Maths Problem: Connect the towns solution (Motorway Problem)

[MrTanookiMario]

This is your coolest video I've seen so far.

[xanshriekal]

I love the graph: energy vs something

[vilkav]

this is fucking brilliant

[Redflowers9]

but if you haven't been... then no thanks

what's great about maths, I think, is that you experiment with your intuition at the same time which betters your approach to life in general

[zavatone]

uh Haiche?

You mean "an h", right?

[eddyproca]

4:46 MIND BLOWN!

[FL0myFL0]

I was surprised that I actually learned something new in this video but the same time I was disappoint because you didn't show other viewers how you can actually calculate that. Or you just assumed that they already knew how to calculate it (like me) but only wanted to show a different, neater way to solve this.

[singingbanana]

@FL0myFL0 I wasn't trying to make a lecture.

[StikManJones]

@singingbanana jesus christ where the HELL were you in from 1997-1999 when i tried stuff like this and got called a downie by my maths teacher. 

[prajwalsuhas]

This is reducing to a problem of finding a Local minimum. Interesting.

[nessdude14]

@prajwalsuhas He's using the local minimums of the bubble's free energy to describe why the bubbles form certain shapes, but this concept doesn't necessarily allow you to calculate the geometry which 'connects' the towns.

[shriyash134]

Does it also work on irregular positions of cities ?

[singingbanana]

@shriyash134 Yes it does.

[kalfen]

"Murray? Present!"

[matematikosburelis]

I wanted to correct you at @3:18 - there is another possibility - if one of the corners of original triangle is larger than 120 degrees. What happens then? :)

[gjermundification]

@matematikosburelis Where is the correction? I only see you state a condition and question that condition.

[selinadenseje]

Im writing a huge paper on soap films and optimization problems. This helped me a lot. You are awesome! :D

[alexglew]

You are brilliant

[xCelsius451x]

I love the axis labels as 3:56

[mildlydiverting]

Applause! Hey, did you ever see a bloke called Cyril Eisenberg demoing this? I remember being taken to one of his lectures when I was small. Never forgotten the trick since then!

[singingbanana]

@mildlydiverting No I haven't, but it's a cool trick that goes round mathematical circles. It's nice to hear it stuck with you! It must have impressed you! :D

[mildlydiverting]

@singingbanana Woh! Turns out he actually wrote the book on the subject - check Amazon under Cyril Isenberg - and got an MBE!

He was a nice man, worked at the University of Kent. Had a great line in smoke-ring physics, too.

[mildlydiverting]

@mildlydiverting Erm, and now i read your full description, I see you link to an article by him. Cough. Sorry.

[singingbanana]

@mildlydiverting I thought I recognised the name! Sorry, I haven't thought about this problem for a while. Yes, he's the man on this stuff.

[lailamnma]

creative !



[valkirikiri]

Analogic mathematics <3

Thx

[djcordeiro]

This happens to be the topic of our math circle lecture this Saturday (December 10, 2011). Drop by if you happen to be in the Dallas area. Just google Metroplex Math Circle.

[hnkang]

great video, thanks. maybe put the u-shape drawing back up at 4:22?

[chulk607]

Very cool! Get this chappo on TV. Very good at explaining some genuinely interesting stuff!

[CrestalMyth]

See kids, this is why learning mathematics is useful.

[imamnalog]

If you are organic chemist, you are impressed

[Zanneth]

@imamnalog Or a Computer Scientist. These are fundamental problems in computational geometry!

[tikomichael]

Awesome video, the models are an interesting idea!

[123pammi]

similar to organic bonding, they take the shortest path, optimization

[i103772]

pretty cool stuff..im impressed

[ziyan133]

i, for one, bow down to our new soapy water overlords

[alohasprinting]

Thumbs up if you're from UW and have to watch this haha

[xxSichaye]

How cool! I wrote an essay about the mathematical properties of soap bubbles about a year ago, this one was also included :)! I also had to do a presentation about it and it was a lot of fun to show this to the class.

[kassieanne9]

That was cool ,I wish my math teacher was cool like this XD

[Kurana4390e]

i feel like a retard :(

[jimgati]

ya i dont do math on youtube jk

[vedhasp]

Ok, I can't draw it here, so lets number given points in order from 1 through 7. Lets place 5 points inside this imaginary septagon a through e.

Connections: 1a, 2b, 3b, 4c, 5d, 6e, 7e, ab, bc, de, ea. Is this the most optimal solution? I was also wondering, how should one approach this problem in mind (i.e. without using a soap solution) in general?

[vedhasp]

I was wondering what is the steiner tree solution for vertices of a regular septagon? I was trying to figure out myself, one of the minimizing solution I could think of had a regular pentagon in the middle. Is that right?

[markashleyfilms]

Whilst I didn't completely understand the 'Steiner points', it was completely fascinating. Wish you'd taken mathematics when I was at school. Smashing channel, Jim! I'll be following more of your brain teasers. :D

[akaashbits]

Question:

Shouldn't that be 2.5 instead of (1+√3)?

Proof:

Side of an hexagon = r (where r = distance from center to a corner).

Since, r = 1/2, one Side of Hexagon = 0.5.

There are 5 such sides in your solution (as shown in 2:41), so answer = 5r = 2.5.

I might be wrong here, but am willing to learn!

[vedhasp]

@akaashbits I liked your "approach", really interesting perspective, wish I could think like that. However, 2 things:

(1) r is not 0.5. If AB=BC=CD=DA=1, Ato1=Dto1=Bto2=Cto2=(1/sqrt3), Use Pythagoras/Katyayana 30-60-90 triangle. So, 1to2=(1-1/sqrt3). Add the lengths, you get (1+sqrt3)

(2) Essentially, you cannot "ASSUME" this to be regular hexagon just like that. In fact, as proven, it would be terrible assumption to make. In such a case, AB will be longer than AD, also none of the sides = 1.

[SuperEarnburn]

so energetic

[GammaZero]

why is the soapy water greem?!?!?! D:

[astoma199]

Awesome!

[idkravitz]

Lol, I wish every optimization problem can be solved with a soap

[fatkasuvayu]

This is so Feynman-like ... amazing applications mate.

[rcsparks01]

how can someone with a name like singingbanana be so mathey

[sufilix]

Fucking awesome. WTH it didn't even have boobies and i watched it from start to end.

[soundslave]

And there I was saying practical mathematics was an oxymoron.

[brageyboy]

Wish my math teacher did stuff like this.

[BachikoiBabi]

This guy is a freaking magician! Watch out David Blaine!

[phasespace]

Very good connection between nature and mathematics. Very well demonstrated!



[xetrius]

I think that I find your bowl of soap way too interesting

[MadTimmy]

Soapy water is smarter than man?

[techvids21]

@MadTimmy nature is smarter than human!

[arcticbanana69]

thumbs up if weebl brought you here!

[TheViewOfCalvin]

No way... He made maths interesting! 0o

[NerdDog16]

i love pies :3

[Jiskemarije]

Ok, now I feel dumb

[theph33r]

bahahaha, liverpudlian accent ftw

[robiniroven]

cake

[Florence00pi]

This is very cool!

[jakoreilly]

I genuinely enjoyed this.

[ChickenIzMLG]

LOL. He said haych.

[kenderpl]

This is mindporn! :)

[merpzilla]

He looks like he fucking loves maths

[Benawisan]

what kind of wizardry is this lol

[CyanideXCS93]

i laughed my ass of with how simple this was :P

Nice vid man :D

[JeefCakes]

That was fucking interesting.

[batllama]

Why didn't weebl favourite this last week :/ would've passed maths

[recoil669]

Great video, one thing though, next time you say "energy" you may not want to make a fisting motion. 

[icecremer]

I don't know why any of this is important, but that was quite entertaining.

[sathvikmail]

Just came to my mind that , smallest route for 8 points , looks like honeycomb, where I guess Honeybee knows the smallest route to connect points or to create an efficient way of creating honeycomb ! Awesome !

[KinoftheFlames]

those internal local minimums look an awful lot like molecule formations

[Direnaar]

@KinoftheFlames That's just nature being efficient :)

[ScorpiaX]

@KinoftheFlames Yeah thats what I was thinking..VSEPR.

[Mascaraud]

I nearly died at 4:45

[Leruster]

Amazing!



[Ketsui]

A cross works fine, if you put an extra turn in the roads, you've got more traffic! Dislike!

[khorneboy888]

Very cool..

[forwardreza]

Neocon70, bet you get your butt rammed X to infinite. Its because guys like this we owe everything too, from toothpaste to cars to anything science. What the hell have you done to make human life better, Ohhhh ya, you get laid, congrats you stupid monkey

[Monkeyspass]

What about 2 points?

[Bubdudder]

I don't like math and I don't like logging into YouTube but this was so awesome I just had to let you know.

[Styroplank]

are you a wizard

[TheBigMclargehuge]

6 people were fired from their highway planning jobs.

[gugolski]

it just blown my mind :(

[drew2000four]

MatheMagic! 

[emarkman1]

Amazing

[AdenFlorian08]

This needs more views.

[theodorehui]

this is one of the best demonstrations i have seen on youtube

goodjob jim!

[theodorehui]

jim actually shot both videos on the same day lol

[AlienX3124]

I would replace him for my math teacher any day



[webmastertool]

@AlienX3124 i would replace him for Mathematics any day.

[wrightmath]

1. Finding the "solution" using bubble fluid? I see what you did there.

2. This (great) video reminds me of an interesting book called "The Mathematical Mechanic."

3. You make it look really hard to speak with an English accent. My face hurts when I watch your videos. No offense intended; maybe it's just me.

[GSA14101996]

The original video description said What is the minimum amount of roads needed to connect these four towns together? Not how much road or least distances of it

[balluduku]

@singingbanana You should try adding a step in your setup (it would basically simulated different costs for the construction of the road, or the fastest way to reach someone drowning in the sea when you're on the beach). You'd see the bubble bend just where the step is, and choose a longer way in the part "on" the step (at least if you put the step in the middle of the way), where the height of the bubble is smaller. I guess with a slope you'd see a curvy bubble (never tried).

Beautiful to see!

[aao198]

Too bad you can't use soapy water in the classroom ;)

[LAHMOS]

loved that <3



[mik3p0wer]

wait... if the 8 towns "soapwater solution" is just a bit smaller than conecting them in a circle, would leaving towns a and b unconected directly not make there be less road? (this was confusing to write and id understand if you didnt understand it.)

[singingbanana]

@mik3p0wer You're right it would be. I was just showing the internal solution, including steiner points, was longer than the external solution.

[Gameboygenius]

@singingbanana I think what mik3p0wer meant is that you could take the external solution (a continous octagon) and remove one road. Everything would still be connected, but the solution would use !7( less road.

[fog340]

Im not a fan of math and im personally not good at it,so belive me when i say this,You just sparked an intrest of math in me..plus you deserve a sub.

[ToppersMovieCorner]

i didnt understand anything...but it was nice to watch :D (maybe my english is not that good) xD

[skydive777]

Thumbs up if 5 people didn't understand anything this guy said=))

[ThePassiveWatcher]

I knew about Surface Tension and stuff but THIS application is completely in a whole new level for me.

[mickyjunior88]

I'd like to see this applied to roads separating real towns. Just because i'd like to see roads built like that.

[singingbanana]

@mickyjunior88 There's a link in the description about slime mold and the Tokyo railway system. Turns out slime mold grows in the same way and gives the same result as the railway network.

[StargateMunky]

@singingbanana what about issues of geography and simple matter of fact issues like how towns evolved due to other reaons such as natural resources...

[Dmon1Unl]

What about drawing all possible lines that could be used between points, state their lengths between points then apply dijkstras algorithm?

[Emejapazco]

Amazing. Only response I could give for this video!

[paddycalla]

Superb



[davh27]

So proud to be #British right now :')

[MrAbdulmaster]

to get to the lowest dancer you have to put in some energy first XD

[TheNich8888]

yes i totally guessed it before i saw the end

[deathgiver365]

Mind equal blown....

[khantatat]

bio-inspired methods rule!!

[dxjan]

‎"This is were nature(?) is going to help us"...Physics are fine, but when it gets more complex I prefer living organisms:

Watch "Tokyo rail network designed by Physarum plasmodium"

[NormalIsGreat]

Nice .. very clever

[MrChump0]

Phys Chem and Maths go well together :)

[cballew57]

NERD POWER!!!!!!!!! FTW

[ThePunkkapoika]

SOAP #FTW

[thaer12345]

1:08

Wtf is a "Haych"? Thumbs down.

[lilsokzmuzic]

you should seriously become a professor at Harvard University. haha!

[ChnDragun]

interesting...

[bobbyweelki]

OMG YOU HAVE BEEN TO MY SCHOOL :D

[amfikz]

i saw this video on rodo(dot)lt , but just came here to tell, that i really didn't expected that :)

nice video bro

[shingfunger]

so awesome

[crimsonninja6995]

this video pisses me off just because i've had to learn years of calculus to even comprehend how to solve this problem on paper...and you do it in a few seconds with freaking soap. >.<

[shoseki]

@crimsonninja6995 Not only that, but he has now hands that do dishes that feel soft as your face...

[crimsonninja6995]

@shoseki oh wow, thanks for letting me know i got the top comment haha

[Jacob2Israel]

awesome video, great screen name "singing banana" LOL!!!

[dracomister7]

i got close. I didnt know how to solve it but just doodling i got 2.79 and almost exactly the hexagon one

[kyledude120]

I love it when people explain math in a visual way, especially if it's higher level math like calculus of variations, awesome video man!

[luckyw4ss4bi]

4:47 blew my mind

[unclesam115]

your accent is sexy

[mattysterling]

You're a great speaker, great props also. Very interesting!

[TheSnappy121]

Love how you said "pythag" like a G6 :L

[edenite]

i found that utterly fascinating

[MyAwesome999]

you are litteraly the BEST person ever!!!!!!!!!!!!!!

[MrKumbayah]

thats fkn awesome

[macnolds]

fantastic vid. i did not expect that experimental approach.

[anticorncob6]

The smallest solution is 1 + sqrt(3)? PAROVE IT!

I wanted you to prove that there's no smaller way but you didn't! I guess I'll have to figure it out myself... *sigh*

[HappyApple330]

About the 8 towns, one of the roads on the perimeter can be cut. that way you would use seven roads and you can still get around the towers. (however it may not be convenient)

[aznlalaland]

Is their an actual outlined proof? Out of curiosity, are the lengths always constructable?

[cdplayerx50]

@JohnnyLukeB -part 3-average of your horizontal velocity and your final vertical velocity, which (assuming you use the same energy for jumping away as you would if you were jumping upwards) will always be the smallest speed, unless you jump away from the building EXTREMELY fast, even though you will still hit the ground with the same force as if you just fell off the building. Sorry for using three comments while writing this lol - but if some of the things i said didn't make any sense, i'd be

[cdplayerx50]

@JohnnyLukeB -part 2-drop in height from the building will both be added to your kinetic energy (movement energy) powering your downward velocity (velocity is your speed in a certain direction), which will be greater than your downward velocity if you just fall off the building, and just have the energy for the height of the building added to your kinetic energy. If you jumped away from the building, your end speed would be even less! This is because your final speed would basically be an ave

[cdplayerx50]

@JohnnyLukeB You would reach the highest speed if you jumped upwards off the building first. This is because when you jump, you are turning your chemical energy into potential energy (which is basically a measure of how far away from the earth you are) to push yourself away from the earth. Once gravity overcomes your upward velocity however, you will fall the distance you just gained, and the 40 storeys of the building, so the potential energy which you created and the potential energy of the d

[JohnnyLukeB]

This has nothing to do with this video, but i was wondering: If you were on the top of a 40 story building, would you have more speed right before you hit the ground if you jumped off of the building outwards, if you jumped off upwards, or if you just fell off of the building? Please put a lot of details in the video (if you choose to make it) and put in some details, like aerodynamics, and please answer this because ive been pondering over this question for days!

[realesethesteam]

That's thinking inside the box!

[1dexlab]

Its so cool!!

[RichPlaystation]

Wow, never thought I would actually hear some maths explained, and not ONLY would I understand, but wthen hear the phrase "and here is how it applies to the real world".

Proof once again you would make an awesome teacher or something, because not only do you teach, you also bother to give a reason WHY you are teaching any given subject or problem. Though maybe it was just all my teachers that were rubbish, who knows.

[fix520]

YOU SIR ARE EINSTEIN OF YOUTUBE.

[charizard1357911]

beast



[tk7kyle]

dude I wish you were related to me, you're going to be a legend

[alquiora]

Excellent video!

[BaXeD22]

You never shared - what is the solution for 8 towns?

[Chessmaster777]

A graph of energy and something.

awesome.

[bugshirt4]

I've seen this work with a cube before, too. Is that the same principle at work?

[facilvenir]

I said it was the cross....but I'm a lay people!!!!

[illusionboy10]

cool vid mate keep it up i love watching these vids:)

[Tolstoievsky]

so there's no clever math solution to this... is the soapy water really the best way?