuck?

    • @AdelaeR
      @AdelaeR Год назад +3

      @@axiomfiremind8431 The answer is: 2.

    • @BobBeatski71
      @BobBeatski71 Год назад +14

      I'm not a furniture mover, I'm a corridor arranger.

  • @Bunny1sAw3somesauce
    @Bunny1sAw3somesauce Год назад +830

    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
      @mrdraw2087 Год назад +46

      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
      @benjaminpedersen9548 Год назад +55

      @@mrdraw2087 What is required to be a sofa? The largest volume may simply be the largest in 2d filling the entire height.

    • @jamielondon6436
      @jamielondon6436 Год назад +10

      Meh, all you have to do is pivot. Piiivoooot! ;-)

    • @doncarlodivargas5497
      @doncarlodivargas5497 Год назад +37

      Mathematicians: struggle moving a sofa for decades
      A random moving grunt:instantly move the sofa on the side

    • @Malekariel
      @Malekariel Год назад +17

      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.

  • @duvasrealm
    @duvasrealm 11 месяцев назад +67

    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.

    • @DevtheViolinist
      @DevtheViolinist 4 месяца назад +1

      The size possible is only limited by the parts allowed.
      IKEA teaches this the hard way.

  • @huzzzzzzahh
    @huzzzzzzahh Год назад +37

    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
      @chekhov-and-his-gun 10 месяцев назад +3

      No school will tell you that though.
      That's why people tend to dislike math because it's shown as only equations.

    • @emissarygw2264
      @emissarygw2264 8 месяцев назад

      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.

    • @GamezGuru1
      @GamezGuru1 8 месяцев назад

      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...

    • @emissarygw2264
      @emissarygw2264 8 месяцев назад

      ​@@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.

  • @MedlifeCrisis
    @MedlifeCrisis Год назад +82

    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
      @RussellChapman99 Год назад +5

      Dirk Gently detective. Read it years ago and this video immediately reminded me of the story.

    • @MonkeyJedi99
      @MonkeyJedi99 Год назад

      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
      @bpj1805 Год назад

      But can you get a swallowed toy sofa around the first corner of a person's small intestine?

    • @quantisedspace7047
      @quantisedspace7047 11 месяцев назад

      @@MonkeyJedi99 Was the resolution of the sofa thing done across two books ?

    • @MonkeyJedi99
      @MonkeyJedi99 11 месяцев назад

      @@quantisedspace7047 IIRC, it was across two different book series.

  • @JosephBlanch
    @JosephBlanch Год назад +473

    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
      @testales Год назад +78

      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
      @curtisowens750 Год назад +29

      They never mentioned that the sofa could be stood on it's end .... I've had to do that before

    • @-YELDAH
      @-YELDAH Год назад +23

      ​@@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
      @error.418 Год назад +13

      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
      @testales Год назад +3

      @@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.

  • @Kaanin
    @Kaanin Год назад +123

    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!

  • @julien1426
    @julien1426 Год назад +7

    6:24 "sofa we've been..."

  • @softerseltzer
    @softerseltzer Год назад +28

    I can already hear Ross yelling "Pivot! Pivot!"

    • @JMannus65
      @JMannus65 Год назад

      My first thought

    • @gladitsnotme
      @gladitsnotme Год назад

      It's in the first 30 seconds of the video, so yeah, I'd hope you could hear it lol

    • @softerseltzer
      @softerseltzer Год назад

      @@gladitsnotme I commented a minute after the vid was uploaded, hadn't seen it yet 🙂

  • @alanhilder1883
    @alanhilder1883 Год назад +88

    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
      @bjorntantau194 Год назад +2

      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
      @alanhilder1883 Год назад +3

      @@bjorntantau194 It wasn't Gently's computer, it was " The Client " and old school friend whose name eludes me at the moment.

    • @bjorntantau194
      @bjorntantau194 Год назад

      @@alanhilder1883 Ah, been too long since I've last read the books.

    • @alanhilder1883
      @alanhilder1883 Год назад

      @@bjorntantau194 I will have to re find them, it was last century that I got to read them...

    • @babelchips
      @babelchips Год назад +6

      Dirk Gently’s “interconnectedness of all things” applies here! This video came out on Towel Day 😊

  • @saiganeshmanda4904
    @saiganeshmanda4904 Год назад +16

    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 :)

  • @kbrown4ou
    @kbrown4ou 11 месяцев назад +8

    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.

    • @MateusSFigueiredo
      @MateusSFigueiredo 7 месяцев назад +1

      This is some Douglas Adams plot

    • @MohsinExperiments
      @MohsinExperiments 6 месяцев назад +1

      You should rotate its legs towards the inner corner. That's how you can easily get it out from your home.

  • @DeclanMBrennan
    @DeclanMBrennan Год назад +245

    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
      @bjornmu Год назад +21

      -""Eddies in the space-time continuum!" -"And this is his sofa, is it?" 😄

    • @iriswaters
      @iriswaters Год назад +21

      This was the FIRST thought I had when I saw the episode.

    • @renedekker9806
      @renedekker9806 Год назад +16

      Yeah, I immediately thought of "Dirk Gently's Holistic Detective Agency" as well. Excellent novel!

    • @vylbird8014
      @vylbird8014 Год назад +23

      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.____.....__...__
      @I.____.....__...__ Год назад +2

      @@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).

  • @Shamazya
    @Shamazya Год назад +70

    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!

  • @stacksmasherninja7266
    @stacksmasherninja7266 Год назад +1

    This is the best mathematical puzzle I've ever seen ! Such a simple puzzle yet difficult and quite an elegant solution !

  • @uselessgamedev
    @uselessgamedev Год назад

    Very nice! I like the visualizations of the paths of the hallway

  • @nightpups5835
    @nightpups5835 Год назад +59

    I do love how the couch created so far is actually a reasonable enough shape. giving this a mathematicians favorite accomplishment, practical application.

    • @jamielondon6436
      @jamielondon6436 Год назад +16

      You're thinking of engineers. Mathematicians scoff at applicability. ;-)

    • @nightpups5835
      @nightpups5835 Год назад +4

      @@jamielondon6436 Indeed

  • @randysmith9715
    @randysmith9715 Год назад +25

    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
      @leftmono1016 11 месяцев назад +1

      Great comment. There’s a Laurel and Hardy scene similar to this. Hilarious 😂

  • @davidshelton1898
    @davidshelton1898 Год назад +3

    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! 😀

  • @SirRandallDoesStuff
    @SirRandallDoesStuff Год назад

    I love your channel. I have degree is Astrophysics and I love to watch others and how they teach and explain topics. You are a great teacher and one of the few channels that does it right. Keep up the great work.

    • @quantisedspace7047
      @quantisedspace7047 11 месяцев назад

      Degree in Math and another in Astrophysics. Must be back to the dole queue on Monday.

  • @buzbuz33-99
    @buzbuz33-99 Год назад +78

    When confronted with a narrow hallway, we generally solved this problem by tipping the sofa on it's side.

    • @boggers
      @boggers Год назад +7

      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
      @secondarycontainment4727 11 месяцев назад +6

      Wrong approach. Just cut the sofa to fit around the corner.

    • @LineOfThy
      @LineOfThy 7 месяцев назад

      Issue is you can’t do that in a 2D world

    • @LineOfThy
      @LineOfThy 7 месяцев назад +1

      @@boggersbeauty of most math problems lie in their simplicity. Being more complicated does not automatically make it a better problem

    • @boggers
      @boggers 7 месяцев назад

      @@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. :)

  • @johnchessant3012
    @johnchessant3012 Год назад +23

    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

  • @gustavoforestobritodealmei888
    @gustavoforestobritodealmei888 Год назад

    Wow... Such a great content! Brilliant video! Thanks... 🙏🏾

  • @anthonynorman7545
    @anthonynorman7545 11 месяцев назад

    Your prop making and work made this so much more digestible!

  • @wetterschneider
    @wetterschneider Год назад +35

    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.

  • @devluz
    @devluz Год назад +33

    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!

  • @atomicdmt8763
    @atomicdmt8763 7 месяцев назад

    LOVE these videos~ and your sweet energy!

  • @alextaunton3099
    @alextaunton3099 5 месяцев назад

    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!

  • @gamechep
    @gamechep Год назад +13

    "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
      @danielyuan9862 Год назад +1

      The problem is more applicable than other math problems I see. I would be surprised if absolutely no one had this sofa made.

  • @BrainWeevil
    @BrainWeevil 11 месяцев назад +2

    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.

  • @williamtell1477
    @williamtell1477 8 месяцев назад

    Just found your channel, really like your style, subscribed!

  • @saschaschneider9157
    @saschaschneider9157 Год назад +5

    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
      @grandetaco4416 Год назад

      she had me at sofa and small hallway.

    • @DeclanMBrennan
      @DeclanMBrennan Год назад

      @@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.

  • @keithmichael112
    @keithmichael112 Год назад +23

    In my experience it can be much larger than the corner, as long as you're willing to break it

  • @saadrashid8825
    @saadrashid8825 10 месяцев назад

    Thank you very much for new perspectives

  • @WaffleRune
    @WaffleRune 11 месяцев назад

    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.

  • @MathOrient
    @MathOrient Год назад +7

    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.

  • @BrickTsar
    @BrickTsar Год назад +4

    We put a sofa upstairs and it had to include 3 dimensions - hitting the ceiling happened.

  • @JulianOShea
    @JulianOShea Год назад

    Excellent video, mate.

  • @clockworkkirlia7475
    @clockworkkirlia7475 Год назад +1

    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!

  • @kanjakan
    @kanjakan Год назад +67

    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
      @techman2553 Год назад +6

      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
      @Mueller3D Год назад +1

      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
      @milesgould8288 11 месяцев назад

      ​@@techman2553based on that comment, you do not suck at math!

  • @SmrutiDashiamironman
    @SmrutiDashiamironman Год назад +4

    Pivot!!!!!!!😂😂😂

  • @Sef_Era
    @Sef_Era Год назад +13

    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.

  • @mrpennywize
    @mrpennywize 7 месяцев назад

    This. What a video. I love it. Thank you.

  • @me0101001000
    @me0101001000 Год назад +10

    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.

  • @Tiqerboy
    @Tiqerboy Год назад +11

    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.

  • @daveslamjam
    @daveslamjam 2 месяца назад +1

    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 😊

  • @mathewmunro3770
    @mathewmunro3770 8 месяцев назад +3

    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.

  • @usvalve
    @usvalve Год назад +10

    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.. 🙂

    • @svz5990
      @svz5990 7 месяцев назад

      Minimum size can just be a size of a person for you to fit

  • @bwillan
    @bwillan Год назад +8

    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
      @pranavid Год назад +7

      A collapsible one. 🤯

    • @DaP84
      @DaP84 Год назад +1

      @@pranavid a rope ladder rofl

    • @pingnick
      @pingnick Год назад

      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!?!?🤯

  • @bluesque9687
    @bluesque9687 9 месяцев назад

    Well done!! me is new subscriber, and the more I watch on your channel, the more I feel like I have found something really wonderful!!

  • @stromzardan5821
    @stromzardan5821 11 месяцев назад

    Brilliant explanation

  • @Szymmon614
    @Szymmon614 Год назад +3

    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.

  • @diskritis2076
    @diskritis2076 Год назад +3

    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

  • @karthik999x-narrowone8
    @karthik999x-narrowone8 3 месяца назад

    You come up with the weirdest complicated problems that are completely random and I absolutely love it.

  • @ertugrulsenturk8439
    @ertugrulsenturk8439 10 месяцев назад

    Very interesting and unique video. I like your channel. I hope you'll grow more without losing your uniqueness.

  • @SAOS451316
    @SAOS451316 Год назад +3

    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
      @vylbird8014 Год назад

      Then you learn that the involute gear pretty much perfected the practical engineering of gears.

  • @x7heDeviLx
    @x7heDeviLx Год назад +3

    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

  • @oliverwilson11
    @oliverwilson11 Год назад +1

    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.

  • @dimaratosgeorgiadis2672
    @dimaratosgeorgiadis2672 11 месяцев назад

    One way to further enlarge the sofa maintaining him parallel would be to bend the inner curve while adding space to the inner corners, that so it will still be able to rotate through the wall. The question is if Gervers shape sits at the spot of this analogy where the area is maxed.

  • @jeffwhite1334
    @jeffwhite1334 Год назад +10

    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
      @leftmono1016 11 месяцев назад

      I think you’re probably right 😂💤

  • @Frightning
    @Frightning Год назад +10

    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).

  • @gordonwallin2368
    @gordonwallin2368 Год назад

    You're back! Yay!. In Canada we have Chesterfields, not Sofas-well used to. Cheers from the Pacific West Coast of Canada.

  • @jimhutton2390
    @jimhutton2390 Год назад

    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.

  • @leonardharris9930
    @leonardharris9930 Год назад +3

    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.

  • @husaynbootwala1729
    @husaynbootwala1729 Год назад +4

    12:29 I think the bigger question is whether the largest sofa is waiting to be discovered or invented 🤔

  • @hippopotamus3025
    @hippopotamus3025 Год назад

    Best calc2 problem to learn optimization. thanks mr fomin

  • @andrewharrison8436
    @andrewharrison8436 Год назад +3

    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
      @Blacksoul444 11 месяцев назад

      well, every combination of translation and rotation can be reversed of course.

  • @markchapman6800
    @markchapman6800 Год назад +5

    "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?😊

  • @prabhakarrao4922
    @prabhakarrao4922 11 месяцев назад

    Absolutely brilliant

  • @dheekeol1269
    @dheekeol1269 10 месяцев назад

    That is a piece of cake, solving it is super easy.

  • @b2gills
    @b2gills Год назад +8

    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.

  • @RHLW
    @RHLW Год назад +4

    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.

  • @glenneric1
    @glenneric1 Год назад

    Nice video! I'd never heard of the problem.

  • @LeoAngora
    @LeoAngora Год назад +1

    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)

  • @AlexandHuman
    @AlexandHuman Год назад +2

    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?

  • @MikesTropicalTech
    @MikesTropicalTech Год назад +4

    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
      @jamesphillips2285 Год назад

      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
      @peetiegonzalez1845 Год назад

      Came here just for this comment. PIVOT!

  • @Its_just_me_again
    @Its_just_me_again 11 месяцев назад +1

    lover the intentional or unintentional pun of "what is the biggest sofa....so far"

  • @DarkMatter1919
    @DarkMatter1919 9 месяцев назад

    The Gerver shape solution is Sofa King awesome.

  • @blue_champignon5738
    @blue_champignon5738 Год назад +3

    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

  • @Flying0Dismount
    @Flying0Dismount Год назад +16

    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
      @erikburzinski8248 Год назад

      I was thinking the ikea sofa

    • @goldernie
      @goldernie Год назад +2

      You've just invented bean bags

    • @joachimfrank4134
      @joachimfrank4134 Год назад +1

      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
      @SmallSpoonBrigade Год назад +2

      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
      @PJ-oe6eu Год назад

      @@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.

  • @shlokpawar1131
    @shlokpawar1131 Год назад

    At 8:27 when you move the sofa your not considering the longer edge that's also being cut of (the one on the right of the green line) so don't you think that the area might have reduced?

  • @dubleblitz
    @dubleblitz 10 месяцев назад

    I feel so smart after guessing the cutting of the corners to get more room at the top before it was mentioned in the video. I can't believe it took 24 years to be found. Maybe it comes from the fact that I once had an internship where I wrote a website about bodies of constant width and how you can transform any body with corners into a body of constannt width. Also I am surprised that there is no word for such bodies in english, whereas there is the word "Gleichdick" in german which translates to "evenly thick".

  • @BruceAFairchild
    @BruceAFairchild Год назад +5

    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.

  • @wilgarcia1
    @wilgarcia1 Год назад +3

    Has anyone reimagined this in three dimensions? I bet it would be much more fun =D

    • @karabenomar
      @karabenomar Год назад +1

      For a suitable definition of "fun".

    • @tarmaque
      @tarmaque Год назад +1

      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.

  • @user-fx5hp4ru1l
    @user-fx5hp4ru1l Год назад

    Thank you for 0:43, as soon as I saw your thumbnail I had to think of this.

  • @b1ff
    @b1ff 10 месяцев назад

    “Let’s watch a movie”
    “Sure thing, just let me move my hallway real quick”

  • @bsjeffrey
    @bsjeffrey Год назад +5

    what if it's a gigantic plyable sofa, like a bean bag sofa?

  • @sylver369
    @sylver369 11 месяцев назад

    When considering the hallways, yes, you're working with only 2 dimensions. But when considering the couch, you are actually working with 3. A couch that can't fit around the corner, might fit if it's rotated forward or pitched up on one end. The doorways are actually the trickier part because you have less width to work with and more often than not a couch, love seat or lounge chair are bigger than a doorway, but people manage to get them through.

  • @seedmole
    @seedmole Год назад

    If only this video came out before I tried to get my old desk into my attic.

  • @bleachmobile
    @bleachmobile 11 месяцев назад

    Incredibly well made video

  • @koopalad4
    @koopalad4 Год назад +1

    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

  • @jcbradley1386
    @jcbradley1386 Год назад +1

    To prove the strength of flex-tape clear, I sawed this couch in half!

  • @RyanStonedonCanadianGaming
    @RyanStonedonCanadianGaming Год назад +1

    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
      @TheRAYviewYT 10 месяцев назад

      I can’t believe math geniuses didn’t understand this😂

    • @LineOfThy
      @LineOfThy 7 месяцев назад

      Try tilting your sofa upwards in a 2D world

  • @jwester7009
    @jwester7009 Год назад

    how high is the ceiling? I would lift the sofa upright to move it around the corner. Also a corner sofa usually cones in two parts and is assembled at it's corner. That means I can move one part at the time. If the room at the end of the hallway has a terrace door I would consider moving the sofa through that way instead

  • @j.desroches1497
    @j.desroches1497 4 месяца назад

    Fascinating