Pythagorean theorem | 3 Visual Proofs |

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  • Опубліковано 10 вер 2024
  • Some of my favorite proofs of Pythagorean theorem. Enjoy:)
    _________________________________________________________________
    Support my animations on:
    / think_twice
    _________________________________________________________________
    Any further questions or ideas:
    Email - thinktwiceask@gmail.com
    Twitter - / thinktwice2580
    _________________________________________________________________
    Programs used:
    - Cinema 4D
    _________________________________________________________________
    Music:
    "FollowHer" - • LoFi Type Beat -- "Fol...

КОМЕНТАРІ • 175

  • @oliot4814
    @oliot4814 6 років тому +75

    I know where he lives btw. So if you want his address, message me.

  • @typo691
    @typo691 6 років тому +124

    Nice.
    The pieces moving in sync with the music is also quite nice.

  • @dambotg89
    @dambotg89 6 років тому +42

    Channel name: Think Twice
    Content: Three proofs
    Okay

    • @EduardoEscarez
      @EduardoEscarez 6 років тому +16

      Think Thrice

    • @mattgsm
      @mattgsm 6 років тому +1

      And the original thought you had too so it's Think quadrice right?

    • @HomeofLawboy
      @HomeofLawboy 6 років тому +1

      Me: Watch a thousand times

    • @_yellow
      @_yellow 6 років тому +1

      Eduardo Escarez I was going to say exactly that!

  • @rfpeace
    @rfpeace 6 років тому +73

    BTW 3blue1brown sent me
    cheers!

  • @ARBB1
    @ARBB1 6 років тому +28

    Next, a visualization of the Fundamental Theorem of Calculus would be good

  • @Inyrth
    @Inyrth 6 років тому +5

    Even if somebody doens't understand what everything means, it's still so nice to look at. Great style.

  • @MahmoodMuhenned
    @MahmoodMuhenned 6 років тому +17

    So informative and relaxing in the same time.
    Thanks

  • @sinom
    @sinom 6 років тому +18

    Do you want:
    360p
    1080p60
    No in-between.

    • @jow_angelow
      @jow_angelow 6 років тому +2

      LOL

    • @ThinkTwiceLtu
      @ThinkTwiceLtu  6 років тому +5

      there should be 480p and 720p60

    • @sinom
      @sinom 6 років тому

      Think Twice still not there. Might take UA-cam a while longer to process it.

    • @jow_angelow
      @jow_angelow 6 років тому

      Think Twice i dont see it yet tho, i watch in 360p anyway 😂😂

  • @kylebryancagasan4447
    @kylebryancagasan4447 6 років тому +7

    This is so soothing. Glad to have found out about your channel :)

  • @briann363
    @briann363 6 років тому +8

    super appealing, thanks for making this

  • @N0Xa880iUL
    @N0Xa880iUL 6 років тому +1

    The synchronization with music is so soothing

  • @NcKyPmHzPPcrnTEat
    @NcKyPmHzPPcrnTEat 6 років тому +10

    Your videos are the perfect balance between informative and simple.

  • @leux0
    @leux0 6 років тому +1

    A VERY beautiful visualization of a very popular proof (side note; loved the music)

  • @user-vj7uc9tj7c
    @user-vj7uc9tj7c 6 років тому +6

    Very nice.
    Came from 3B1B.

  • @46pi26
    @46pi26 6 років тому +59

    Explain this, atheists

    • @clumsyjester459
      @clumsyjester459 6 років тому +26

      If you have one geometrical proof relying on area equality for a theorem it usually isn't very hard to come up with arbitrarily more complex versions of the same proof. The theorem won't suddenly get wrong, if you toy around with your right sided triangles for longer. They will still fit together nicely in plenty of combinations.
      Does that suffice?

    • @46pi26
      @46pi26 6 років тому +29

      Clumsy Jester Well, um, yeah. I guess it does suffice. Good job, atheists.

    • @gredangeo
      @gredangeo 6 років тому +2

      What does this have to do with Atheism?

    • @46pi26
      @46pi26 6 років тому +23

      gredangeo It's basically just me ripping off a satirical joke based around the idea that something is so beautiful that it could've only been created by God Himself.

    • @ceruleanmemoir
      @ceruleanmemoir 6 років тому +1

      46 & pi something like " e^iπ + 1 = 0"

  • @rfpeace
    @rfpeace 6 років тому +19

    what a beautiful way to say this!

  • @ChurchOfThought
    @ChurchOfThought 6 років тому +21

    Very soothing, thank you Think Twice!

  • @lucianorodriguez7726
    @lucianorodriguez7726 6 років тому

    MY GOD, MAN, IS A PERFECT CHANNEL! IN LESS THAN 30 MINUTES I'M LOOKING ALMOST EVERYTHING AND I'M NOT BORING

  • @mac_3952
    @mac_3952 6 років тому

    I just discovered your videos today, and they are absolutely beautiful! Thank you so much for sharing them. Keep up the good work!

  • @edgarw5872
    @edgarw5872 6 років тому

    your videos are super smooth and awesome, you deserve way more recognition

  • @Tondadrd
    @Tondadrd 6 років тому +1

    Had to watch about 4 times to agree and to look for what the comentators ment.
    Great vid! Still here from 3b1b

  • @uzKantHarrison
    @uzKantHarrison 6 років тому +1

    The second one is so simple and cool!

  • @mattgsm
    @mattgsm 6 років тому +1

    The music fits with the visuals!

  • @tophu7903
    @tophu7903 6 років тому

    A new Think Twice video?
    AMAZING!

  • @oussamawahbi4976
    @oussamawahbi4976 6 років тому +1

    best youtube channel ever

  • @Telozz
    @Telozz 6 років тому +1

    Keep up the great work!

  • @jaysprenkle1026
    @jaysprenkle1026 6 років тому +1

    Now I know how to explain the principles of algebra to my math phobic friends. Thanks!

  • @0xffox
    @0xffox 6 років тому +6

    Python 1:21

  • @joshuaancog9833
    @joshuaancog9833 6 років тому +1

    The music is so relaxing.

  • @Andrew-yj7mj
    @Andrew-yj7mj 6 років тому +2

    those animations are amazing! what software are you using to make them?
    you deserve more subscribers!

    • @ThinkTwiceLtu
      @ThinkTwiceLtu  6 років тому

      thank you:) for this one i used cinema 4d

  • @rodolfobt1020
    @rodolfobt1020 6 років тому +1

    Nice Video @a
    It’s kinda confusing for me but the video quality is as ever very nice
    Waiting for the next

  • @taharahmani1547
    @taharahmani1547 6 років тому

    is it the right way to understand science : visualising in very particular dimensions theorems .
    you guys have reminded me of the Einstein's approach; trying to understand concepts by imagining thought experiments and finding physical interpretations of fundamental science. that is extraordinary .
    still is there a remarkable opinions about the nature of mathematics and it's concerns : Henri Poincarré said that one mathematical object can express a non-finite and different phenomena's and as as a consequence it can have an infinite interpretations . as I shall take an example of what I am talking about let us consider the Pythagorean theorem not from the geometrical view but from the one of probability and statistics:
    we have a pocket which contains "a" balls with different colours ("a" is whichever number we choose). Now, we can only pick 2 balls successively with reset . the number of possibilities ,of combination according to Pythagoras is equal to the number of possibilities if we use another pocket which contains "b" balls of different colours plus the number of possibilities in a pocket of "c" balls . and all of that done in the same conditions of experiment (successively and with reset) .
    and finally we have our new interpretation witch totally different from the one with cubes (geometric ) .
    a²=b²+c²

  • @castur_
    @castur_ 6 років тому

    This channel should be much more popular than what it is now

  • @edmundolicona3443
    @edmundolicona3443 6 років тому

    Gracias
    Esto me ha ayudado para generar mis demostraciones formales.
    ¡Increíble trabajo!

  • @GrandMoffTarkinsTeaDispenser
    @GrandMoffTarkinsTeaDispenser 6 років тому +2

    I thank you
    twice

  • @KungFuPanda1223
    @KungFuPanda1223 6 років тому +1

    i really love your channel

  • @PixelatedFolf
    @PixelatedFolf 6 років тому +1

    This is visually satisfying

  • @Makasu
    @Makasu 6 років тому +1

    so satisfying

  • @77mcgiver
    @77mcgiver 6 років тому +1

    Great video!

  • @D3tyHuff
    @D3tyHuff 6 років тому +1

    My god, that pleased my eyes.

  • @Deuxice
    @Deuxice 6 років тому +1

    This channel's so effin underrated. :(

  • @logandarbz1257
    @logandarbz1257 6 років тому +1

    Finally. This was inevitable.

  • @brutexx2
    @brutexx2 6 років тому +1

    That made me _Think Twice_

  • @bunbunnbunnybun
    @bunbunnbunnybun 6 років тому +1

    Beautiful

  • @ismailnurmaghribi1702
    @ismailnurmaghribi1702 6 років тому +1

    super nice video...

  • @denismazurak2925
    @denismazurak2925 6 років тому

    I've already seen many proofs, but still don't get the theorem intuitively)
    Very nice and smooth animations!

  • @cikas4965
    @cikas4965 6 років тому

    it's....just amazing!!

  • @liangpaiyi6609
    @liangpaiyi6609 6 років тому +1

    very great.

  • @antoniolewis1016
    @antoniolewis1016 6 років тому +1

    View 7000 here. Just beautiful

  • @AmitKumar-mb6iy
    @AmitKumar-mb6iy 5 років тому

    Excellent job sir very interesting

  • @tudorgeaman
    @tudorgeaman 6 років тому +1

    This channel is incredible, I watched all the vids !! But only 32K subs :(

  • @jasonli7883
    @jasonli7883 6 років тому

    just earned yourself a new sub

  • @okoyoso
    @okoyoso 5 років тому

    What do you use to animate? Processing?

  • @DynestiGTI
    @DynestiGTI 6 років тому

    Why isn't your channel blowing up already!

  • @DiegoMathemagician
    @DiegoMathemagician 6 років тому

    Loving this channel

  • @badhbhchadh
    @badhbhchadh 5 років тому

    I liked the last one the most.

  • @wiggamia4685
    @wiggamia4685 6 років тому

    How smood and very simple to explain it ☀😀

  • @LimeEffy
    @LimeEffy 6 років тому +1

    Cool stuff 😍

  • @pitadomu
    @pitadomu 6 років тому

    Even people who can't do math knows:
    Your videos = Awesome

  • @flaviusclaudius7510
    @flaviusclaudius7510 6 років тому

    How does the first one prove the Pythagorean theorem?

  • @cubicardi8011
    @cubicardi8011 6 років тому

    Holy when did you gain so many subscribers? When i watched your last video you had like 3K Subs but now!

  • @akanshavishwakarma272
    @akanshavishwakarma272 3 роки тому +1

    Keep it up dear 😍👌👍

  • @funkysagancat3295
    @funkysagancat3295 6 років тому

    Beautiful as always :)

  • @user-hr7ty1jo8m
    @user-hr7ty1jo8m 6 років тому

    greets from 3blue1brown.. very beautiful proof

  • @Kryptovaluutta
    @Kryptovaluutta 6 років тому +2

    Math + art = marth?

  • @GaleAeras
    @GaleAeras 6 років тому

    I enjoyed this, but I couldn't quite get the second one. Can anyone help me?

  • @drenz1523
    @drenz1523 4 роки тому

    I want to ask, in the first proof, how we proof that the square has a side length of sqrt(a^2+b^2) or c?

    • @mattmatt9324
      @mattmatt9324 4 роки тому

      look at the sides of the square, they are the hypothenuse of a rectangle triangle with two sides of lenght a and b respectively (keep an eye on the animation to check those lengths)

    • @drenz1523
      @drenz1523 4 роки тому

      @@mattmatt9324 is that the 3rd proof?

    • @mattmatt9324
      @mattmatt9324 4 роки тому

      @@drenz1523 no the first one

    • @drenz1523
      @drenz1523 3 роки тому

      @@mattmatt9324 ok thx!

  • @italyball2166
    @italyball2166 6 років тому

    Really nice animations!

  • @catnamedsaturnus
    @catnamedsaturnus 6 років тому

    It is wonderful

  • @codedragon6237
    @codedragon6237 6 років тому +1

    Nice

  • @tg.amitgandhi
    @tg.amitgandhi 6 років тому

    Which software do you use to make such animations?
    Can you please tell

  • @vaprin2019
    @vaprin2019 6 років тому +1

    amazing

  • @Ettenra1
    @Ettenra1 6 років тому

    beautiful ~

  • @ffggddss
    @ffggddss 5 років тому

    Nice ones!
    Fred

  • @Brixey55
    @Brixey55 6 років тому

    can you please do a video on Gabriel's horn. i'm not sure of what about it but i bet you could make some mind blowing visualization

    • @ThinkTwiceLtu
      @ThinkTwiceLtu  6 років тому

      yes:) Actually one of the first videos that I uploaded to this channel was about Gabriel's horn, however I made it unlisted because I felt like the visual quality wasn't so good and the video was a lot more text heavy compared to my recent videos.

  • @JM-us3fr
    @JM-us3fr 6 років тому

    Can you do a proof of Pick's Theorem?

  • @SVP-uy9qb
    @SVP-uy9qb 6 років тому +1

    Yay

  • @satviksingh5436
    @satviksingh5436 6 років тому

    Great vid

  • @lehuyvo3812
    @lehuyvo3812 6 років тому

    wow very smooth lol

  • @fenzz5511
    @fenzz5511 6 років тому

    Reupload? Well, I’m not complaining 😏

    • @fenzz5511
      @fenzz5511 6 років тому

      Beautiful as always!

  • @oliot4814
    @oliot4814 6 років тому

    bit of a fan, I am

  • @fawadmirza.
    @fawadmirza. 6 років тому

    Can you make a video on binomial coefficients like how sum of first half coefficients = sum of last half coefficients.

  • @Aric-ls7bf
    @Aric-ls7bf 6 років тому

    Yo i watch 3blue1brown but i found this channel separately

  • @merve4759
    @merve4759 5 років тому

    your videos 😍

  • @NarutoShippudenIntro
    @NarutoShippudenIntro 6 років тому +3

    Oof nice stuff

  • @Abhinandan_Bang
    @Abhinandan_Bang 6 років тому

    Subscribed

  • @poweredbysergey
    @poweredbysergey 6 років тому

    Cool

  • @ListentoGallegos
    @ListentoGallegos 6 років тому

    Can a picture be a proof? My teacher insisted it's not.

  • @imaratokay
    @imaratokay 6 років тому

    *let gasp*
    I know this

  • @ferniarex
    @ferniarex 6 років тому

    *r* *u* *ok*

  • @EchoHeo
    @EchoHeo 6 років тому

    Wow

  • @user-bb3kz6my4j
    @user-bb3kz6my4j 6 років тому +1

    wait what

  • @arnavdas3139
    @arnavdas3139 4 роки тому

    Wizardry

  • @mkwarlock
    @mkwarlock 5 років тому

    This is A R T.

  • @LimeEffy
    @LimeEffy 6 років тому

    Part 2 when?

  • @WordsandNumbers1
    @WordsandNumbers1 6 років тому

    👍👍

  • @IQ.oo.
    @IQ.oo. Рік тому

    cinema 4D?

  • @chiquiflautro
    @chiquiflautro 6 років тому +15

    In the first proof, you never proved that c is the hypothenuse of a right triangle with sides a and b

    • @chiquiflautro
      @chiquiflautro 6 років тому

      Nuno Mateus I know, it's just a pity the proof is not finished though

    • @ThinkTwiceLtu
      @ThinkTwiceLtu  6 років тому +20

      at 0:17 the white line which connects the green triangles is the hypotenuse

    • @marcotavano4681
      @marcotavano4681 6 років тому +1

      Think Twice I had the same doubt, thanks for clarifying

    • @chiquiflautro
      @chiquiflautro 6 років тому

      my bad, looked at it before but failed to see it

    • @SSJ3Tim
      @SSJ3Tim 6 років тому

      Yes, of course it is the same length, but in what way does the video demonstrate this?

  • @khirgis7224
    @khirgis7224 2 роки тому

    2

  • @raghafazkamuhammad8576
    @raghafazkamuhammad8576 6 років тому

    Don't think once. Think twice.