The Moving Sofa Problem - Numberphile

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Featuring Dan Romik from UC Davis.
More footage from this interview soon on Numberphile2.
Dan's comprehensive page on this topic: bit.ly/movingsofa
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Опубликовано:

20 окт 2024

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Комментарии : 1,7 тыс.

@TheTruthSentMe 7 лет назад

What do you do when you can't solve a problem? You create a new problem, that you can't solve either. Genius!

@schizophrenicenthusiast 7 лет назад

That may be true, but whoever's gonna solve this problem in the future will definitely have gained perspective because of this. Check out Buffon's needle problem. One way to solve that problem is by basically creating a new harder problem similar to the original. It's one of many examples that show the importance of creativity in mathematics.

@metroidM1A1 7 лет назад

+Schizophrenic Enthusiast You mean a *reduction*

@theywalkinguptoyouand4060 7 лет назад

Mandalore unneccessary

@SuperKako17 6 лет назад

It IS genius. That's why we do math, because solving problems is fun. The more problems, the more fun. Quite unlike real life, I guess.

@vitalnutrients744 6 лет назад

Claudio Melendrez in real life, it might not be fun because it might be personal, and to those people that hate to problem solve, don't take it personally. Always solve problems before people have mentioned them. Always seek to find and always innovatw

@legygax 5 лет назад

I have discovered a truly remarkable optimal shape which this corridor is too tight to contain.

@angelmendez-rivera351 4 года назад

legygax Wait....

@ivanhui6051 4 года назад

Angel Mendez-Rivera what

@joda7697 4 года назад

nice reference

@trickytreyperfected1482 3 года назад

@@joda7697 what

@joda7697 3 года назад

@@trickytreyperfected1482 That is a reference to Fermat's last theorem, where in his notes he wrote: "I have discovered a truly marvelous proof of this which this margin is too narrow to contain." where the margin is referring to the space in his notebook.

@shield543 7 лет назад

This problem may be extended to n degrees of freedom, which is trivial and has been left as an exercise for the reader

@antimatter2417 7 лет назад

It would be an open ball of radius one for the l1 norm.

@IVIegadude 7 лет назад

one of my favorite comments ever.

@Toshinben 7 лет назад

Those statements were sometimes true, other times they were infuriating.

@Filip6754 7 лет назад

Classic Gauss banter

@obsoleteprofessor2034 7 лет назад

I flunked math.. but somehow I think you're pulling my leg with your comment.

@SWIFTY_WINS 5 лет назад

Solution: An endless beanbag sofa that's flexible like a snake and the exact size of the hallway.

@LeafLeafy 4 года назад

SWIFTY_WINS I feel like this is the chaotic neutral response to the problem.

@eve_the_eevee_rh 4 года назад

Lol

@PronteCo 4 года назад

well if it's endless it may as well be half the thickness for easier handling, the area is the same

@nicholasninos5688 4 года назад

I see we have an engineer

@MrManniG 4 года назад

@@LeafLeafy would cou consider the hecksaw as the chaotic evil solution?

@farnhamclose11 4 года назад

You just need to yell: PIVOT! PIVOT!

@bunbury4620 4 года назад

I saw the title of the video. I looked for "pivot" in the comments. I found you within seconds.

@sarthakpatel314 4 года назад

shut up! shut up! SHUT UP!

@vinuxcyldrik 4 года назад

And then, you end up cutting the sofa in half and giving it back to the store asking for a refund … classic situation XD

@uforob5601 3 года назад

@@bunbury4620 the same :D

@godjavan 7 лет назад

Professor Romik is one of my favorites! Anyone in math at Davis should definitely take the opportunity to have him!! He gave cute math puzzles to students with the highest score in linear algebra and would bring fruit from the farmer's market to differential equations

@MojoBeast 7 лет назад

Brady, you do realise you're going to have to create the official limited edition sofa of Numberphile now, right? 😉

@charliespinoza1966 7 лет назад

MojoBeast - your Modsauce and Redstone Yeti! +

@ipadair7345 7 лет назад

@paulpeterson4216 7 лет назад

It is clearly a love-seat, just add an S-shaped back to it. I'd go with a different color though.

@davidfinch7418 7 лет назад

A use for his brass leather stamp when the shoes are done.

@SuperKako17 6 лет назад

I'm totally getting one if they do.

@mindstormmaster 7 лет назад

Never did I expect to see a Zoolander reference in a Numberphile video. I am not displeased.

@00bean00 7 лет назад

Amazing edit

@sirpopovot9877 6 лет назад

mindstormmaster Is that you Ernesto?

@PersonManManManMan 2 года назад

I am happily surprised

@PlayTheMind 7 лет назад

*Solution:* Chairs

@DUCKDUDE4100 7 лет назад

*Solution:* PIVOT!

@ssnoyes 7 лет назад

Pivot tables are completely different.

@Stryyfe84 7 лет назад

Damn dude, you really excel at this.

@dingbat6596 7 лет назад

PlayTheMind Better solution: Floor

@ssnoyes 7 лет назад

Word.

@ShadSterling 7 лет назад

Now I want a Gerver Sofa. Maybe even a Gerver Desk. Where's the Numberphile store where we can buy these things?

@NonDelusional74611 7 лет назад

Shad Sterling you will have to make it.

@crafty1098 5 лет назад

I'm getting into woodworking. Originally I wanted to try my hand at making a Chesterfield, but now I'm thinking a Gerver sofa next to my Morris chair, Chippendale highboy, and Sheraton desk.

@forloop7713 5 лет назад

Reminder for myself to make this in a few years

@prenestina 4 года назад

@@forloop7713 the time has come.

@petergustafsson1670 4 года назад

Contact IKEA! ;)

@cosmoscepanovic1129 7 лет назад

I love this channel. I can watch any video and feel like a mathematical prodigy even though I'm just seeing the results of someone else's hard work!

@sebastianzaczek 6 лет назад

*moves sofa into 4th spatial dimension*

@cyrilsubramanian4883 5 лет назад

outstanding move

@DarkMoonDroid 5 лет назад

They didn't even use the 3rd yet!

@mwu365 4 года назад

*you weren't supposed to do that*

@JohnSmith-vs9rs 4 года назад

Dirk Gently?

@joshandrews8913 4 года назад

I bet Clifford Stoll has a solution involving Klein bottles.

@TheConnor12500 7 лет назад

This seems like the kind of question a computer could optimise through evolution very well. Of course it wouldn't give the perfect solution, but if it can be seen to be converging to one of these shape that's very strong support for the conjecture.

@FlutterBug 7 лет назад

I was thinking the same thing, this would work very well with an evolution simulation; the only problem I can think up is programming it to do the right motion around the corner, but I am sure someone more knowledgeable than me could figure it out hehe.

@Foxclip 7 лет назад

Wiki says: "A computation by Philip Gibbs produced a shape indistinguishable from that of Gerver's sofa giving a value for the area equal to eight significant figures.[6] This is evidence that Gerver's sofa is indeed the best possible but it remains unproven."

@fergusmaclachlan1404 7 лет назад

But where's the fun in that?

@jakubpekarek6400 7 лет назад

I'd say that the actually interesting part is how to solve such a problem rather than the solution itself. Simply because there can be many variations of the problem. Computer solution may confirm that your solution is indeed optimal, but if you want to know why in order to solve the other variants, you are exactly where you were before, holding no tools to approach the problem in general.

@Mew__ 7 лет назад

What about an evolutionary algorithm that is designed in a way that it wouldn't always return the same shape as being optimal? I don't have any idea how it could be programmed, but suppose it'd work: either all optimal sofas eventually become Gerver's, OR it returns a variety of optimal sofas, all with the same optimal surface area that is greater than or equal to Gerver's, through which we can derive the criteria for an optimal sofa.

@bruno3 4 года назад

This is some groundbreaking stuff in sofa technology. When it first came out, it completely reshaped the sofa-making and sofa-moving industries. And this is what humans can achieve when they really put their mind to it. Quite inspiring.

@FreeFireFull 7 лет назад

I wonder what sort of solutions you get if the turn isn't a 90° angle, but something like 30 degrees

@roceb5009 7 лет назад

Freefle or one hall wider than the other

@davidb5205 7 лет назад

Huh. If one hall was wider than the other, does that necessarily mean that the couch takes the shape of a Gerver sofa but only limited to the width of the smaller hallway?

@ijpete98 7 лет назад

No, but it might mean that it's a Gerver sofa that's been elongated on the front end.

@kordellcurl7559 7 лет назад

Freefle it would be the same shape because 30 degrees is less than 90 degrees

@Insertnamesz 7 лет назад

Ooh, the ratio of the two hallways might be able to apply to the functions of the gerver curves as a weighting factor

@easty6667 5 лет назад

Just cut it up, move each piece individually, and use flex tape to put everything together at the end

@dboldersgaming7152 4 года назад

To show the power of Flex Tape, I moved this sofa through a narrow hallway

@solarean 3 года назад

@@dboldersgaming7152 and so it fits, i cutted it in half!"

@nickarutunov2114 7 лет назад

Problem proposed by Augustin-Louis Couchy

@4ltrz555 4 года назад

wow

@TheLesserWeevil 7 лет назад

This guy has a fascinating voice. No matter how loud I turned up my speakers, he still sounded quiet.

@zergreenone8111 7 лет назад

Any fans of Douglas Adams in the house? Reminds me of Dirk Gently's Holistic Detective Agency

@tamaspolyak5564 7 лет назад

You just need a time machine for the door to appear. Or you need to pivot.

@andrewknorpp9716 7 лет назад

i LOVE hitchhikers guide to the galaxy I want them to review it on their podcast!

@andrewknorpp9716 7 лет назад

Also I feel the sofas in the swamp need to know about this

@A8nton 7 лет назад

That was the reason why i clicked on this video

@JLPicard1648 7 лет назад

Andrew Knorpp I thought those were mattresses

@muhammedali8025 7 лет назад

Joke reference to Zoolander but not the more pertinent Dirk Gently's Holistic Detective Agency "Sofa stuck on a stair" by Douglas Adams

@spihs 4 года назад

Yes this is the main reason I watched this!

@gold4963 7 лет назад

The problem is that my mom doesn't know where to move it. :/

@victorkhan5960 7 лет назад

GOLD 1515 Hits way close to home.

@orionred2489 7 лет назад

That may be one of those equations that can't be described in closed format!

@fuckandroid9648 7 лет назад

GOLD 1515 next: the decision conjecture

@reedclippings8991 2 года назад

To display this level of expertise, and still not be tempted to claim certainty without sufficient evidence. This type of math seems trivial to a lot of people, but the world could learn a thing or two from this humble mindset.

@MAMAjAMAj8 7 лет назад

Pivot!

@geico105 7 лет назад

As some who is taking Linear Algebra, this triggers me.

@lu933964 7 лет назад

typical oppressive 3 dimensional behavior

@joehart1057 7 лет назад

MAMAjAMAj8 i get the joke

@tanayjyotidas6007 7 лет назад

Shut up! Shut up!shut up 😁😁

@chinadan86 6 лет назад

I came down here expecting to see this

@vedhasp Год назад

where's the extra footage on numberphile2? I can't seem to find it, nor it is there in the video as a clickable link by the end. Please put in here as a reply to the comment, thank you! 🙏🙂

@jordanjohnson714 7 лет назад

I remember looking through Wikipedia a while ago about unsolved mathematical problems and I saw this one.

@skakdosmer 5 лет назад

“More footage from this interview soon on Numberphile2“ No link? After more than two years?

@austynhughes134 7 лет назад

No matter the topic, these videos are always fantastic! Thank you for doing what you do Brady!

@XxChronOblivionxX Год назад

I'm imagining mathematicians buying sofas with these precise shapes for their houses, and waiting for someone to get the joke.

@karlcole5617 Год назад

i want to be that guy for some reason

@af252 7 лет назад

Nah I just twist it every single angle and manage somehow

@RitobanRoyChowdhury 7 лет назад

Sometimes, that's mathematically impossible

@poopinfruz9771 7 лет назад

Just like trying to move a 2d sofa down a 2d hallway in a 3d reality?

@kushpatel3553 7 лет назад

you just didn't twist it enough

@frechjo 7 лет назад

I recently moved a bed mathematically impossible to fit through the corridor. The mattress took some pushing. The bed took a window...

@zappawoman5183 6 лет назад

Dirk Gently wants to know if you can help him move his sofa.

@sayandas5 3 года назад

I was thinking the same thing 😂😂

@hitchikerspie 7 лет назад

To me! To you! To me! To you!

@LaurusHG 7 лет назад

HitchhikersPie Oh dear oh dear oh dear.

@diamonddave2622 7 лет назад

I 'chuckled' at this one

@ryangranato5010 7 лет назад

What??

@vinayseth1114 7 лет назад

+HitchhikersPie I didn't get it :/

@tokyoDRIFTA 7 лет назад

Chucklevision chuckle-chucklevision

@habenzaid3028 7 лет назад

Romik was really fun to listen to! I'd like to see more videos with him in them.

@Twatical 7 лет назад

Your channel got me through year 9, thank you.

@fishboss77 4 года назад

Wanting to shout "PIVOT" every time they start to rotate it around the corner.

@connorcriss 7 лет назад

Congratulations on 2 million subscribers!

@numberphile 7 лет назад

thanks

@thexavier666 7 лет назад

International giveaway of 2 million pies?

@bakergreg 7 лет назад

636619.772368 Pi to make 2 million

@bakergreg 7 лет назад

i did 2000000/pi

@christinebeames2311 3 года назад

Hi I’m a 76 year granny who can’t do algebra but find your explanations interesting , I am in awe of your mind ,

@scottsmith4204 7 лет назад

So how many people have these shapes of sofas? Mine is rectangle.

@entropyzero5588 7 лет назад

I've actually seen curved ones (stretched hemicircles) as well as ones where the inner angle of an 'L' shape is rounded off

@talesseed 7 лет назад

Entropy Zero there is no entropy zero

@suwinkhamchaiwong8382 6 лет назад

Mine is [_][_][_] [_]

@Josho4096 4 года назад

That's because you're a square.

@Ryuuuuuk 4 года назад

Do you even know what entropy is? The entropy is defined as S=- sum_i p_i log p_i , with p_i a probability mass function. If you now consider a (fair) coin flip the probability for each side would be 1/2 and therefore S=1, taking the logarithm with base 2 (measuring information in bits) and using some logarithm rules or a calculator if you aren't familiar with logarithms. But now consider the completely boring case, that the coin is twoheaded, so the probability for head would be 1. Plugging this into the entropy formula S = - ln_2(1)*1 = 0 - zero entropy, meaning that we have complete information of the system.

@Eurotool 4 года назад

2:34 one of the most satisfying animations I've ever seen

@8ytan 7 лет назад

Solution: you park your time machine in the stairwell, open the door, and then use the extra space you created to manoeuvre the sofa into place.

@ufotofu9 7 лет назад

Woe woe woe, easy chair buddy.

@8ytan 7 лет назад

robberynl Fantastic.

@TheMusicalFruit 7 лет назад

I shot a blue portal in the floor under one end of the couch. Then I shot an orange portal on the wall facing down the hallway in the direction I wanted to move it. Then I went back and pushed the couch into the blue portal and gravity did the rest.

@moje641 7 лет назад

John Reynolds 5schtzgjg zsfgb0ougmm kg xzzzvnm0yyb u

@seansammons3639 5 лет назад

Don't forget your abacus!

@Elgintensity 7 лет назад

12:50 is that THE Tony Fadell scrolling by?

@angusheath5321 3 года назад

Who knew the roaster of CrossFit himself would end up on Numberphile.

@nathanrussell1794 3 года назад

ZERO

@superj1e2z6 7 лет назад

This is math solving real world problems.

@JorijnLamberink 7 лет назад

That's not what math is about ;)

@Mark_Cook 7 лет назад

PlopKonijn But it should be. If math isn't applicable in the real world at all, then it is as useful (and at the same level) as the sci-fi writer dreaming up an ultraproto-gadget that launches laser guided shark-bots. Fun to think about, but ultimately useless.

@ze_rubenator 7 лет назад

Clearly you know nothing, Mark. Surprisingly often physicists and engineers come across obstacles in practice that were solved mathematically centuries prior. Take for example George Boole, in 1847 he invented what would later be called Boolean agebra. At the time it was perhaps a "useless" theorietical exercise, but about a century later it proved instrumental in the development of computers, and arguably kickstarted a whole new field of math that would become known as computer science, way before computers were even imagineable. Or maybe you just think computers are "ultimately useless." This whole idea that everything has to be applicable is just ridiculous.

@numbers9to0 7 лет назад

Nope. In the real world you make your sofa in three parts you can take apart, not in an ugly shape.

@novosell9694 7 лет назад

Ze Rubenator In the end what he came up with was applicable though... He never said it had to be useful immediately.

@geefreck 7 лет назад

Very well done. That said, everyone knows the largest surface area sofa which can go around corners is the liquid metal sofa developed by skynet.

@akashdwivedi2456 7 лет назад

so nature designed ANT like this

@tzisorey 7 лет назад

See, this is why engineers invented modular sofa suites ;)

@rebeccahughes8734 4 года назад

This reminds me a lot of Dirk Gently's Holistic Detective Agency. Love it! :)

@c13rmusic 3 года назад

It bothered me that they didn't mention it, nor Douglas Adams. (Especially when they've mentioned 42 in the past) Of course, Dirk's computer was working in 3 dimensions which they also didn't mention. So... maybe they're just not up for it yet. 😜

@TheLynneee 3 года назад

The reason I clicked into this was because of Douglas Adams! They have done a video on Douglas Adams's answer to Life, Universe and Everything (42)!

@standing_around 2 года назад

Yes! Forget Friends, I'm here for the endlessly spinning couch simulation

@indrajitjana 6 лет назад

I watch numberphile videos. But it was a pleasant surprise to watch Prof. Romik here. It was a pleasure to have him as a professor in my grad school :)

@xystem4701 7 лет назад

Ooh this is really cool. I love the unsolved/unproven ones

@rayhanroesli2803 7 лет назад

Mathematician is one awesome job, u can literally have problem with anything and the problem will confuse not only other mathematicians but also everybody in the world

@UnimatrixOne 6 лет назад

I thought this vid is about the problem with the sofa which is irreversibly stuck on the staircase to Richard MacDuff's apartment, in the book Dirk Gently's Holistic Detective Agency.

@standing_around 2 года назад

@mansoorwahab8934 7 лет назад

I had Prof. Romik for Abstract Linear Algebra. One of the best teachers.

@koppadasao 7 лет назад

The smartest way to move a sofa is a Philips screwdriver

@justinward3679 7 лет назад

Go away you filthy engineer

@entropyzero5588 7 лет назад

Ugh, who uses Phillips srews anymore? Pozidriv is the way to go! (Plus, to deconstruct most sofas I've ever seen you'd need a saw, not a screwdriver… Hey, maybe you could optimize the number of cuts you'd have to make to get an arbitrary shape through a corridor and around a corner? xD)

@xl000 5 лет назад

@@entropyzero5588 Pozidriv?

@alexwang982 5 лет назад

Entropy Zero Nah the minus head screws

@crafty1098 5 лет назад

@@entropyzero5588 If you were Canadian, I'd forgive you for saying Robertson. But Pozidrive is right out. Torx or go home.

@completeandunabridged.4606 7 лет назад

This is why I love maths, it is the rules underlying whatever situation you can imagine.

@j.vonhogen9650 5 лет назад

What I would like to know is this: if the path would have to be a unique path (from 'start' to 'finish'), would the Hammersley Sofa be the optimal shape?

@JorgetePanete 7 лет назад

Dear Numberphile, it is 1:52 AM for me, and i'm watching strange sofas... i will watch 'Incredible Formula - Numberphile'. i love your channel

@lcuthbert1 7 лет назад

Douglas Adams, Dirk Gently's Holistic Detective Agency, his solution was better!

@imhocanguro2993 7 лет назад

Lawrence Cuthbert I've always wondered if Douglas Adams was thinking about this problem when writing Dirk Gently

@blazebluebass 7 лет назад

This was one of the most interesting videos I've ever seen! The premise was entertaining, but in itself it was very exciting to listen how the problem was approached :D

@jonathanhurst6211 7 лет назад

What happened to the extra footage being added to Numberphile2?

@blairkilszombies 7 лет назад

This is what I want to know.

@karlduckett 3 года назад

If I ever need to move a sofa, I'd call upon the helpful team at the Sofa shop.

@brunolevilevi5054 7 лет назад

I wonder if Douglas Adams wrote Dirk Gently with this problem in mind, since there is a sofa that got into a position from which couldn´t be removed or something like that

@sreejithpro 7 лет назад

“Odd,” agreed Reg. “I’ve certainly never come across any irreversible mathematics involving sofas. Could be a new field. Have you spoken to any spatial geometricians?” -Douglas Adams, “Dirk Gently's Holistic Detective Agency” This is from the introduction of Paper that present this solution of Ambidextrous Sofa by Dan Romik DOI: 10.1080/10586458.2016.1270858

@brunolevilevi5054 7 лет назад

hehe I usually dont go through the description. Thats actually pretty cool, thanks for showing it to me! I didnt remember the exact text where the sofa problem is described, but seeing as how it is written is looks obvious that adams knew about this problem

@mypaswordisdad 7 лет назад

Possibly the best edited numberphile video to date. I'm not an ambiturner

@vincentpelletier57 7 лет назад

Did you guys talk to Dirk Gently about that problem yet? He might have some interesting insights.

@barto1035 4 года назад

Ok, I was wondering which sofa should i choose. Now I'm gonna go to the shop and buy this sofa. Thank you for advice!

@CntryBronco 5 лет назад

Has someone tried this with 3 dimensions? Having a square tube with an X, Y, and Z turn. Im curious if it would just be his shape rotated along the longer axis 360 degrees.

@razvannicolescu6185 Год назад

Maybe this will be the next unsolved problem in mathematics.

@jassandhar9442 7 лет назад

Congrats on 2 million! Objectivity deserves the same love

@horadaalgebra2358 7 лет назад

numberphile=π numberphile2= 2π thanks for listening!

@mathematicssteves9921 7 лет назад

Hora da Álgebra you're welcome!

@Gameboygenius 6 лет назад

numberphile2=τ if I may...

@MGSLurmey 6 лет назад

2π or not 2π? That is the question.

@brokenwave6125 6 лет назад

Its cool that his ambidextrous sofa is still a little better than a semi-circle which can only turn one way. It would make sense for an ambidextrous one to be way smaller but the fact that its actually bigger is cool.

@Gamahamel 7 лет назад

Zoolander in a Numberphile video, i would never have imagine that!

@danielcollins3492 6 лет назад

I had Dr. Gerver as a professor twice at Rutgers University. Very interesting professor. He retired recently in December 2017.

@AA-100 6 лет назад

Now to pose an even bigger problem. What if the length, width and *height* is also 1m now what is the largest object (doesn't have to be a sofa) in cubic metres that can go through the gap. Rotating, flipping etc is allowed. The object can be of any shape and have any length, width and height. So you guys can thank me for adding yet another problem to the list of unsolved math problems.

@prophetzarquon1922 6 лет назад

A: 1 meter tall Gerver sofa.

@rainworldenthusiast 5 лет назад

B: the tardis

@crafty1098 5 лет назад

A 1m cube. You don't rotate it at all.

@AA-100 5 лет назад

Surely you can do better with a semicircle with 1m height, but surely the semicircle can be beaten again...

@ThommyTheThird 7 лет назад

The animation at 5:40 is incredible!

@jamesrcdude1 5 лет назад

What's the largest volume sofa if allowed to rotate in 3d. Assume 8' high ceilings 😉

@laila-vp9ee 5 лет назад

James Cotter probably the exact same thing, but with a depth of 8’? Dunno, just my guess

@michaelkrapish3537 4 года назад

Have a Question about measurements .. and will It Fit before I buy .. Have 31 maybe 31-1/2 front foor Looking at A big couch says 34" door opening 98ninch long is that measure to just slide in ... Is it possible to angle fit the arm first 45*it ... then ""roll """ it in

@austoful 7 лет назад

this is a very satisfying to watch, like an interrupted gear system.

@timsullivan4566 5 лет назад

This is sofa is ALSO a solution to the famous problem, "What are the MINIMUM dimensions for a sofa-bed adequate for Siamese twins who are 1 unit tall?"

@gedstrom 5 лет назад

An interesting sub-problem might be what is the size of the largest sofa that can go around a corner of X degrees, where X is some value from zero through 180 degrees? Obviously, with a zero degree corner, the size of the sofa could be unlimited since you just continuously slide it. At the other extreme, if it has to go around a knife edge type corner of 180 degrees, I believe the semi-circle would be the optimum shape. But to find the maximum sofa for values in-between those extremes.

@MatthewHaydenRE 7 лет назад

Was this inspired by Dirk Gently's Holistic Detective Agency?

@redscott5029 7 лет назад

Just need to have the sofa model in 3D and let the computer run simulations.

@prophetzarquon1922 6 лет назад

Other way 'round, I'm sure. Although ... there was a time machine involved, so...

@kevinjohnson4531 7 лет назад

When I was in college, our professor posed the question of what's the largest 3D prism you can you turn in a hallway that meets another hallway of different width but with the same height. Solution left as an exercise to the reader.

@Adilio14 7 лет назад

What is this? A sofa for ants!?

@NonDelusional74611 7 лет назад

Adil Rahim the sofa must be......THREE times bigger!

@davemarm 6 лет назад

I was going to comment that the ambiturner sofa is in the shape of an ant and wondered if ants were shaped that way for evolutionary reasons related to the sofa problem (navigating small passageways). Then the damn Zoolander quote about ants got stuck in my head.

@jonrpearce 7 лет назад

As discussed in the wonderful Dirk Gently.

@jimaanders7527 3 года назад

This is very interesting! A math problem that fits a practical real life situation, I like it!

@andrewknorpp9716 7 лет назад

can this work with people?

@andrewknorpp9716 7 лет назад

and hello internet

@lc9245 Год назад

If we want to upgrade the problem we could add third dimension for even more chaos.

@TheEightshot 7 лет назад

This is what happens when mathematicians have too much time on their hands i think :)

@gui18bif 7 лет назад

TheEightshot actually this is a fun geometric problem

@jakubpekarek6400 7 лет назад

Thank you so much for saying "3D-printing" in the end! I was wondering the whole time whether those shapes are curved out of pineapple and mango or not. Now I can be at peace with that question.

@robinfreeman1810 7 лет назад

1:54 OMG THAT'S TOM HANKS

@DICACIO1 4 года назад

oops, my bad! I thought it was Dave Gahan from Depeche Mode 😂💀

@rowdy35967 7 лет назад

So if you stand the sofa up on end, the shape you have moving through the hallway is its side profile (the back, seat, and arm), not the overhead view. Then you'll probably hit the ceiling before it's completely upright, so you've gotta tilt it a little so the shape is skewed. I delivered furniture for ~3 years and we performed feats of ingenuity on a weekly basis.

@jsl151850b 7 лет назад

How can you NOT mention Douglas Adam's Dirk Gently? A number of elements in the novel were inspired by Adams' time at university. For example, one plot thread involves moving a sofa which is irreversibly stuck on the staircase to Richard MacDuff's apartment; according to his simulations, not only is it impossible to remove it, but there is no way for it to have got into that position in the first place. In a similar incident that occurred while Douglas Adams attended St John's College, Cambridge, furniture was placed in the rooms overlooking the river in Third Court while the staircases were being refurbished. When the staircases were completed, it was discovered that the sofas could no longer be removed from the rooms, and the sofas remained in those rooms for several decades.

@dasgafs6297 7 лет назад

Reading the title of this video I started to think of Dirk Gently's Holistic Detective Agency. I still loved the video.

@TrainTsarFun 5 лет назад

It can turn left! Lol

@jpdemer5 3 года назад

Now for the real challenge: a sofa that also fits through the 3-D space that is the stairwell leading up to my apartment.

@yoloswaggins2161 7 лет назад

Can't you throw CPU time at this? Some evolutionary stuff.

@jort93z 7 лет назад

you probably could create a neural network with the goal of maximising the size and getting it around the corner. but i dont think it would get anything better.

@Ludix147 7 лет назад

Yolo Swaggins has been done, produced the same Gerber's shape. according to some other comment that references they Wiki .

@yoloswaggins2161 7 лет назад

Proposing NN for this type of problem seems novel to me, which architecture would you use? I was thinking of something like the algorithm that shaped the NASA ST5 antenna, with the collective line equations from 5:46 as constraints.

@entropyzero5588 7 лет назад

Someone has done this and their program produced a shape whose area "agrees with the computed area for Gerver’s sofa to nearly eight significant figures".

@yoloswaggins2161 7 лет назад

Entropy Zero, that's very interesting thank you for that.

@godbelow Год назад

This guy looks like he's desperately holding back the giggles the entire time he talks.

@oskarj6311 7 лет назад

Now I can have the perfect sofa!!!!

@rodschmidt8952 6 лет назад

The fact that the path is not unique (while at the same time the shape is optimal) is really interesting.

@evandroandrade4909 7 лет назад

10:04 such a wierd image...

@lpsp442 7 лет назад

I really like how that special any-corner sofa looks, but really at that point it's just two chairs with a frustrating interlinking bit.

@kenny-cj6jr 7 лет назад

just drill millions of microscopic holes into the sofa and bam. much larger surface area.

@kevinmcneill468 5 лет назад

Having tried in my youth to move three folding bed sofas down a circular staircase from the third floor of a Montreal walkup this hits home with me.

@Satchboy71 7 лет назад

He should have made his sofa out of steel that is blue.

@KnakuanaRka 7 лет назад

Satchboy71 I don't get it.

@Satchboy71 7 лет назад

It's another Zoolander reference.

@problematic7993 7 лет назад

I really like the visual problems in the last two videos.

@morpheus6749 7 лет назад

An engineer's solution: stand the sofa up on its end, and then it won't matter how long or wide it is (to a large extent).

@mnikhk 7 лет назад

Yes but the problem here is how much can you fit without 3d manipulation only in 2d

@oliverjenks 7 лет назад

Morpheus yes, but the question still then remains. it's just instead of asking how big the footprint is, we need to ask what's the biggest side.

@morpheus6749 7 лет назад

I get that there is a very interesting underlying geometric problem to be solved here. But the problem is posed as moving a "sofa", and as such comes with certain constraints on dimensions and aspect ratios. And I was careful to say "an engineer's solution". Engineers are less concerned with the abstract and more interested in solving the actual problem at hand, capitalizing on its particular constraints. The question should probably be posed as what is the largest piece of _furniture_ that can be moved around a hallway corner to remove any reasonable assumptions on dimensions.