Round Peg in a Square Hole - Numberphile

  • Published on Mar 5, 2018
  • Featuring Tadashi Tokieda - more Tadashi videos at:
    More links & stuff in full description below ↓↓↓
    Tadashi Tokieda is a Professor of Mathematics at Stanford University (though this was filmed when he was at Cambridge, in the UK).
    Animation by Pete McPartlan.
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  • Science & TechnologyScience & Technology

Comments • 586

  • Edward Lau
    Edward Lau Month ago

    Reminds me of Miegakure the 4-D game.

  • Daniel olsen
    Daniel olsen Month ago

    If i try'd this trick drunk, i think the men in the white coats would come knocking lol

  • John Walker
    John Walker 3 months ago

    I folded it twice more, and now I can fit a dinner plate through it.

  • Red Ace
    Red Ace 4 months ago

    Obviously you cheated by changing the angles. smh

  • eric altenbach
    eric altenbach 4 months ago

    Not nearly as interesting as i thought it would be. Its paper. You warped the square. It definitely was not a square when you fit it through.

  • KP guitarzan
    KP guitarzan 5 months ago

    I can actually use this information to make military, and fighting experts look amateur...thank you for more knowledge. (bows in humble respect)

  • vaibhav jain
    vaibhav jain 5 months ago


  • MachineGun
    MachineGun 5 months ago

    All it takes for me to click on a video is Tadashi in the the thumbnail

  • Ro Man
    Ro Man 6 months ago

    The most obvious thing ever. I'm surprised people have such lousy spatial perception

  • Lamawalrus
    Lamawalrus 6 months ago

    I don't mind the robot noises and similar, but they are slightly too loud for a Tadashi vid in this last one, in my opinion. Just reducing their volume and/or how much they stand out would be sufficient

  • Neapolis26
    Neapolis26 7 months ago

    Tadashi is my hero!

  • Lamawalrus
    Lamawalrus 7 months ago

    I only occasionally watch Numberphile, but I always watch Tadashi (no offense meant to anyone)

  • Szabolcs Binkl
    Szabolcs Binkl 8 months ago

    Simple primary school maths. There is no genius or discovery in it.

  • allan de medeiros martins

    Fantastic! %-)

  • Jimmy Catalina
    Jimmy Catalina 8 months ago

    Those that can, do. Those that can't, teach.

  • vanhouten64
    vanhouten64 8 months ago

    Besides all that, that's a pretty sharp origami hat!

  • fish butt
    fish butt 8 months ago

    CGP grey fails us yet again

  • Maxim Marchal
    Maxim Marchal 8 months ago

    Simple yet powerful. Still can't wrap my head around it

  • Folko
    Folko 8 months ago

    I only show up for Tadashi videos

  • Tuc
    Tuc 8 months ago +1

    Take your shoes off!!

  • AlyoshaK
    AlyoshaK 8 months ago

    So cool. I can't wait to show my grandson!

  • Edward Camilo Rodriguez

    Cuales son las medidas del cuadrado y el diámetro o radio del circulo????

  • oldcowbb
    oldcowbb 8 months ago

    TADASHI makes topology super fun

  • Daniel Harris
    Daniel Harris 8 months ago

    That is not immediately apparent.

  • Little Lion
    Little Lion 8 months ago

    *Now show how it would work in 3D/4D!*

    • Irek Jakobik
      Irek Jakobik 4 months ago

      It's easy. You just fold a 3d cube in 4th dimension until its volume equals 8 volumes of the original cube, and then you pass the 3d sphere, which diameter is slightly bigger than the side of the original cube, through that new cube. Voilà! Your puzzled audience sees that you can put a bigger sphere into the smaller cube!

  • jose casillas
    jose casillas 8 months ago

    basically, all I got was, in order to make the gap bigger in 2 dimensions, you need to add extra space in that dimension. But you can't just create space. So other parts of the paper must get smaller OR size must change in a higher dimension. Is this right?

  • I leave mean comments
    I leave mean comments 8 months ago

    Aside from the handsome Russian guy... this guy is my favorite.

  • Orville Reid
    Orville Reid 8 months ago +1

    Really cool

  • D Hoffman
    D Hoffman 8 months ago

    So in other words you cheated.

  • しらいさん
    しらいさん 8 months ago


  • Galenus
    Galenus 8 months ago

    Cute robot :)

  • Saki630
    Saki630 8 months ago

    best animation of the year

  • Dan
    Dan 8 months ago

    I have no problem with Tadashi's demonstration or explanation, but I do have a bit of criticism for Brady's title choice, because a 2d coaster, which is relevant to this demonstration, is not the same as a 3D cylinder that comes to mind in a round peg scenario.

  • Damstraight68
    Damstraight68 8 months ago

    Everything I knew was a lie

  • Harshul Pandav
    Harshul Pandav 8 months ago

    Round Peg in a It's-No-longer-a-Square hole.

  • DerSibbe
    DerSibbe 8 months ago

    *we just push move it a little along the 4th Dimension, push it over and move it back along the 4th Dimension*

  • gorillaau
    gorillaau 8 months ago

    A round peg in a square hole may not fit, but a square peg will mostly go into a round hole... just hit it hard enough with a big enough hammer.

  • C Lopez
    C Lopez 9 months ago

    Basic application of pythagorean theorem, I think a kid could figure that out though if you can fold the square why not just fold the circle? Tadashi gets paid to do this?

  • Gregory Weis
    Gregory Weis 9 months ago

    I doubt I could ever have figured this out in my head, but having the paper in front of me...maybe then. (Nah.)

  • pyre pro
    pyre pro 9 months ago +1

    No international Pie Day special this year ? 😔😔

  • clickaccept
    clickaccept 9 months ago

    Really? You ran out of content and brought us this? Oh dear.

  • John Runyon
    John Runyon 9 months ago

    But it's no longer a square hole - it's a rectangular hole. And also, it's not a round peg (implying height is somewhat larger than diameter) - it's a round disk. Both of those things are important.

  • Philip Mitreski
    Philip Mitreski 9 months ago

    You must do a video in remembrance of Stephen Hawking

    • Gooscar
      Gooscar 9 months ago

      He did, on the Sixty Symbols channel

  • 76forever
    76forever 9 months ago +1

    Happy π day!!!

  • Skettles
    Skettles 9 months ago

    It pi day

  • gajbooks
    gajbooks 9 months ago

    I prefer being able to walk through a notecard.

  • ifroad33
    ifroad33 9 months ago +1

    Where's the obligatory video on Pi day??

  • Mind Blow
    Mind Blow 9 months ago +2

    *PI DAY!!!!!*

  • gblawrence03
    gblawrence03 9 months ago +1

    Wait what I thought I was already subscribed to this channel? Oh well. Fixed that now!

  • Rjinxil
    Rjinxil 9 months ago

    there was a series of some guy about large numbers where he goes from addition over multiplication to up arrow notation etc. it was i think a 20 part series but i can not find it anymore. can anyone help me? thanks in advance

  • sepp31415
    sepp31415 9 months ago

    I knew this as a magician's "trick", but not the mathematical background/explanation. This now raised a question for me: Is the concept shown also valid for the 3rd dimension (or the 4th or 5th or nth...). A simple yes/no/not proven yet ist enough for me (I probably wouldn't understand the explanation anyway...)

  • John Brewer
    John Brewer 9 months ago

    Hey guys do the math on this one. I'll give you the questions and the setup (mixed). How many people would you need and/or how big of a city would you need (spread out in a large city like they're going about their business during the day to (if possible) to see a regular bic lighter on a satellite picture of said city during the night. Mind you this is a perfect situation. No other artificial light pollution. On top of that in a real-world situation I wonder if that would be possible with emergency services and things like that still running of course.

  • vacri54
    vacri54 9 months ago

    I love the ambient 3rd dimension. I spend all my time there.

  • Sonny Song
    Sonny Song 9 months ago

    That's so cool! Thanks for the new trick that I can show my friends!

  • Samier
    Samier 9 months ago

    dont sit down cuz i moved ya chair

  • XxXDeadlykingdxXxX
    XxXDeadlykingdxXxX 9 months ago +1

    i think the animations are annoying and not needed

  • Zhong Ping
    Zhong Ping 9 months ago

    Would this be how the TARDIS is bigger on the inside by folding 4th dimensional space?

  • Kai Na
    Kai Na 9 months ago

    - paper unfolds and has hole smaller than the circle -
    me: WITCHCRAFT!!!! *falls off chair*

  • Lakshay Modi
    Lakshay Modi 9 months ago +1

    Love those animations

  • Zed
    Zed 9 months ago

    What a wonderful accent. Light Japanese, mixed with something else that I can't quite identify - will gladly listen to for hours.

  • Ian M
    Ian M 9 months ago

    Very cool :)

  • Luca Masters
    Luca Masters 9 months ago

    Seems it's equivalent to folding the disk 90 degrees.

  • Brandon Ginn
    Brandon Ginn 9 months ago


  • Quinson Hon
    Quinson Hon 9 months ago

    I wonder if this concept can be used to understand things in the 4th dimension....

  • Omega742000
    Omega742000 9 months ago

    130 People Hate this Video, citing Witchcraft 😊

  • upalonyTony
    upalonyTony 9 months ago

    earth is flat

  • 6beat
    6beat 9 months ago

    This is awesome!

  • Sirwan Qutbi
    Sirwan Qutbi 9 months ago

    It makes sense, but you still tore a bit of the paper.

  • ualgun
    ualgun 9 months ago +1

    First ever numberphile video where the answer just came to me before having it explained in the video. The dopamine rush is immense you guys

  • John Faulkner
    John Faulkner 9 months ago

    A coaster isn't a peg

  • David Devine
    David Devine 9 months ago

    In the future, I would suggest that instead of panning up to the creator while they're doing the trick, that you dolly back or zoom out so that it is clear that you're not simply replacing one piece of paper with another while the desk is out of view.

  • Michael Jørgensen
    Michael Jørgensen 9 months ago


  • Twistr
    Twistr 9 months ago

    Beautiful. ^_^

  • saintpsu
    saintpsu 9 months ago


  • Sahaj Amatya
    Sahaj Amatya 9 months ago

    Tadashi needs a patreon page

  • Michael A
    Michael A 9 months ago


  • BigVtheVanity
    BigVtheVanity 9 months ago


  • Eric Williams
    Eric Williams 9 months ago

    Every time I see a new Tadashi video I get giddy. This did not disappoint. Thank you for continuing to share the wonder of mathematics with the world!

  • Cesar Perez-Cardenas
    Cesar Perez-Cardenas 9 months ago

    Beautiful. Love your videos.

  • Somniad
    Somniad 9 months ago

    Does this extend to fourth-dimensional space, then? Could a cubic cavity be manipulated to accomodate extra volume? My brain has trouble figuring out exactly what that means, but I'm pretty sure it would work

  • Thales Schuster
    Thales Schuster 9 months ago

    Insane that this is actually mind blowing for some people... Indeed its cool but this should be normal for an educated human being

  • Lord Turles97
    Lord Turles97 9 months ago

    ..... *Flux Capacitor*
    Where's my shiny badge?

  • Soft4Namjin
    Soft4Namjin 9 months ago

    🤤🤤🤤what how?????I still don't understand. Wait let me get some paper

  • Farpas MasterFarpador
    Farpas MasterFarpador 9 months ago

    What about a parker square hole?

  • Sunny Macwan
    Sunny Macwan 9 months ago

    There was Takeshi's castle and now there are Tadashi's toys..

  • eliotgillum
    eliotgillum 9 months ago

    Tadashi never disappoints

  • Scott Lutz
    Scott Lutz 9 months ago


  • Genghis Khan
    Genghis Khan 9 months ago

    there is something oddly satisfying in that ending animation of the robot inserting the round peg in the square hole

  • Sergio Lennon
    Sergio Lennon 9 months ago

    "This little journey that you take into the extra degree of freedom gives you this wonderful magic."
    Awesome choice of words. Now this man is passionate about what he does.

  • Soralella71
    Soralella71 9 months ago

    My brain hurts.

  • Vamp Hunter Z
    Vamp Hunter Z 9 months ago

    The knowledge is out of this world 😃

  • Tom T.
    Tom T. 9 months ago

    Too much beeping.

  • trefod
    trefod 9 months ago

    What's with the silly animations? Tadashi is so interesting that the animations take away from the experience!

  • BassmasterBling
    BassmasterBling 9 months ago

    Maybe we can pay off the national debt using this method.

  • blazebluebass
    blazebluebass 9 months ago

    Is that Grey?

  • ZipplyZane
    ZipplyZane 9 months ago

    It's essentially like having a loop of string that you pull flat out to get something through.

  • Matt Hollenberg
    Matt Hollenberg 9 months ago

    It’s nice to see CGP Grey showing up in your animation here ;)

  • atimholt
    atimholt 9 months ago

    I had a thought: if you tug on the opposite corners of an n-dimensional cube, where its 1-d edges are rigid and their meeting points are flexible, you will be able to pull the opposite corners apart by n units (× the side length).
    Now I’m wondering if you can pull the corners of a teseract away from each-other if the 2-dimensional edges are rigid. I’m thinking no, but can you increase the dimensions to a point where you can?
    I’m still thinking no.

  • Brian Pawlik
    Brian Pawlik 9 months ago

    Thanks for sharing! This is fascinating! Now, what would this look like in 3 and 4 dimensions, instead of just 2 and 3??THAT would be neat!

  • Tommy Dies
    Tommy Dies 9 months ago

    What does this mean if we apply it from 3 to 4 dimensions? Could I take a box, fold it in the 4th dimension, and then fit a larger sphere inside it?