Optimization Problem: Maximum Length of a Pipe Through Two Corridors OR 🚪 Can You Fit That Pipe? 🚪

[@patrickjmt]

i don't know. i guess it depends on what you want out of life and out of your education. you need to decide for yourself how much work you are willing to do.

[@heltok]

Great now do this for 3 dimensions so I can figure out if I can take the sofa upstairs!

[@patrickjmt]

ha, yes. 21 minutes for a problem is child's play :) people have devoted years and even lifetimes to problems (without ever getting them correct). andrew wiles spent around a good 10 years or so (i think) to solve fermat's theorem. others spent longer than that to no avail.

[@darkBender99]

It's amazing how 1 math problem could take 21 minutes, in college I took an exam with only 4 math questions which took the whole day to finish. Keep up the good work!

[@timewarptrio11]

I hope you do post question like this every week or so, it was awesome to learn how to solve this one!

[@patrickjmt]

yes, of course the diameter would make a difference. in practice, i think one would take the width of the corridor and subtract the width of the diameter as that would effectively give you the space that you have to work with.

[@karlylindenberg1499]

You are the greatest explainer. I do not like math and need it broken down like this to understand. Thank you so much for all of your videos. You are really the reason I can get through Calculus successfully and get the degree I need to get and become a PA.

[@patrickjmt]

you are very welcome

[@DarlsC]

this one's pretty complicated

[@Shawn9081]

I love seeing a genius at work

[@patrickjmt]

glad you feel that way, that is a good feeling to have :)

[@gouzbekistan1]

The video like this every week sounds great!

[@Goproflying]

You did an excellent job. Sub question: How do you set up your camera? (sorry if it's been asked before)

[@alexleviyev]

i understood everything you did. but how do you get that intuition? knowing what to do when you see a problem. i would never in my life draw triangles and start doing what you did

[@BareClause]

Yes, please do more.

[@patrickjmt]

i kept waiting for it to show up, but never saw it

[@Goproflying]

I knew triangles were involved, but didn't think it would be this long to figure it out.

[@patrickjmt]

you just use your imagination and try things. of course, experience counts for something.

[@patrickjmt]

no problem :)

[@pwngo]

Keep doing these, they are very interesting

[@alxjones]

I really wish you simplified the y equation before you plugged in numbers. You can do the factoring you did while you still had numbers, which would have given a nicer version of the general equation.

[@patrickjmt]

would it matter?

[@patrickjmt]

we went through all of this in the comments when i first posted the video :) not rehashing it all here.

[@BodhayanPrasad]

Instead of y, take b as a variable, that will be more elegant to solve the problem. Moreover, why don't you take (b^2/3-a^2/3) common? Doing it this way, equation, simplifies to: y^2/3=b^2/3 - a^2/3 Anyways, great job buddy :)

[@patrickjmt]

ya can't win em all. seems the same to me though.

[@patrickjmt]

why is that?

[@patrickjmt]

it is not a trivial problem :) if it was, i would not have posted it!

[@patrickjmt]

if you are happy with C's, go for it. i never was.

[@blairseaward5560]

This literally saved my life!

[@bradleymarka]

This solution is actually incorrect, even thought it gives a correct answer. Instead of maximizing the length, b, of the pipe, you minimized the width, y, of one of the corridors for a fixed pipe length, a different problem. The corridor width is constant (y=27), so y' is zero even when not optimized. You assumed that y is a maximum when the cosine equals the cube root of a/b and skipped the 2nd derivative test. Had you done the test, you would have discovered it's actually a minimum!

[@matthewjiao7233]

Yeah

[@pjtrusci]

nice catch

[@ginayang95]

I had the same question when I first read the question. It must be impossible to solve the pipe's length without knowing its width, too many variables and too little given information!

[@forNOreason100]

Fantastic explanation!

[@patrickjmt]

congrats! :)

[@simpsiano123]

what level of math would this problem be considered?

[@DoggoWillink]

I didn't even try. I saw angles and said ugh. So much for my education and math ability. I really don't know how I get by, honestly. Electromagnetism, principles of astrophysics 2, here I come. I can't even get a theoretical pipe through a theoretical corridor. Cool problem though, I see it now.

[@patrickjmt]

calculus 1

[@supergreatsuper]

After you get that cos(theta)=a^(1/3)/b^(1/3), how do you know that the side lengths of the triangle are a^(1/3) and b^(1/3) and not some constant times a^(1/3) and b^(1/3)?

[@sawensh8223]

nice job sir thank you so much

[@alxjones]

True, it's just a personal preference of mine.

[@sjsawyer]

Depends a lot on your university also. I am 1 term away from getting my BMath! What makes you want to major in mathematics?

[@FuzzuBlue92]

great patrick!.

[@Bimjay436]

Wow thanks sir❤

[@NxyDolli]

Nothing in my four years of university study prepared me for that problem...and I have a Masters degree. Perhaps I should run before the uni tries to take my degree back xD

[@sawensh8223]

thanks

[@deezynar]

You didn't say what the ceiling height is.

[@ginayang95]

I know exactly what you're talking about, in fact I get stuck all the time! haha :)

[@patrickjmt]

well if i was not explaining it, i could do it in about 5 minutes or less.

[@JoeHernandez-lp2tw]

Or or you can just use a measuring tape and figure it out in less than min :)

[@mayurchawla1918]

solve this bro =a rectangular metal sheet of length 30cm and breadth 25cm is to be made into an open box of base area 300cm by cutting out equal squares from each of the four corners and then bending up the edges find the length and the side cut from each corner

[@woahdaggies]

He already did bro. Its in another video.

[@FarhadADeven]

allright this was not fun

[@maxyar0n]

More difficult examples please.

[@Ignaciodxd]

Dude This video has 5YEARS

[@ShaneBlaze94]

One does not simply push a pipe through a wall. 1:44

[@xXWinja52Xx]

oh how i wish you were my math teacher lol

[@DoggoWillink]

Thank god for tape measurers.

[@timewarptrio11]

The length of this video makes me feel better about not getting the correct answer after about 5 minutes.

[@sjsawyer]

Thanks =)

[@Cityj0hn]

Simple logic.

[@hashemlukasha1311]

were can i find the other video responses??? please help !!

[@patrickjmt]

unfortunately, youtube did away with video responses a few months back. not sure how to find them now other than to do a search

[@ultravidz]

Holy hell

[@asdfghjkl36958]

Smart

[@boomguy12345]

Hey patrick, I really like math and I think it's beautiful, but I'm unable to see the solutions to problems such as this one mathematically. Is there anything free one can do that would help with this? Best regards

[@mazenabraham8338]

I did not start the video yet but this seems very hairy problem

[@johnparker2057]

You sure know how to complicate a simple solution

[@patrickjmt]

thanks john!

[@anonymoususer2271]

@@patrickjmt lololol

[@supergreatsuper]

I suppose not. I really should have been asleep when I posted that comment :P

[@Immortalprodigy1]

cool

[@therealjordiano]

nice problem imo :)

[@carodejXXX]

Because you aren't genius as Patrick :D