Squared Squares - Numberphile

Featuring Dr James Grime.
More links & stuff in full description below ↓↓↓
Extra footage from this interview: • A Nice Square - Number...
Blog post about the old photo: www.bradyharanblog.com/blog/th...
Check out www.squaring.net for loads of great info.
Objectivity: / objectivityvideos
James Grime: singingbanana.com
Parker Square: • The Parker Square - Nu...
Squaring the Circle: • Squaring the Circle - ...
New Parker Square Mug and Buttons: store.dftba.com/collections/n...
Nice Square merchandise
US: teespring.com/nice-square-us
EU: teespring.com/nice-square-eu
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[@ricarleite]

"Or does it?" "... no it doesn't." Dreams crushed

[@TieMaxx]

probably too complicated

[@distraughtification]

It was probably proved to be impossible.

[@sinner6]

I was hoping for a number file extra on that.

[@dyld921]

"Oh..."

[@UnitaryV]

Plex My guess is that the method probably isn't all that interesting either. Rather than an elegant deduction, it was probably proved by means of exhaustion, using a computer to test every way of putting the squares together, and finding that none of the configurations fit within a 70x70 box.

[@Chris_Cross]

*"Or does it?"* *VSause music starts "No." *Music stops abruptly

[@NStripleseven]

Christopher Dibbs Funny you mention VSauce, right? Wrong!

[@skfok8472]

@@NStripleseven haha vsauce2

[@Ryumare]

Nice flash of the Parker Square over the imperfect square at 1:24

[@h4lo]

You're both right. There were two flashes, one at 1:24 (assuming we're taking the floor of the time) and another at 1:25

[@cumberbtcheswiththehats8209]

Ah, so that's what that is.

[@clarianken4223]

Caloom whats that?

[@JPO1618]

Check out the Parker Square video on this channel. It's a bit of a joke on Matt Parker and his imperfect Magic Square

[@andregon4366]

I was about to give a like but you have 1234 likes so I'll leave it at that.

[@medkitty]

"Because they're nerds!" Wise words from a wise man.

[@word6344]

I fell out of my bed laughing at that line

[@liaaaaaaaaaaaaaaaaaaaaaaav]

Yes exacly becuase they're nerds!

[@idjles]

Brady's entire goal with this video was to troll Matt.

[@rikwisselink-bijker]

Why not call one version that comes close 'the Grime Square'?

[@user-me7hx8zf9y]

729 likes... 27 squared...

[@PC_Simo]

@@rikwisselink-bijker True 😅👍🏻.

[@rosserobertolli]

A perfect squared square doesn't exist? Maybe you should let Matt Parker have a go at it! I don't think it will be perfect, but it will be at least something!

[@joaovitormatos8147]

Oh... I see what you are doing there...

[@cubethesquid3919]

I'm sure he'd use 2 pi in his 'proof'

[@utuber1789]

and Chuck Norris has not started working on the problem yet

[@PlaybyPlay225_2.0]

rosserobertolli a parker-squared parker square

[@thefamousarthur]

@@cubethesquid3919 PI, NOT TAU!!!!!!

[@-fitzy-3335]

OR DOES IT.... no it doesn't :p

[@tomasalvim1022]

No, it doesn't.

[@DekuStickGamer]

oh....

[@Xerxes1337]

Hey Vsauce, Michael here.

[@Liliou]

Haha! Savage James..

[@MarkWaner]

So cold "no"

[@YaStasDavydov]

*parker square joke*

[@Sagano96]

spotted at 1:25 :3

[@brushybrushyfan677]

Sagano96 1:24 for me. but still :D

[@tacticalkiller1]

Kurt Green best meme from Numberphile

[@maciejzwolinski2381]

Yep, went t post on the spot, you were first :)

[@BrotherAlpha]

As soon as he talked about reusing squares, I knew they had to mention the Parker Square.

[@superstarjonesbros]

I saw that Parker Square... senaky sneaky.

[@davecrupel2817]

superstarjonesbros i got a screenshot. Hehehehe

[@OrangeC7]

Who's Senaky Sneaky?

[@ariesunderground5936]

OrangeC7 Octotube!............. am I the only GDer here?

[@turkeytangogaming1341]

Senaky?

[@JorgetePanete]

sneaky*

[@jordantistetube]

I love that you can easily conceive certain objects in mathematics, like that 70x70 square, that are just forbidden to exist. "So disappointing that it doesn't exist!". If he was talking about a unicorn, it wouldn't have had the same meaning. A unicorn could potentially exist somewhere in the future. Saying "unicorns don't exist" is like saying that "t-rexes don't exist". They don't exist in our immediate reality. That 70x70 squared square is impossible now, in the future and past, everywhere and forever. Yet we're capable of discussing the properties and qualities of this fundamentally impossible object.

[@bscutajar]

jordantiste The fact that, unlike biology, chemistry or even physics, maths is always true whichever universe you live in is why people love maths.

[@Icenri]

I like so much how Dr. Grime makes any topic clear and understandable. We want more Grime!

[@warriorraisani425]

Yeah, i have same views..

[@stevenvanhulle7242]

00:40 James: Why have they chosen this as the logo for their Society? Brady: 'Cause they're nerds. Answer like a boss!

[@camilohiche4475]

That should have been the end of the video right there.

[@WontonTV]

I'm Flat mic drop and walk out of the room

[@12tone]

So, is there an explanation for why this seemingly unrelated geometry problem happens to share those properties with electrical circuits?

[@frankenshizzle]

ya

[@RiccardoPazzi]

I know this question is one year old but I wanted to answer anyway. The fact is that the sum of all the squares sides going top to bottom must be constant (equal to the bigger square side). It means that this quantity is the same even though it's split among different squares, this is the same kind of behavior you find in circuits but also many other physical objects, because ultimately it's about conservation of something and we know how much physics loves conservation :)

[@davictor24]

@@RiccardoPazzi great answer!

[@Ampheon181]

Because math is magical!

[@trequor]

Geo-metry. Geo is earth. Back when the subject was invented, the earth was the whole universe.

[@AtomicShrimp]

No cubed cubes - related to Fermat's Last Theorem?

[@captainsnake8515]

AtomicShrimp this should have way more likes

[@theranger8668]

@@captainsnake8515 Sure, but please explain what is Fermat's Last Theorum?

[@pizzatime7431]

@@theranger8668 i think it is a^x+b^x=c^x has no solutions if a,b,c,x>0 are integers and x>2

[@SuperYtc1]

It would only be ONE tiny part of Fermat’s last theorem relating to ONE tiny part of this mathematics. So no, not really, only a very small cross over.

[@pizzatime7431]

tiny part or not related still means related, and that was the question

[@minatogames3462]

"Cuz they are nerds!" Hahaha, this made my day

[@charonder]

James Grime came to my school a few weeks ago and when I told him I was going to be doing maths and physics at uni he said he didn't really like physics, so it's funny to see him talking about electrical circuits here

[@BMBOX94]

I love how passionate he gets and how happy it all makes him

[@KasabianFan44]

Are there any triangled triangles?

[@ricarleite]

Imperfect, yes. Triforce symbol.

[@stevethecatcouch6532]

Yes. One example is a 15, 20, 25 right triangle made of a 12, 16, 20 right triangle and a 9, 12, 15 right triangle.

[@aitor2623]

ricarleite But those are equally sized triangles

[@KasabianFan44]

Steve's Mathy Stuff I mean equilateral triangles...

[@aeriumsoft]

don't think so, there would always be a gap (but if you're joking that's fine lol)

[@millamulisha]

"Or does it!?...", "No, it doesn't". Perfect encapsulation of a maths person's ability to squash enthusiasm. Haha...

[@joshnoble07]

One of the most fascinating videos from the past little bit! I really enjoyed this.

[@martynasmalikenas1736]

Thanks for the upload, I really love videos with Dr. Grime!

[@furrane]

9:42 - "Or does it ?!" - "No it doesn't." Killed me there xD

[@harrysvensson2610]

9:46 "or does it?" 9:47 "no it doesn't ;("

[@coosoorlog]

that one second era of hope

[@Shit_I_Missed.]

Dr. Grimes set him up for that one, it was amazing. xD

[@Lightning_Lance]

Sure it does, it's the Grime Square.

[@pneumaniac14]

thanks for the second time stamp I was struggling to find the part where he says that

[@styleisaweapon]

It would be nice to see an episode about other math societies "logos." Many of them should be interesting.

[@biaroca]

"Cause they're nerds?"

[@mistertapman]

My favorite part haha

[@Arthur-qe8xc]

Well yeah, and that...

[@ffggddss]

This is largely a (really well done) synopsis of one of the early Mathematical Games columns by Martin Gardner, in Scientific American (from 1959?). The very first of those columns (actually, an article, which then led the magazine to give Mr. Gardner a monthly column), in the Dec. 1956 issue, was about hexaflexagons. Those were invented & investigated by another group of four students, one of whom was the very same Arthur Stone of the squared square story. The other 3 were Bryant Tuckerman, John Tukey, and Richard Feynman - yes, that's right - the famous, Nobel-laureate-to-be, physicist!

[@DavidKlausa]

Martin Gardner deserves credit for at least half of all youtube videos involving math.

[@g0mikese]

I really loved this one. I thought their solution methodology was really interesting with this problem.

[@davidsweeney111]

Of late I've been finding myself deleting emails from this channel because the stuff was way over my haed and not interesting, but I saw that it was this young man, so I watched, and boy was I rewarded, what a fantastic set of videos from this chap, he certainly knows how to hold attention and make a great video!

[@OwlRTA]

In the University of Waterloo, they named a side road "William Tutte Way" after Bill Tutte, and they even put the 33 by 32 squared rectangle on the sign, and mentioned the Squared Squares

[@Deveron4]

Aw, I was hoping for more Parker Squares... 😂😂😂

[@kalebbruwer]

Damodara Kovie 1:25

[@Nemilime]

Very interesting video and James is great as usual.

[@drojf]

finally I can use my electrical engineering degree for something even more useless than usual /s

[@spur3]

Heh, "techniquest".

[@BertGrink]

John Rogers I suppose that nowadays you'll just feed the numbers into a computer, right?

[@notar2123]

Seriously? I thought electrical engineering was the most useful of all fields of engineering.

[@whatisthis2809]

"/s" Html broken?

[@fortidogi8620]

@@whatisthis2809 its a tone indicator. cuz its hard to tell sarcasm in text. so /sarcasm to be clear

[@BEP0]

Lol, the Parker square at 1:25!

[@ALZlper]

If you use the same size twice it is called a squared parker square

[@RallyRat]

To really drive the electrical analogue home: If you imagine the rectangle ( 4:08 ) is built of a resistive material with the top and bottom edges connected to a battery with voltage equal to the height, then you are setting up a uniform unit electrical field with uniform current flowing across the whole area from top to bottom. Since there is no horizontal electric field, you can place wires along any horizontal and make any vertical cuts without affecting any current flows. Any square you cut out of the area will have the same resistance, no matter its size. With this in mind and without any change in electrical flow, a cut can be made at each vertical line, each horizontal line can have a wire with zero resistance laid over it, and each square can then be replaced with a unit resistor. Now you have exactly the same resistor network with the associated currents and voltages.

[@complexobjects]

This problem is kindof similar to the 'ways to overlap circles' problem in another numberphile video. They place a certain criterion on what is an allowed form and try to find the different forms that exist. And, it's tricky to come up with a way a searching through the possibilities.

[@joshs.6426]

I will now go on my quest to find the circled circle, wish me luck!

[@mversantvoort]

This is genius, it's amazing how they linked a maths problem to electrical circuits.

[@ThomasBaxter]

This one blew my mind. Such fun.

[@ejesbd]

Extra thumbs up for the link to the Parker Square video at the end!

[@andrewkovnat]

How about a Squared Squared Square? Can you create a square out of these squares, without using more than one of the same square? You also can't have the squared squares being the same size as well. Well, I guess this would just be a bigger Squared square, then. :/

[@TheReacTT]

Matt Parker could definitely fit those squares together!

[@MLDeS100]

That's a pretty great way to solve it, awesome.

[@vojtechjanku2534]

0:40 "Why have they picked this as their logo for their society?" "Cause they're nerds!" Oh, Brady :D

[@AlucardNoir]

Imperfect squares? he surely meant Parker Squares.

[@stevenvanhulle7242]

Squared squares (which are geometric constructions) are completely different from Parker squares (which are just matrices). A perfect squared square doesn't have duplicate subsquares, while imperfect squared squares do.

[@AlucardNoir]

That joke that when over your head didn't it?

[@stevenvanhulle7242]

I see what you did there. But you must be joking if you call it a joke.

[@whatisthis2809]

@@stevenvanhulle7242 it's a joke whether you get it or not

[@stevenvanhulle7242]

@@whatisthis2809 Don't worry, I got it alright. I just wondered if a joke is still funny if you heard it 200 000 times...

[@BrokebackBob]

Next useless problem: Make a square from circles.

[@OrangeC7]

Circling the square?

[@xavierstanton8146]

Oh wait...

[@fahrenheit2101]

Haha nice.

[@owenpeter3]

This was seen in Scientific American in Gardner's column in the 1950s. Using the technique he showed I designed a garden path several metres long and two metres wide all squares being different. Never got around to making it.

[@jroemling]

1:24, you are killing me! 😂😂😂 Love Dr. Grime, more of him, please!

[@hookerWithATool]

*parker square intensifies*

[@joryjones6808]

So now we finally found a useful application of electric engineering that can be used to solve real world pure math problems.

[@yellow5876]

Such an inspiring topic

[@NatCo-Supremacist]

"I'm not even sure what it is, but I can tell you what it is"

[@philmertens2673]

Does the fact that there are no cubed cubes relate to Fermat's Last Theorem somehow?

[@CanadaJarod]

Phil Mertens My initial response was "yes" based on the content of the video alone this seems almost implied. However I think the issue is to do with the rate of size increase for each successive cube making it much harder to fit them together geometrically. I'm doubtful that you could even build a rectangular prism out of cubes, though I'd like to be proven wrong on this since there's more to be learned from that

[@frogkabobs]

I don't really think so. Here is the Wikipedia page explaining why there can be no cubed cube: en.wikipedia.org/wiki/Squaring_the_square#Cubing_the_cube. However, the proof does use infinite descent, which was the same method that was used to prove Fermat's Last Theorem for certain powers.

[@UpstairsPancake]

Fermat's Last Theorem shows that there are no natural numbers x,y,z such that x^3 + y^3 = z^3 which does mean that you can't find two cubes whose volumes add together to give you the volume of a third cube, but that's all.

[@chriswilson1853]

I was about to ask that

[@morpheus6749]

No.

[@TheMiggy9]

1:25 Parker square!

[@fafnir242]

That was really cool!

[@phoenizboiisawesome]

That little Parker square flash got me

[@kwak0]

Hey Vcause, Michal here

[@vodkacannon]

This is like the most creative solution to a problem ever

[@moideenkuttymc4610]

Moideenktt

[@acer2310]

James Grime is the best explainer.

[@davidwilkie9551]

That's impressive, well worth some pride in achievement.

[@Lightn0x]

James posting not one.. but TWO videos? Is this real life?

[@bomberdan]

Lightn0x Queen

[@datenegassie]

EDIT: except for that one frame

[@markmayonnaise1163]

*/>

[@DominikRoszkowski]

Thanks for saving the world with the ending tag.

[@jonathanwalther]

< I would like to add

[@jacksonpercy8044]

2 frames with a single frame between them*

[@want-diversecontent3887]

Dominik Roszkowski Heheh…

[@NimrodTargaryen]

Lovely, thanks

[@Pygmygerbil88]

fantastic.

[@lelouchyagami703]

*Insert Parker square joke here*

[@rpan9196]

9:46 Vsauce?

[@WombatSlug]

Interesting how Kirchoff's Law crops up in the most unique locations. It's one part that I've had the hardest time with when it comes to electrical theory.

[@LanceThumping]

I wish this had more details on why we know there is only 1 smallest squared square and how we know it's the smallest.

[@marcinukaszyk4698]

Or dose it? No it doesn't. I'm so disappointed :(

[@TheRedKorsar]

Hello, Numberphile. Some day, i have a question. And i cant find it out. Rubiks Cube. It has many of possible combinations. Them all can be solved by 20, and less turns. But question is: Is there a combination, that can solve cube from any combination? I'm a programmer, an i have wrote a programm, that count iterations of algorithm to get to start position. And i have found Easy one. RFL'B only 4 turns, but it takes 1680 turns to get back.

[@AdamSpanel]

Yup, there is. It is called "Devil's algorithm" (analogy to the God's algorithm). There has been done some research on it, you can google it up. I don't think a specific algorithm has been found though (but I think it has been proven that such algorithm exists)

[@TheRedKorsar]

Algorithm is really possible. You can solve each combination, and write all moves, it will be huge algorithm, but it exists. But what the smallest one?.. For now, i'm trying to get it on simple twisty puzzle. Just get 6 circles, place them in grid 3*2, and it give you simple puzzle. It has only 360 possible combinations (!6 / 2) and Devil's algorithm, i think has 6 moves... But it not tested. I didn't write test for all algs program. It is next step.

[@ABaumstumpf]

You mean a sequence that when all steps are taken solves all startingpositions? Nope. But it is easy to make a sequence that, at one point or another, solves any starting position - but you would have to terminate it at the right step.

[@TheRedKorsar]

It is real. And prove is simple. You have decent amount of combinations. 43*10^19, i guess. So you can solve each combination in about 10 moves(average) So Devil's algorithm will take 43*10^20 moves. One big algorithm, witch will go from one combination to another. And, because of it cycles all possible combinations, it will solve cube in 100% But length, of this algorithm is realy realy big :D

[@AdamSpanel]

From my understanding, devil's algorithm is the shortest sequence of moves which will get to all the combinations of the cube if repeated infinitely.

[@sarmadali7674]

Just Beautiful

[@pinoficara]

I don't understand the thumbs down. This was great!

[@coosoorlog]

You can't make a cubed cube. Can you make a tesseracted tesseract?

[@zhufa07]

There cannot be a perfect cubed cube in dimension 3 or higher. We know that there is no perfect cubed cube. Suppose that there exist a perfect tesseracted tesseract, then each of its "sides", which are cubes, must also be perfectly cubed, which leads to a contradiction.

[@coosoorlog]

yes of course. that makes perfect sense :)

[@azzteke]

There a no "Kirkhoff rules", but Kirchhoff rules!

[@DaniErik]

Numberphile is basically a series on mispronouncing German names.

[@TaiFerret]

Isn't "Kirkhoff" the best English approximation though? I'm pretty sure you're not supposed to pronounce the "ch" like the English "ch", right?

[@aeriumsoft]

ich liebe kartoffelein

[@Yotanido]

TaiFerret: v=ohh2NZKhskc It was ridiculously hard to find a video that even comes close to the correct pronunciation...

[@xcheesyxbaconx]

I've always heard it pronounced like they pronounced it in this video.

[@mastheadmike]

Subliminal Parker Square reference was awesome!

[@spykey312]

I like the little flicker of the parker square over the imperfect square 😂😂

[@wazul7676]

Or does it? :)

[@TSTypeR]

Or does it? 😏........

[@joshyoung1440]

James: what's the smallest squared square? Me, an intellectual: one

[@listenerofrealrap]

I saw that sum of squares from 1 all the way to 24 on a John Baez video about string theory. Funny seeing it here as well, and it's a real shame that the squares can't be arranged into a squared square (makes for a nice pyramid, though).

[@bodenharris1484]

Who’s here from vsause

[@navetal]

I mean, a 1x1 suqre is technically a square made of squares and it's smaller, right? I know this is the boring solution, but it's still a solution.

[@ragnkja]

Nave Tal Unity is considered too trivial for puzzles like these.

[@navetal]

I know, I know...

[@gojoubabee]

Nave Tal Well, if you count a 1x1 square, then you could also count a 2x2 square, and a 3x3 square, etc. That's infinite squares, but all are trivial solutions.

[@Shit_I_Missed.]

I'd say it's not a solution based on the language of the problem. one square is not a plurality

[@prelude9954]

they want integers squares

[@mac1991seth]

Imperfect square... where have I heard this before?

[@beamjohn9753]

Wow that was awesome

[@sansamman4619]

OMG JAMES GRIME, the legend of Numberphile is back :D James is the best mathematician i think he is better than Euler in maths

[@GodsOfMW2]

perhaps a little too much there

[@Luisitococinero]

He is better than Albert Einstein in maths. And Albert Einstein has been considered a genius.

[@stuartofblyth]

Kirchhoff (4:14) is pronounced "Keer'-choff" with the ch as in loch and Bach. Just sayin'.

[@azzteke]

No, wrong. "Keerch-hoff". There are two types of "ch", by the way. This ch is NOT the scotch one.

[@stevenvanhulle7242]

Actually, the "i" in Kirchhoff has to be pronounced like the "i" in "bit".

[@nab-rk4ob]

That's fascinating.

[@katiekawaii]

That is so cool.

[@Djorgal]

There is none that uses fewer than 21 squares? Well yes there is, I can make a square made of only one square with none used twice.

[@numberphile]

trivial

[@Djorgal]

Indeed. Trivial answers are the best ones! By the way, you said that there is no square made of the first 24 squares, but is there a sqare made of consecutive squares? Not necessarily starting from 1.

[@Yerrik]

Are there solutions that can be constructed out of rectangles, and still be solved with Kirchhoff's Law? Or is there something special about the squares (other than that they are nice, and possibly unique)? I could imagine applying this method to a bunch of problems that rely on graph theory, but this would have to be generalizable to rectangles.

[@saikatazad5631]

just perfect

[@Somebodyelse141]

"or does it" "No it doesn't" his sudden seriousness lol

[@prestont1007]

the connection between the squared square and circuits is rather interesting

[@Rmac524]

YES James Grime

[@bowlchamps37]

1:44 I love how Wilkinson, the Senior Wrangler of 1939, is right in the middle of the 3 student´s triangle.

[@nomekop777]

This man has never worked a day in his life because he loves what he does so much

[@lochies5407]

Ooh, shiny new Numberphile video. \o/

[@metrogman2409]

I love the end about 70^2. Wow.

[@safyan9442]

There's something spooky inside that's making him smile

[@00BillyTorontoBill]

More ! please on everything.

[@yaseen157]

I like the cheeky editing at 1:24