A Mathematical Fable - Numberphile

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  • Опубліковано 12 гру 2024

КОМЕНТАРІ • 687

  • @darkosimonovic2896
    @darkosimonovic2896 9 років тому +284

    On the 4th day the king returs and says that the blob is actually a fractal.

    • @gavinjenkins899
      @gavinjenkins899 8 років тому +66

      +Darko Simonovic Dude needs to fire that surveyor.

    • @RobbyBoy167
      @RobbyBoy167 8 років тому +6

      The funny thing is if you increase the length (along a side perpendicular to the triangle) of one of the blobs then a^2 + b^2=c^2 doesn't work for their areas anymore. This idea is only considering the increase along the blob side that is parallel to the triangle sides but not the perpendicular one. At perpendicular expansion the areas In my opinion doesn't fit the Pythagorean blob theorem anymore. It will only work if the blobs area always respects Length=Width constraint.

    • @BagelBrain
      @BagelBrain 7 років тому +4

      What kind of fractal?
      Some fractals have a finite area, others don't, I believe.

    • @globalincident694
      @globalincident694 7 років тому +5

      2d fractals usually (but not always) have infinite perimeter, but they only ever have finite area. A 3d fractal usually (but again, not always) has infinite surface area, but only ever has finite volume. And so on for all dimensions.

    • @alexwang982
      @alexwang982 5 років тому +1

      It’s because of fractal dimension

  • @Zeturic
    @Zeturic 10 років тому +751

    I think the bigger question is how the King ended up with land that forms a perfect right triangle and three perfectly similar shapes.

    • @darkmage07070777
      @darkmage07070777 10 років тому +182

      Obviously, his previous surveyor (may his soul rest in peace) was far more competent then the moron who can't tell the difference between a square and a non-quadrilateral blob who replaced him.

    • @HisCarlnessI
      @HisCarlnessI 10 років тому +103

      Politics man, politics.

    • @JorgetePanete
      @JorgetePanete 7 років тому +7

      darkmage07070777 than*

    • @Lightning_Lance
      @Lightning_Lance 6 років тому +19

      The perfect right triangle is unlikely but possible. First, a straight road is built. Then they build another straight road that intersects it such that the point where the roads meet forms a + sign. Then they build another straight road that connects two different parts of that same road. Then someone claims the land in between those roads. It could happen, though roads are normally not perfectly straight: they're made to fit the landscape.
      The other three shapes are much less likely of course.

    • @tonaxysam
      @tonaxysam 4 роки тому +1

      Maybe his surveor gave him wrong the informacion

  • @ShiroKage009
    @ShiroKage009 10 років тому +354

    That surveyor is crap.

  • @OmegaRainbow
    @OmegaRainbow 10 років тому +47

    Counsellor: "There you are..."
    King: _"Where am I?!?"_
    lol, *I love this king* XD
    Story telling and the animation are excellent, thanks for making this!

  • @ToastyBoy17
    @ToastyBoy17 10 років тому +83

    This was very amusing. I loved it. The narration was simply fantastic, I couldn't stop smiling and giggling. Not only that, but I learned different uses for the Pythagorean Theorem.

  • @allyourcode
    @allyourcode 9 років тому +301

    The king needs to chill out. Counselor's got the situation on lock down.

  • @numberphile
    @numberphile  10 років тому +73

    There is a Numberphile2 channel you can subscribe to if you are REALLY keen on our stuff!!! This will be extras and stuff that didn't fit here!
    ua-cam.com/channels/yp1gCHZJU_fGWFf2rtMkCg.html

    • @stachestar
      @stachestar 9 років тому +2

      This is great. Majestic. YES.

    • @carlahelga6882
      @carlahelga6882 8 років тому

      this man is so amazing:) i love his courage and he looks and sounds so friendly

    • @thefullestcircle
      @thefullestcircle 7 років тому

      product placement

  • @Travmann777
    @Travmann777 10 років тому +79

    This guy's voice is greeeeaaat

  • @andrewhall6342
    @andrewhall6342 9 років тому +130

    Spoiler Alert: The King says 'Ah'...

  • @Xalnop
    @Xalnop 10 років тому +114

    This video was really fun to watch. The animator did a great job :)
    I hope you make more videos like this.

    • @numberphile
      @numberphile  10 років тому +37

      thanks - the animator was Pete McPartlan and the music was by Alan Stewart

    • @stachestar
      @stachestar 9 років тому

      This is like something straight off Normalboots

  • @psychotic17
    @psychotic17 10 років тому +149

    The king says "Ah..." and executes the guy for being a witch... warlock... thingy.

  • @PrenticeNeto
    @PrenticeNeto 10 років тому +10

    I like how passive-agressive the counsellor is. 4:31
    _look_
    _look at this_

  • @blazebluebass
    @blazebluebass 10 років тому +78

    Fantastic video! Good job to the whole team behind the animation and music!
    The story was very well told, too. It was very entertaining to watch.

  • @magister343
    @magister343 10 років тому +95

    What if one of the fields is extremely fertile and the others barren? What if one field has better access to water, or to markets.
    We really need to consider the market value of the lands, not merely their areas, if we want to divide the land fairly.

    • @stumbling
      @stumbling 9 років тому +48

      magister343 You could add a third dimension representing mean soil fertility and then calculate the volumes of the solids. I'm sure they'd all end up with perfectly proportionate volumes thanks to the suspiciously convenient reports from the surveyor.

    • @alexwang982
      @alexwang982 5 років тому

      Splitting rent tho

  • @JanickGers0
    @JanickGers0 8 років тому +57

    I've been teaching the Pythagorean Theorem in high school for a couple of years now. I can't believe I just discovered this video. I'm definitely going to use this in my class. Now I just have to find a translation for 'blob' in spanish. That is the tricky part!

    • @lxjuani
      @lxjuani 8 років тому +5

      JanickGers0 ¡"Coso"!

    • @JanickGers0
      @JanickGers0 8 років тому +3

      Juan Garay Jaja, eso puede funcionar!

    • @dfmayes
      @dfmayes 3 роки тому +4

      el blobbo

    • @Xayuap
      @Xayuap 2 роки тому

      sólo es una figura

    • @walkerorr341
      @walkerorr341 2 роки тому

      Try “chingadera”

  • @ralphlee781
    @ralphlee781 8 років тому +32

    WHERE AM I?! says the king

  • @mrsenman27
    @mrsenman27 10 років тому +24

    I'm going to say 'WHERE AM I?' any time someone says 'there you are' to me now

  • @Harlequin314159
    @Harlequin314159 10 років тому +70

    Wonderful job with the illustrations Mr Brady!

    • @numberphile
      @numberphile  10 років тому +41

      there is no way I could have done them!

  • @CountlessColumns
    @CountlessColumns 10 років тому +86

    Simply amazing: both the video and the content.

    • @guycomments
      @guycomments 10 років тому +3

      Are the video and the content not the same thing?

    • @werter260
      @werter260 10 років тому +5

      Keppit No.

    • @bichonche
      @bichonche 10 років тому

      Keppit Maybe he wanted to say that both the video editing and the content were amazing. :)

    • @guycomments
      @guycomments 10 років тому

      werter260 And explanation would be appreciated. How are they separate? The content of the video is the visuals and the audio... which is just the video itself.

    • @DarksteelPowerchord
      @DarksteelPowerchord 10 років тому

      Keppit By video he means the animation+montage etc, and by content he means the story and the lesson it teaches. But I'm really hoping you figured that out already and you're just being a smartass

  • @30LayersOfKevlar
    @30LayersOfKevlar 10 років тому +15

    Well that was actually pretty entertaining, both narration and animation worked well together.

  • @NoriMori1992
    @NoriMori1992 5 років тому +1

    This is still one of my favourite Numberphile videos. The proof is elegant, the story used to present it is great, Barry Mazur tells it beautifully, and Pete's animations tie it all together.

  • @UltraWindow
    @UltraWindow 10 років тому +90

    finally i understand that Pythagorean theorem.. it only took like 10 years.

    • @VRichardsn
      @VRichardsn 9 років тому

      Ultra Window Likewise! See, they should teach it this way!

  • @AnastasisGrammenos
    @AnastasisGrammenos 10 років тому +48

    aaaah! The audio!! :D BRAADDYYY!!!!

    • @numberphile
      @numberphile  10 років тому +66

      you got your revenge with all CAAAAPPPPITLS and repeated letters, which annoy me back. :)

    • @Reydriel
      @Reydriel 10 років тому +2

      Numberphile
      The guys voice goes from soft to loud almost randomly. I know it's how he speaks, but at least put some compression :P

  • @bakunicorn
    @bakunicorn 9 років тому +16

    There were three medieval kingdoms on the shores of a lake. There was an island in the middle of the lake, over which the kingdoms had been fighting for years. Finally, the three kings decided that they would send their knights out to do battle, and the winner would take the island. The night before the battle, the knights and their squires pitched camp and readied themselves for the fight. The first kingdom had 12 knights, and each knight had five squires, all of whom were busily polishing armor, brushing horses, and cooking food. The second kingdom had twenty knights, and each knight had 10 squires. Everyone at that camp was also busy preparing for battle. At the camp of the third kingdom, there was only one knight, with his squire. This squire took a large pot and hung it from a looped rope in a tall tree. He busied himself preparing the meal, while the knight polished his own armor. When the hour of the battle came, the three kingdoms sent their squires out to fight (this was too trivial a matter for the knights to join in). The battle raged, and when the dust had cleared, the only person left was the lone squire from the third kingdom, having defeated the squires from the other two kingdoms, thus proving that the squire of the high pot and noose is equal to the sum of the squires of the other two sides.

    • @NoriMori1992
      @NoriMori1992 8 років тому

      I don't get it.

    • @bakunicorn
      @bakunicorn 8 років тому +2

      =the square of the hypotenuse is equal to the sum of the square of the other two sides

    • @NoriMori1992
      @NoriMori1992 8 років тому

      +Skizzofonik And...?

    • @parvathisnambiar133
      @parvathisnambiar133 6 років тому

      Bravo!

    • @NoriMori1992
      @NoriMori1992 5 років тому

      I don't know why I commented three years ago that I didn't get it.
      Now my comment is: You. Asshole. +1

  • @newspaperlightbulb
    @newspaperlightbulb 10 років тому +2

    The captions and illustrations that follow Dr. Mazur's voice and tone exactly are hilarious.

  • @PhilBagels
    @PhilBagels 10 років тому +13

    The moral is: No matter how ignorant the king is of basic mathematics, if you're his councillor, be sure to answer all his questions patiently and politely.

  • @NoriMori1992
    @NoriMori1992 9 років тому +3

    This was _wonderful!_ I wish you explained all math theorems this way! :D
    That ending was perfect… "The king says…'ah'."
    I also love how literally you transcribed Barry's speech in the captions. XD

  • @AdrianLikesFlags
    @AdrianLikesFlags 10 років тому +22

    That last 'Ah' was so anticlimatic!
    I was expecting Red Wedding shit or something LOL

  • @zelda12346
    @zelda12346 10 років тому +18

    That's a beautiful proof.

  • @darkmage07070777
    @darkmage07070777 10 років тому +4

    Not only do I like the animation style, but the story was awesome and the math exercises were interesting to boot! Great stuff today!

  • @nerdbot4446
    @nerdbot4446 10 років тому +169

    The daughters will dispute anyway. At least one of them will claim that the land of the other daughter is more beautiful then theirs

    • @philipjohansson3949
      @philipjohansson3949 10 років тому +17

      Mr Counsellor!! How should I split my daughter between my lands?

    • @nerdbot4446
      @nerdbot4446 10 років тому +34

      No Problem! Just take your daughter and push her somewhere else!

    • @cowplod
      @cowplod 10 років тому +10

      Patrick Star Replying to your own comment eh?

    • @cowplod
      @cowplod 10 років тому +20

      ***** Two can play at that game

    • @flunkshsucksattoribash5566
      @flunkshsucksattoribash5566 10 років тому +1

      ***** No.

  • @KjeldSchmidt
    @KjeldSchmidt 10 років тому +19

    Amazingly funny animations. At first I wondered why you would have a video about just the pythagorean theorem and why it's eight minutes long, but it turned out very, very interesting. Love it!

  • @8bit_pineapple
    @8bit_pineapple 10 років тому +3

    Councillor : "There you are."
    The king: "Where am I!"

  • @silvereaglexi3888
    @silvereaglexi3888 7 років тому +1

    i think this is my favourite Numberphile video so far.

  • @terapode
    @terapode 10 років тому +19

    The animations are great.

    • @numberphile
      @numberphile  10 років тому +11

      thanks - they are by Pete McPartlan who animates a few of my videos....

    • @oO_ox_O
      @oO_ox_O 10 років тому +1

      Numberphile His channel: Pete McPartlan

  • @sigurdhendsethyan5641
    @sigurdhendsethyan5641 10 років тому

    Gotta love the attitude of that counsellor. "No Problem!". Every king should have a counsellor like that. Patient and pleasant.

  • @pinomial9888
    @pinomial9888 8 років тому +12

    Why doesn't the counsellor go "you're a bad messenger, send me the surveyor"
    That would make this so much faster

  • @DjVortex-w
    @DjVortex-w 10 років тому +9

    I'll be sure to read this to my children as a bedtime story.

  • @moe.a.4091
    @moe.a.4091 10 років тому +5

    I'm so glad I waited until it was bedtime for me to watch this video. Such an amazing bed time story.

  • @Pepsodent08
    @Pepsodent08 8 років тому +4

    I hadn't thought about the pythagorean theorem in this way before, as literal squares who's areas are relatable. Really made it click.

  • @stevePHXD
    @stevePHXD 6 років тому +1

    "Three squares, one triangle" sounds like a really wild numberphile video.

  • @MartKencuda
    @MartKencuda 10 років тому +13

    Did the audio get really distorted at 2:58 for anyone else?
    Edit: It seems to happen in some other parts as well. Like the guy tried to eat the mic or something.

  • @brandon-butler
    @brandon-butler 10 років тому +7

    This was really nice.

  • @linforcer
    @linforcer 8 років тому +6

    Woah, that is some Shyamalian plot twist, right there!

  • @Iamcake2001
    @Iamcake2001 10 років тому

    Those markers scratching the paper always give me goosebumps.

  • @upscbt
    @upscbt 10 років тому +1

    It's the first time I see this proof of the Pythagorean Theorem and I find it beautiful!
    It's simple, short and easy to understand, in a word: elegant.

  • @SamOliver4
    @SamOliver4 10 років тому

    I love the king in these animations. He just looks like he's in a constant state of amazement and wonder. XD

  • @MatrixangeI
    @MatrixangeI 10 років тому +5

    Brilliant video, loved the animation too

  • @UnmaskArt
    @UnmaskArt 10 років тому

    King says "Ah." Lol made my day. Love the video, it was excellent!

  • @antoniomario8037
    @antoniomario8037 10 років тому +2

    This was mind-blobing.

  • @fyapicula
    @fyapicula 10 років тому +3

    Such a nice video, wonderful animation and wonderful storytelling.

  • @timothymclean
    @timothymclean 8 років тому +7

    So...it's the Pythagorean Theorem.

  • @oO_ox_O
    @oO_ox_O 10 років тому +48

    The councillor is Patrick?

  • @JacobManifolds
    @JacobManifolds 10 років тому +2

    - There you are.
    - Where am I?
    Hilarious!

  • @cosmicwatermelon3927
    @cosmicwatermelon3927 7 років тому

    The way this man speaks by randomly pausing or saying a worldly loudly is so funny! I need more!

  • @Czeckie
    @Czeckie 10 років тому +2

    Hi, Brady, nice video again! I have a little suggestion or demand, depends on the point of view. As you probably know, Barry Mazur is one of the current most prolific mathematicians in the entire world. He made, among others, a seminal contribution to the theory that lead to the Wiles' proof of Fermat last thm. The relevant area of study is called Elliptic curves. I think you and prof. Mazur should make series on elliptic curves; provided he's such a good teacher, I believe, he could approach that subject in an elementary and motivated way, that would suit your style, Brady. Recently, you've featured videos on Ricci flow - a rich tool of modern mathematics. Elliptic curves are similiarly recent and far reaching. Please, continue with this awesome challenge of popularizing modern math. :) greetings from czech rep.

  • @satchelfrost6531
    @satchelfrost6531 9 років тому +4

    This video..... was incredibly boss

  • @GregoMorgan
    @GregoMorgan 10 років тому +5

    That's unfair from the start ! One of the daughters will have to see her father each time she wants to go from a small blob to the other and the other daughter can just live in her big blob forever and see none of that crazy family.

  • @UnderAcheiver1
    @UnderAcheiver1 10 років тому +5

    WHERE AM I?? -King, circa once upon a time

  • @Spocchio
    @Spocchio 10 років тому +1

    I laughed so hard @ 2:07 when you strike the wrong "the".

  • @Zarkonoth
    @Zarkonoth 10 років тому

    A really enjoyable video. It's nice to see something different from this channel once in while.

  • @kghandi
    @kghandi 10 років тому

    That is a very illuminating proof. A totally different approach from the typical construction we saw in school involving cutting the large square into 4 pieces...

  • @AustinSpafford
    @AustinSpafford 10 років тому

    Awesome video!
    I especially enjoyed the literal subtitles (eg. exact words and sizes), and small touches such as the music pauses. :)

  • @TheImperatorKnight
    @TheImperatorKnight 10 років тому +1

    Really enjoyed this! Story, music and animation are great. You could do something similar for the Wheat on Chessboard problem

  • @01100001q
    @01100001q 10 років тому

    This is probably the best explanation of the Pythagorean Theorem I've ever seen.

  • @Calismax-whostolemyname
    @Calismax-whostolemyname 10 років тому

    One of your best yet Mr Haran! Also love the brown paper for the animation keeping to the theme =]

  • @josephhargrove4319
    @josephhargrove4319 10 років тому

    What a wonderful demonstration of generalization. I've understood the Pythagorean Theorem since High School (more decades than than I'm willing to admit - I'm 63 year old.) But I had never seen the generalization (the Pythagorean Theorem of Similar Blobs) until I saw this video. Thanks.

  • @JanWey91
    @JanWey91 10 років тому +1

    I just love how silly the animations are, its brilliant!!!

  • @devjock
    @devjock 10 років тому

    This was absolutely beautiful. By far the best explanation of the pythagorian theorem I've ever heard or saw. I Wish I had Barry as my maths teacher back in my schooldays.

  • @AexisRai
    @AexisRai 7 років тому

    The kinetic typography going on in this video is hilarious and amazing.

  • @contingenceBoston
    @contingenceBoston 8 років тому +3

    The text makes this even more hilarious.

  • @djdaz21
    @djdaz21 10 років тому

    wow!! My favourite video from any of Brady's channels so far!!!

    • @numberphile
      @numberphile  10 років тому +3

      gosh, thanks

    • @djdaz21
      @djdaz21 10 років тому +1

      Numberphile It keeps getting harder to choose :)

  • @magnushmann
    @magnushmann 10 років тому

    This is an extreamly good way of proofing a theorem. Nice in so many ways!

  • @gabemoothart7943
    @gabemoothart7943 4 роки тому

    I loved the allusion to King Lear at the beginning.

  • @moerko94
    @moerko94 10 років тому

    That was just beautiful. I was smiling throughout the whole video :)
    Such a nice and informative story! And great animations ofc ;)

  • @AM-ur7uu
    @AM-ur7uu 2 роки тому

    Thanks!

  • @JustinHallPlus
    @JustinHallPlus 10 років тому

    The animation in this video is HILARIOUS.

  • @stefanosmandalas6599
    @stefanosmandalas6599 7 років тому

    Epic production! :D I love the music!

  • @eris4734
    @eris4734 8 років тому +3

    King: No Wait! My land isn't squares! It's Made Of Blobs!
    Counsellor: Don't Worry, Blob Pythagorean Theorem!

    • @incription
      @incription 8 років тому

      How to solve world peace

    • @DozyBinsh
      @DozyBinsh 8 років тому +4

      "Israel and Palestine both claim to occupy the same land!" Exclaims the king.
      "Ah," says the surveyor, "Well don't worry. I have here what's called a 'Two Blob Solution.'"

  • @NoobySammy
    @NoobySammy 10 років тому +1

    This should be used in schools around the world. :) great way of explaining pythagorean theorem.

  • @louis058
    @louis058 10 років тому

    Best explanation for Pythagoras' Theorem I've ever seen

  • @bjarkigunnarsson7288
    @bjarkigunnarsson7288 10 років тому +1

    I love the fact that the counsellor looks like a wise Patrick Star.

  • @alexandercampbell9178
    @alexandercampbell9178 10 років тому

    This is my favourite video on the internet.

  • @raykent3211
    @raykent3211 8 років тому +3

    ta for a charming video. Was the generalisation from squares to blobs known to Pythagoras or did it come later?

  • @CptSkyBlue
    @CptSkyBlue 10 років тому

    Beautiful story, music and animations ^_^
    Keep up good work guys!

  • @snabelkran
    @snabelkran 10 років тому

    This is the best numberphile video to date. Even though it was quite simple and basic it was very very entertaining!

  • @tedchirvasiu
    @tedchirvasiu 10 років тому

    Best.
    Animation.
    Ever!
    Do more!

  • @LeiosLabs
    @LeiosLabs 10 років тому

    Fantastic animation! I wish my friends were as excited as the king was.

  • @LemonChieff
    @LemonChieff 9 років тому +7

    Where am I ? Says the king XD

  • @jim40135
    @jim40135 10 років тому +1

    The moral of the story is; Kings are annoying. And this guys maths is so powerful it distorts the audio.

  • @MariusMuntean
    @MariusMuntean 10 років тому

    Very nice video, good job! The background music gives it that extra something, that makes you (at least it made me) pay extra close attention.

  • @w1swh1
    @w1swh1 Рік тому

    Excellent, didnt know the blob theorem until now and the proof is so simple!! Thank you.

  • @samueldeandrade8535
    @samueldeandrade8535 Рік тому

    Wow. This is actually amazing.

  • @len322
    @len322 10 років тому +1

    the 'where am I?' Just killed me, It's just me in math classe after lunch..

  • @ChompNom
    @ChompNom 10 років тому +8

    The king says "ah"

  • @kyzer42
    @kyzer42 7 років тому +1

    And the moral of the story: Kings ask a lot of questions.

  • @krikoryaylayan6221
    @krikoryaylayan6221 10 років тому

    It's my favorite theorem ,explained in different ways. Thank you for this video.

  • @1959Edsel
    @1959Edsel 10 років тому

    I love the drawings in this video.

  • @Voltanaut
    @Voltanaut 10 років тому +5

    Who knew Patrick Star was such a mathematician.

  • @gheciobanu
    @gheciobanu 9 років тому

    Very interesting stuff! I knew the Pythagorean theorem, but the story and animations are fascinating!