The 60 Year Quest for the Perfect Sofa

[@WrathofMath]

Thanks for watching! I want to apologize for saying 'more simpler' and 'lavas' near the beginning of the video. Please forgive me. Join Wrath of Math to get exclusive videos, lecture notes, and more: kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin More math chats: kzbin.info/aero/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Sources: arxiv.org/pdf/2411.19826 www.math.ucdavis.edu/~romik/movingsofa/ www.math.ucdavis.edu/~romik/data/uploads/papers/sofa.pdf web.archive.org/web/20080107101427/mathcad.com/library/constants/sofa.htm blogs.ams.org/visualinsight/2015/01/15/hammersley-sofa/ arxiv.org/pdf/2407.02587 www.reddit.com/r/math/comments/1h4om4s/solution_to_the_moving_sofa_problem_claimed/

[@StarDotJPG]

Dammit, Jim! I'm a mathematician, not a languager!

[@MichaelDarrow-tr1mn]

how did you manage to do a whole video on this without even saying pivot once

[@minhn-f4p]

fr

[@philipschlaepfer9866]

He managed to not say pivot once but still get a joke in about women

[@Untoldanimations]

what is the reference

[@JorgetePanete]

You forgot the question mark.

[@MichaelDarrow-tr1mn]

@@JorgetePanete we don't need it. you can tell it's a question because it starts with how

[@tomkerruish2982]

How hard was it to avoid saying "Pivot! Pivot!"

[@WrathofMath]

Not as hard as it was to avoid saying more simpler

[@pvanukoff]

The first words that came to my mind lol.

[@seancondon5572]

Depends on how many friends he's got.

[@MichaelPiz]

Adding lava pools and piranha pits somewhat complicates the geometry.

[@WrathofMath]

True, the moving sofa over lava and piranhas problem is the next generalization

[@MichaelPiz]

@WrathofMath I'll hypothesize, however, that adding both lava pools _and_ piranha pits complicates the geometry _less_ than adding either alone. That's only a gut feeling, though.

[@jacobryan9403]

LMAO the the summoning salt music love to see it. I gave up reading the paper after understanding the definitions, but kudos for the breakdown. great video!

[@gcewing]

There's a well-known solution to the sofa moving problem that was published by Douglas Adams. You use your time machine to materialise an extra door in the hallway and open it at the moment the sofa is being moved.

[@atimholt]

I was too young when I read that book to get any of the references. Hadn't even watched Doctor Who.

[@jjcvip]

I attended a talk last year regarding the moving sofa problem at Rutgers Camden, in which Gerver himself was in attendance. I forgot the name of the speaker unfortunately, but based on that talk I would guess Gerver's sofa is optimal. It's a fun optimization problem

[@zihaoooi787]

"i understand the thing as well as i understand women" DAMN

[@thelifeofibo]

by Kendrick Lamar

[@antoniofigueroa887]

Couch companies: make sofas in any shape BUT this

[@dmdeemer]

I'm totally going to go to a furniture store and ask for a Gerver Sofa.

[@ciCCapROSTi]

I wonder if a 1 by 1 3D hallway maximum would be just this shape extruded to 1 meter, or some clever twisting could increase the volume further.

[@duoasch]

this probably depends on the construction, if its just an extrusion of the 2d hallway it might be a simple extrusion of the current optimum, however if we need more than one axis to rotate into the second hallway this will be a new shape i think

[@isobarkley]

great vid! but your summary kinda implied that you can construct any arbitrary region S and then define R and Q(S) to show that whatever you chose S to be is optimal

[@douro20]

Zhipeng Deng is actually a mechanical engineer from what I understand.

[@waffelz604]

sorry im im mistaken, but at 10:08 wouldn't it be possible to use the quadratic formula to find the max by averaging the two roots?

[@reckingcrew2277]

Yup! You could do that! Or convert is to vertex form and use the k value to find the max.

[@VividBagels]

I feel like once you learn how to find maximums using the derivative you never really use any other method

[@imabotatrobloxskyblock6355]

-b/2a is the formula to calculate vertex

[@Tosty159]

18:46 I had to sit up when I was hit with the "We're finally landing" by Home

[@AlanKey86]

Santa Claus is taking notes, getting ready to squeeze down all those chimneys...

[@jasonnathanmason3547]

Pro tip: Don't have a sharp 2D 90 degree hallway in your new house. It will be hard to choose which sofa you will get. 🛋️

[@allfrogsaregay]

tell that to my landlord 😓

[@terraloft]

Moved 44 times in 70 years. Stand the sofa on its end. Momsense

[@sandekv]

That requires a third dimension, and wildly complicates the problem. The biggest 3D shape must be at least the 2D sofa times the height, but it might be possible to construct an even bigger sofa.

[@kiro9291]

20:59 grateful I wasn't drinking water

[@matthewleadbetter5580]

I know it's still more effort, but if you wanted to 3D print them, it might be easier than you think. To model it using OpenSCAD, you just need a list of coordinates for the shapes, which you then put into polygon, which you then linear_extrude. It's just 2 lines of OpenSCAD code. Then you render it and send it to a friend with a 3D printer. Of course what you did worked fine. But then you don't get to keep a nice actual model of them.

[@WrathofMath]

I actually have a 3D printer haha, but it isn't currently working

[@matthewleadbetter5580]

@@WrathofMath Same. My replacement nozzle is in the mail. Looking forward to having it back!

[@gcewing]

There seems to be a gap in your reasoning when deriving the area of the Hammersely sofa. It's not immediately obvious that we get to choose the radius R freely.

[@rewixx69420]

bro proved it at my bday

[@WrathofMath]

We had to celebrate somehow!

[@terraloft]

Thank you guy in his room with snacks

[@Juttutin]

And this is why God gave us squishy padded sofas...

[@VincenzoBarbato]

and this is why we invented God

[@WrathofMath]

The problem is the squishy padded part is the set of cushions, but the 'sofa' part is a big hard rectangle

[@VincenzoBarbato]

@@WrathofMath unless we talk about those new fancy bean bags that are in right now HAHAHA

[@livedandletdie]

@@WrathofMath That is a easily explainable and solvable problem, ask any engineer. You just need to construct the rigid body such that it has one directional squish.

[@danodet]

A furniture company should make Jineon Baek a Gerver’s sofa and a moving company should deliver it to him.

[@tylerlenk6377]

The area of the enclosing region R gives Lebesgue outer measure

[@martinprince8253]

This is the perfect sofa so far.

[@cadekachelmeier7251]

Jineon Baek and the Mystery of the Moving Sofa

[@mathamour]

📐📐In addition to the standard 90-degree corridor, I think it would be beneficial to explore scenarios involving sofas rotating within non-standard corridors, such as those with angles of 120 or 160 degrees. Could you elaborate on the reasoning behind primarily considering 90-degree angles in our discussions?😂😂

[@iantalbot7364]

Now solve for arbitrary corridor angle?

[@josephfredbill]

Where did the maximum bound of 2.83 (at 12.53) come from ?

[@ComplexVariables]

Nice job!

[@WrathofMath]

Thank you!

[@chillwhale07]

14:12 Those look like the hairstyle of that one lady from the Incredibles movie.

[@alanmiraanime]

Bro really made a rigorous mathematical proof for his thesis just to justify buying that ahh sofa 💀💀💀

[@ajai_p]

Area = ∞ (if bought in parts one by one)

[@hello_hi1]

Now do it in 3d

[@yeet6356]

Nah is it just me or does the blue marker look like it’s edited in, it’s so… bright

[@WrathofMath]

I spare no expense to obtain only the finest sharpies!

[@aidenkoh2426]

The link to the original paper is way too far down. It should always be the first link in the description.

[@Quasar0406]

it's the first link now

[@John-egg299]

I hate it when my sofa under the wall

[@coreylapinas1000]

But where do you sit?

[@Cen_t1369]

Why can't we just Rotate the hallway 90 degrees and see at what places the walls didn't go. Like put ink beneath the walls and see what area is covered by the walls. Then check where the walls didn't go and that can be our sofa.

[@nmay231]

Because the optimum requires moving the hallway as well as rotating. If you only rotate, you just get the half circle.

[@artkalbphd]

If you want to learn more about the moving sofa, I conducted an interview with Dan Romik about the solution and the peer review process kzbin.info/www/bejne/a2aqXpiEjtqMfas

[@nmay231]

Good to know!

[@diaklau6361]

An ant was on the screen

[@glumbus-qe7zk]

when

[@X3m.Gaming]

what kind of house has a turn like that so perfectly to ruin your day?

[@WrathofMath]

Maybe not so many, but it's also probably not so unusual to encounter a turn like that in the hallways of apartment complexes/storage buildings where you might store a sofa.

[@iets234]

So he ended up with the universal symbol for ending a call.

[@Juttutin]

"I could really use your help moving my sofa into my new place. Are you free on Saturday?"

[@cubeoi]

or.. the shape of an old phone

[@WrathofMath]

isn't it also the symbol for taking a call?

[@Xayuap]

¡Pivot!

[@AbstractAproach]

Nothing about the upper bound? Just algebra?

[@luongmaihunggia]

Some of the people who have worked on this problem are probably dead by now 😅

[@RilianSharp]

maybe next you could write a dissertation on how to make a math video that doesn't contain misogyny.

[@dj_laundry_list]

You sound like a Trump supporter

[@MrMasterGamer0]

What?

[@dropyourself]

21:02 are you saying this because he says he doesn't understand women? What he said is closer to "all men are trash" than it is to misogyny.

[@samueldeandrade8535]

Oh wow, it's my first time seeing a snowflake in this channel. How special.

[@djridoo]

Didn't say a thing that would be near misogynistic. Maybe you could try writing a dissertation on how not to bark.