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 • 556

  • Orville Reid
    Orville Reid Day ago +1

    Really cool

  • D Hoffman
    D Hoffman Day ago

    So in other words you cheated.

  • しらいさん
    しらいさん Day ago


  • Der_RX
    Der_RX Day ago

    Cute robot :)

  • Saki630
    Saki630 2 days ago

    best animation of the year

  • Dan
    Dan 2 days 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 2 days ago

    Everything I knew was a lie

  • Harshul Pandav
    Harshul Pandav 3 days ago

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

  • DerSibbe
    DerSibbe 4 days 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 4 days 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 6 days 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 8 days ago

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

  • Adrian Jonathan
    Adrian Jonathan 9 days ago +1

    No international Pie Day special this year ? 😔😔

  • clickaccept
    clickaccept 9 days ago

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

  • John Runyon
    John Runyon 9 days 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.

  • Cleaner Clout
    Cleaner Clout 9 days ago

    You must do a video in remembrance of Stephen Hawking

    • Gooscar
      Gooscar 8 days ago

      He did, on the Sixty Symbols channel

  • 76forever
    76forever 9 days ago +1

    Happy π day!!!

  • Jake Weiß Music Creator

    It pi day

  • gajbooks
    gajbooks 9 days ago

    I prefer being able to walk through a notecard.

  • ifroad33
    ifroad33 10 days ago +1

    Where's the obligatory video on Pi day??

  • Mind Blow
    Mind Blow 10 days ago +3

    *PI DAY!!!!!*

  • Diamond Hype
    Diamond Hype 10 days ago +1

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

  • Rjinxil
    Rjinxil 11 days 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 11 days 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...)

  • Mark Hall
    Mark Hall 11 days ago

    Silly, annoying, unnecessary animations and noises

  • John Brewer
    John Brewer 12 days 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 12 days ago

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

  • Sonny Song
    Sonny Song 12 days ago

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

  • Samier
    Samier 12 days ago

    dont sit down cuz i moved ya chair

  • XxXDeadlykingdxXxX
    XxXDeadlykingdxXxX 12 days ago +1

    i think the animations are annoying and not needed

  • Zhong Ping
    Zhong Ping 13 days ago

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

  • Kai Na
    Kai Na 13 days ago

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

  • Lakshay Modi
    Lakshay Modi 13 days ago +1

    Love those animations

  • Zed
    Zed 13 days 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 13 days ago

    Very cool :)

  • Luca Masters
    Luca Masters 13 days ago

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

  • Brandon Ginn
    Brandon Ginn 13 days ago


  • Quinson Hon
    Quinson Hon 13 days ago

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

  • Omega742000
    Omega742000 13 days ago

    130 People Hate this Video, citing Witchcraft 😊

  • Oslo Winslow
    Oslo Winslow 13 days ago

    Video not available! - Why?

  • upalonyTony
    upalonyTony 13 days ago

    earth is flat

  • 6beat
    6beat 13 days ago

    This is awesome!

  • Sirwan Qutbi
    Sirwan Qutbi 13 days ago

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

  • ualgun
    ualgun 13 days 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 14 days ago

    A coaster isn't a peg

  • David Devine
    David Devine 14 days 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 14 days ago


  • Twistr
    Twistr 14 days ago

    Beautiful. ^_^

  • saintpsu
    saintpsu 14 days ago


  • Sahaj Amatya
    Sahaj Amatya 14 days ago

    Tadashi needs a patreon page

  • Michael A
    Michael A 14 days ago


  • BigVtheVanity
    BigVtheVanity 14 days ago


  • Eric Williams
    Eric Williams 14 days 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 14 days ago

    Beautiful. Love your videos.

  • The Luigineer
    The Luigineer 14 days 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 14 days 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 Turles
    Lord Turles 14 days ago

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

  • Georgia E
    Georgia E 14 days ago

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

  • Farpas MasterFarpador
    Farpas MasterFarpador 14 days ago

    What about a parker square hole?

  • Sunny Macwan
    Sunny Macwan 14 days ago

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

  • eliotgillum
    eliotgillum 14 days ago

    Tadashi never disappoints

  • Scott Lutz
    Scott Lutz 14 days ago


  • Genghis Khan
    Genghis Khan 15 days 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 15 days 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 15 days ago

    My brain hurts.

  • Vamp Hunter Z
    Vamp Hunter Z 15 days ago

    The knowledge is out of this world 😃

  • Tom T.
    Tom T. 15 days ago

    Too much beeping.

  • trefod
    trefod 15 days ago

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

  • BassmasterBling
    BassmasterBling 16 days ago

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

  • blazebluebass
    blazebluebass 16 days ago

    Is that Grey?

  • ZipplyZane
    ZipplyZane 16 days ago

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

  • Matt Hollenberg
    Matt Hollenberg 16 days ago

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

  • Eliseo Palit-ang
    Eliseo Palit-ang 16 days ago

    Tadashi is the best.

  • atimholt
    atimholt 16 days 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 16 days 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!

  • Hyrum Diesen
    Hyrum Diesen 16 days 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?

  • Sina Madani
    Sina Madani 16 days ago +1

    Tadashi's discoveries are the most profound on this channel because they are physical and easily demonstrable with household items rather than abstract. Great stuff!

  • Rose Davidson
    Rose Davidson 16 days ago

    Really interesting!

  • 0 1
    0 1 16 days ago

    Tadashi's toys vs Michael's toys

  • Ralph Dratman
    Ralph Dratman 16 days ago

    I like the content but I do not like the noisy animation at the beginning and end.

  • JYT
    JYT 16 days ago

    ouch my ears
    that robot

  • Frydon97
    Frydon97 16 days ago

    Would something like this work in higher dimensions as well?

  • Lemon Knight
    Lemon Knight 16 days ago +1

    Now try it with a sheet of metal.

  • Me and I
    Me and I 16 days ago

    "Tadashi's Toys Corner". A most enjoyable part of Hello Numberphile.

  • panameadeplm
    panameadeplm 16 days ago

    stop it with the awful animations please

  • Irfan Irfan
    Irfan Irfan 17 days ago

    aaaa aaaa aaaa aaaa wwwhhhatt

  • Kevin
    Kevin 17 days ago

    Doesn’t count. Paper has Tares

  • Haley Carrera
    Haley Carrera 17 days ago

    I love his voice !

  • ͛
    ͛ 17 days ago

    *_i love you senpai_*

  • Connor Lennox [AJ Says]
    Connor Lennox [AJ Says] 17 days ago +1

    If they made boring stuff like that this fascinating in school I would have payed attention

  • Korenn
    Korenn 17 days ago

    My two year old puts a round peg into a square hole by jamming the peg in the toy until it's stuck, then picking up the entire contraption, and bashing it against varying surfaces until it either fits or the toy breaks. We try to intervene before our house does.

  • invisible ink
    invisible ink 17 days ago

    that's numberwang

  • James Bond
    James Bond 17 days ago


  • Markle2k
    Markle2k 17 days ago

    Tadashi never fails to deliver.

  • reauddin kazi
    reauddin kazi 17 days ago

    wow! A numberphile video featuring Grey!

  • fredreick weaver
    fredreick weaver 17 days ago


  • Luke R.
    Luke R. 17 days ago

    Eloquent and brilliant. What a man.

  • nab 6215
    nab 6215 17 days ago

    I am so glad you explained such a wonderfully mind-expanding fact in such a simple way.

  • Rex The Thoughtful T-Rex
    Rex The Thoughtful T-Rex 17 days ago +1

    Did Tadashi just try to circle game us in the thumbnail?

  • Deconverted Man
    Deconverted Man 17 days ago

    I like this guy!