The Napkin Ring Problem

Ойын-сауық

Brain Candy Live FALL TOUR: www.braincandylive.com/tickets
The Curiosity Box: www.curiositybox.com/
LINKS TO LEARN MORE BELOW!
my twitter: / tweetsauce
Adam and I (but mainly Adam) making a kendama: • Adam Savage and Vsauce...
Orange Oil: en.wikipedia.org/wiki/Orange_oil
Napkin Ring Problem: en.wikipedia.org/wiki/Napkin_...
Cavalieri's Principle:
schoolyourself.org/learn/geom...
en.wikipedia.org/wiki/Cavalie...
www.cut-the-knot.org/Curriculu...
BIG THANKS:
Eric Langlay stayed up all night with me so that this video could come out today. MUCH LOVE / ericdraven30
Grant from 3Blue1Brown helped me wrap my head around this topic: / @3blue1brown
music by
Jake Chudnow: / jakechudnow
and via AudioNetwork: www.audionetwork.com

Пікірлер: 28 000

  • @Vsauce
    @Vsauce6 жыл бұрын

    Sorry Napkinheads, but the solid shown from 0:18 to 0:24 is not a proper mathematical "napkin ring." It shouldn't have flat faces on the top and bottom. That's a mistake I missed in my rush to export this episode before my flight to Montreal this morning :( But I'm glad to be in Montreal! I'm here working on an episode about the power of suggestion ...

  • @tenzinsmith7991

    @tenzinsmith7991

    6 жыл бұрын

    Vsauce first

  • @annoythefish

    @annoythefish

    6 жыл бұрын

    first

  • @hopelesslyhopeful4009

    @hopelesslyhopeful4009

    6 жыл бұрын

    That's okay we love you anyways!

  • @mitchkiines7425

    @mitchkiines7425

    6 жыл бұрын

    Vsauce not good enough 😡

  • @tarika4633

    @tarika4633

    6 жыл бұрын

    Vsauce hey Vsauce overused meme here

  • @aliensguy4291
    @aliensguy42914 жыл бұрын

    3:04 why is nobody talking about that INCREDIBLE seamless transition!

  • @onionvlogs5222

    @onionvlogs5222

    4 жыл бұрын

    Lovely transition

  • @omarrihani2599

    @omarrihani2599

    4 жыл бұрын

    You are

  • @GerstBladeworks

    @GerstBladeworks

    4 жыл бұрын

    Because nobody cares. That is expected with a video coming from a channel of this caliber

  • @paperluigi-gs8cs

    @paperluigi-gs8cs

    4 жыл бұрын

    @@GerstBladeworks yep

  • @ImXyper

    @ImXyper

    4 жыл бұрын

    because noone noticed it

  • @brendanfasolino
    @brendanfasolino6 жыл бұрын

    Vsauce you should do a face reveal.

  • @ZakMcallister

    @ZakMcallister

    6 жыл бұрын

    lol

  • @josephsmith3961

    @josephsmith3961

    6 жыл бұрын

    Not until 15M subscribers tho

  • @mariokart7286

    @mariokart7286

    6 жыл бұрын

    wtf is your channel it's lowkey genius.

  • @zackirvine7152

    @zackirvine7152

    6 жыл бұрын

    Setting Things Down u legend

  • @BluJellu

    @BluJellu

    6 жыл бұрын

    Zack Irvine s

  • @kindlekiran
    @kindlekiran3 жыл бұрын

    I feel like “orange oil is flammable” is going to be important in some obscure future event in my life

  • @jellisgaming

    @jellisgaming

    2 жыл бұрын

    Well, yeah.

  • @Acquies

    @Acquies

    2 жыл бұрын

    Like when you'll be burning and try to remove the fire from your body by jumping in the orange juice swimming pool you just bought last week and remember it will juste make things worse.

  • @jeremiahlopez1791

    @jeremiahlopez1791

    2 жыл бұрын

    @@Acquies Almost happened to me ngl

  • @Acquies

    @Acquies

    2 жыл бұрын

    @@jeremiahlopez1791 Gosh what happened

  • @jeremiahlopez1791

    @jeremiahlopez1791

    2 жыл бұрын

    @@Acquies I jumped in my apple juice pool instead

  • @MindTiltDuo
    @MindTiltDuo10 ай бұрын

    "But currently, we're talking about balls and coring them" Best sentence of the year

  • @user-se4tn9cq9m
    @user-se4tn9cq9m6 жыл бұрын

    *What I learned from this video: Orange oil is flammable.*

  • @AbiRizky

    @AbiRizky

    6 жыл бұрын

    i still have no idea what orange oil is

  • @terabitdefiance8022

    @terabitdefiance8022

    6 жыл бұрын

    Abi Rizky when you squeeze the OJ peel.

  • @pek5117

    @pek5117

    6 жыл бұрын

    what did you do with your childhood? also corn chips are vey flammable

  • @yellowsubmarine649

    @yellowsubmarine649

    6 жыл бұрын

    whoa, didn't think I'd find you here, Alex

  • @tanesimons6501

    @tanesimons6501

    6 жыл бұрын

    A. Lee Composer Pretty much lol 😂😂😂😂😂🤣🤣

  • @goldfished
    @goldfished5 жыл бұрын

    0:50 when u walk into a spiders web

  • @scotty9173

    @scotty9173

    5 жыл бұрын

    Vsauce is just a giant meme at this point

  • @sebb7162

    @sebb7162

    5 жыл бұрын

    @@scotty9173 his name is michael

  • @scotty9173

    @scotty9173

    5 жыл бұрын

    @boognish4ever _ I know that... but vsauce is more direct and well known and easier to just write out instead of "michael stevens".

  • @almightygregyboi280

    @almightygregyboi280

    5 жыл бұрын

    😂😂😂for real

  • @powderedwater4742

    @powderedwater4742

    5 жыл бұрын

    @@sebb7162 stfu

  • @conred5158
    @conred51582 жыл бұрын

    Watching VSAUCE is always fun, but it’s even better now that I understand all the math he’s using 😅

  • @eggs_rat

    @eggs_rat

    2 ай бұрын

    if you pretend like you understand it then you MIGHT understand it

  • @6daysago167
    @6daysago16710 ай бұрын

    I’m so confused but at the same time I am envious of those able to completely understand this. I love to learn even when I don’t fully understand what I’m being told, and I accept this :/

  • @1nt3rD1ct0r

    @1nt3rD1ct0r

    8 ай бұрын

    Technically, the math involved here is only at the level you'd learn in a highschool trigonometry class. To be sure, it's not immediately intuitive and even if you knew how all the math involved worked that's not a guarantee you could figure this proof out on your own; but if you really would like to learn more about these kind if things, the math involved would not take very long to learn. I don't know what your education level is, but a single college level algebra class would likely cover more than anything you'd need. As far as Vsauce videos go, this one has a fairly low bar for entry and I'd encourage you to maybe pick up a book or two talking about trigonometry if you don't feel like taking a class. Knowing about angles and some of the more involved proofs for shape structure function has helped me a lot to intuitively understand my surroundings in every day life. It has certainly helped me to visualized objects better and increased my spacial understanding. I wish when I did trig back in high school I paid more attention, maybe learning Calc would have been easier if I didn't botch my basics.

  • @lucky43113

    @lucky43113

    8 ай бұрын

    @@1nt3rD1ct0r We didnt have that at my school only basic math

  • @Antnee659

    @Antnee659

    4 ай бұрын

    I was in algebra 1 3x in highschool😂 Got through basic arithmetic, geo, and pre alg. Then i just hit a brick wall. My mind can understand the concept of the napkin ring and sort of the order of operations hes trying to prove to a certain point, but then i look at the equations on this paper and it starts to look like spaghetti

  • @garkeinbock7103

    @garkeinbock7103

    Ай бұрын

    Maybe it's helping if you watch it bit after bit and pause to ponder. Are there any specific questions?

  • @Lem00nBoy
    @Lem00nBoy4 жыл бұрын

    “I’m Renata Bliss, your freestyle dance teacher.” 0:50

  • @dylan__nayld8595

    @dylan__nayld8595

    4 жыл бұрын

    Oh my fucking God I forgot about that video

  • @farbrorforgasare8872

    @farbrorforgasare8872

    4 жыл бұрын

    Oooooh so that's what she said her name was, holy fuck I can now die in peace

  • @fbi1649

    @fbi1649

    4 жыл бұрын

    But right now we're talking about balls

  • @harveybritland3112

    @harveybritland3112

    4 жыл бұрын

    Reminded me of Gina Linetti from B99.

  • @boldrain

    @boldrain

    4 жыл бұрын

    nice

  • @alexs6746
    @alexs67463 жыл бұрын

    Me who is barely passing math: yeh sounds about right

  • @ThePenguin134

    @ThePenguin134

    3 жыл бұрын

    Me who has an 104% in pre-calc. Yeh seems legit.

  • @alexs6746

    @alexs6746

    3 жыл бұрын

    We are in agreement then

  • @frankcastle1862

    @frankcastle1862

    3 жыл бұрын

    None of you are Asian are you?

  • @alexs6746

    @alexs6746

    3 жыл бұрын

    @@frankcastle1862 my grades are so low if I were I’d be dead by now

  • @ryanbui2046

    @ryanbui2046

    3 жыл бұрын

    @@frankcastle1862 I’m an Asian but I don’t have an A don’t kill me

  • @stupidname02_
    @stupidname02_2 жыл бұрын

    This video has me more enthusiastic about math than any math teacher I ever had back in school

  • @purplepurplepurple2162

    @purplepurplepurple2162

    2 жыл бұрын

    a straw has 1 hole

  • @1saac_xx
    @1saac_xx10 ай бұрын

    so folks, what have we learned from this video? *orange oil is flammable*

  • @apacheattackhelicopter5823
    @apacheattackhelicopter58234 жыл бұрын

    when you just realized you voluntarily watched an entire math lesson

  • @chloe8493

    @chloe8493

    3 жыл бұрын

    Wait.. this isn’t about Napkins you wrap around your finger and then tie it to make it look like a ring?!??!

  • @neilien3317

    @neilien3317

    3 жыл бұрын

    jooooojoooooo

  • @calcifer4297

    @calcifer4297

    3 жыл бұрын

    *oh no*

  • @jyotsnabegam2726

    @jyotsnabegam2726

    3 жыл бұрын

    @Za Worudo Seriously, just out of curiosity, what country are you in? Because we were doing basic trigonometry at 13 years of age. Edit: I'm from India

  • @Yatsu00x

    @Yatsu00x

    3 жыл бұрын

    Speed Wagon Is best waifu even in girl form

  • @alaha8349
    @alaha83496 жыл бұрын

    i love this science teacher he never gives us homework

  • @tammit6142

    @tammit6142

    6 жыл бұрын

    WARNIG:worlds worst comment Alhala omg yes

  • @nakinajay

    @nakinajay

    6 жыл бұрын

    Tammi Tacinelli yep, your comment really does suck.

  • @aleckbo

    @aleckbo

    6 жыл бұрын

    I mean, most of this video is math...

  • @mariosonicboom123

    @mariosonicboom123

    6 жыл бұрын

    Siren7 No, you're right. It is math. Not just technically.

  • @aleckbo

    @aleckbo

    6 жыл бұрын

    SanicDaHergedog Yeah.

  • @magicalhikari5859
    @magicalhikari5859 Жыл бұрын

    I think the takeaway is that you’re removing more from the bigger object than the smaller one, which is why they have the same volume

  • @Hussfromthearea

    @Hussfromthearea

    Жыл бұрын

    I think the takeaway of this comment is that you don't actually understand the mathematics and physics behind it......

  • @FireBeam

    @FireBeam

    Жыл бұрын

    @@Hussfromthearea And you do? This video is the dumbest thing I've seen yet.

  • @Hussfromthearea

    @Hussfromthearea

    Жыл бұрын

    @FireBeam BRO what? Yes I understand. The equation proved that the size of the sphere is not relevant, if they share the same height the volume that it would take up is the same. This guy is saying "oh he took more from the bigger one", but he needed to take more from the bigger one in order to get a napkin ring that is the same height. This concept is really interesting and if you felt this was stupid, then you should have just closed the video.

  • @Hussfromthearea

    @Hussfromthearea

    Жыл бұрын

    @FireBeam also if you deleted your comment, well done, cause I can't see it anymore. For anyone else who is reading this, the guy said "And you do? This video is the dumbest thing I've ever seen yet.".

  • @FireBeam

    @FireBeam

    Жыл бұрын

    @@Hussfromthearea The video proved that people are stupid enough to "not believe thier lying eyes", if a priest in a white coat tells them it to be true. No wonder there has barely been any advancement since WW2

  • @thewarderman1840
    @thewarderman1840 Жыл бұрын

    I was like what are the practical applications of this but that ending cleared it all up.

  • @DrMeepy
    @DrMeepy5 жыл бұрын

    Three things i understood in this video: 1. "Hey, Vsauce! Michael here!" 2. "Orange oil is flammable." 3. "And as always, Thanks for watching!"

  • @NYQINA

    @NYQINA

    4 жыл бұрын

    And 0:50

  • @nathanrandomized3593

    @nathanrandomized3593

    4 жыл бұрын

    @@NYQINA I didn't understand that

  • @NYQINA

    @NYQINA

    4 жыл бұрын

    @@nathanrandomized3593 lol

  • @lulanm9000

    @lulanm9000

    4 жыл бұрын

    Thank you because I was feeling so unintelligent.

  • @uyhg7284

    @uyhg7284

    4 жыл бұрын

    I'm clearly not smart after a while he just sounded like Charlie Browns teacher but I was going to call him out on the mistake he mentioned in the comments whatever that was lol

  • @SomethingsFischy
    @SomethingsFischy3 жыл бұрын

    0:50 My new favorite clip on the internet

  • @fr3e.

    @fr3e.

    3 жыл бұрын

    Yeah its your favorite, but right now we’re talking about balls and coring them.

  • @TheRealHalolad

    @TheRealHalolad

    3 жыл бұрын

    @@fr3e. lol

  • @Goomba456

    @Goomba456

    3 жыл бұрын

    I also like the way he says we are talking about balls

  • @fr3e.

    @fr3e.

    3 жыл бұрын

    @@Goomba456 i mean, we are

  • @DuckDuckDontGo

    @DuckDuckDontGo

    3 жыл бұрын

    @@fr3e. What a coincidence, i readed the comment at the same time when michael was saying this.

  • @felt_presence9996
    @felt_presence9996 Жыл бұрын

    This channel has been such a positive source of comfort in my life for a long time. Whether I completely understand all the topics or not it's entertaining and it's educational and I love it and everyone involved in the process. I've decided I'm getting a vsauce tattoo

  • @grumpsyb9191

    @grumpsyb9191

    10 ай бұрын

    Vsource of comfort 🤭

  • @pontierent734
    @pontierent73410 ай бұрын

    okay the fact that two people from my childhood are going to be TOGETHER (not that they haven't been before) live I want to go, but time and money man... Its a hard thing. Thank you Michael for your videos, you genuinely taught me a lot. Same to Adam Savage you guys are truly the reason I know more today than I would if I was born 10 years earlier.

  • @bruhbobent
    @bruhbobent4 жыл бұрын

    0:49 Micheal dancing is the best thing i've ever seen today.

  • @emil_st1

    @emil_st1

    3 жыл бұрын

    The fact that you said "ever seen today" bothers me

  • @50shadesofmycow

    @50shadesofmycow

    3 жыл бұрын

    @@emil_st1 shit you're right. Now it bothers me too xD

  • @i.pezzotti853

    @i.pezzotti853

    3 жыл бұрын

    That’s the most 2011 dance ever

  • @kingfish5843

    @kingfish5843

    3 жыл бұрын

    Looked like something out of Don’t Hug Me I’m Scared

  • @AmalgraemeV

    @AmalgraemeV

    3 жыл бұрын

    It’s so... chaotic.

  • @baileymaule2582
    @baileymaule25825 жыл бұрын

    Police - “Vsauce your under arrest” Vsauce - “or am I”?

  • @cwillard2761

    @cwillard2761

    5 жыл бұрын

    Bailey Maule *police arrests themselves*

  • @pilsmer

    @pilsmer

    5 жыл бұрын

    *coughs* you're

  • @R7der97

    @R7der97

    5 жыл бұрын

    Best comment on this video

  • @LewisMono

    @LewisMono

    5 жыл бұрын

    _v s a u c e m u s i c p l a y s_

  • @KingJJG2005

    @KingJJG2005

    5 жыл бұрын

    Lol

  • @gameryusic825
    @gameryusic8252 жыл бұрын

    Wow I never felt more smarter after being able to understand properly a math equation in a Vsauce video. It's actually really simple maths. That particular subject literally CARRIED my marks for my exams. I was just shy of a A1 but a A2 is alright.

  • @Sinnerman
    @Sinnerman9 ай бұрын

    Wow! Math is actually crazy. When I was a kid I hated math at school, but the more I the more amazed I am by it. Thank you, Michael

  • @hassanabbas08
    @hassanabbas085 жыл бұрын

    0:50 HOW IT FEELS TO CHEW 5 GUM

  • @lazenby5793

    @lazenby5793

    5 жыл бұрын

    Stimulate your senses

  • @yinyang1217

    @yinyang1217

    5 жыл бұрын

    "im outta gum"

  • @julianfantasia9033

    @julianfantasia9033

    5 жыл бұрын

    There are so many 0:50 comments and I’ve clicked the time in the comment and snorted at every one of them. That clip is pure gold.

  • @fruit_coketail3652

    @fruit_coketail3652

    5 жыл бұрын

    Stimulate your senses

  • @low-keyforce7204

    @low-keyforce7204

    4 жыл бұрын

    This comment is underated

  • @madandkrazy6109
    @madandkrazy61094 жыл бұрын

    "Yay...with teeth". That's how I'll express my excitement from now on.

  • @leavebroomformayo

    @leavebroomformayo

    3 жыл бұрын

    correct’o my friendo

  • @familyguyostrich7463

    @familyguyostrich7463

    3 жыл бұрын

    Yay 😬

  • @deepermind4884

    @deepermind4884

    3 жыл бұрын

    😁---"By the way, orange oil is flammable."

  • @Tubanapoleon
    @Tubanapoleon Жыл бұрын

    Came for a Vsauce video, stayed for the Numberphile video

  • @spacehunter2004
    @spacehunter20043 жыл бұрын

    0:39 therefore you can basically hold an entire reverse halo ring

  • @tacocat835
    @tacocat8353 жыл бұрын

    "it's called a napkin ring, because it looks like a napkin ring" ah yes, the floor here is made out of the floor.

  • @philipphaberland4810

    @philipphaberland4810

    3 жыл бұрын

    Or is it

  • @syitix

    @syitix

    3 жыл бұрын

    @Philipp Haberland nah it is

  • @anthonywentzel4717

    @anthonywentzel4717

    3 жыл бұрын

    It does look like a nr Duh

  • @Bry10022

    @Bry10022

    3 жыл бұрын

    Hmmm, Yes. The Napkin Ring here is made out of Napkin Ring…

  • @_tybpxbzn_1042

    @_tybpxbzn_1042

    3 жыл бұрын

    oi

  • @nirad8026
    @nirad80266 жыл бұрын

    0:50 *_Those are some lit dance moves you got there, kiddo_*

  • @gabevandevere7221

    @gabevandevere7221

    6 жыл бұрын

    I've never seen Vsauce like a comment before lol

  • @Innes1

    @Innes1

    6 жыл бұрын

    they obviously caught (on fire) his attention.

  • @isaiahkellogg9199

    @isaiahkellogg9199

    6 жыл бұрын

    Nirad802 hahaha

  • @Someone-cr8cj

    @Someone-cr8cj

    6 жыл бұрын

    Nirad802 ooooh love from the creator

  • @Kadz

    @Kadz

    6 жыл бұрын

    I laughed at this comment

  • @kartiklatthe7677
    @kartiklatthe76772 жыл бұрын

    "It is called 'napkin ring' because, it looks like a napkin ring" Perfectly explained, VSauce

  • @archonthewings3454
    @archonthewings3454 Жыл бұрын

    I love how intuitive he makes some of the concepts of trigonometry.

  • @phantomxyz_7171
    @phantomxyz_71715 жыл бұрын

    0:50 When Fly’s keep landing on you

  • @thewormholetv7228

    @thewormholetv7228

    5 жыл бұрын

    Legendary.😂

  • @Crispy656forever

    @Crispy656forever

    4 жыл бұрын

    Its gonna be buzzzzy *late reaction*

  • @DieWithRob

    @DieWithRob

    4 жыл бұрын

    LMAO

  • @onionvlogs5222

    @onionvlogs5222

    4 жыл бұрын

    Doesn’t matter how many times I see the 0:50 Time stamp I laugh

  • @ripspaz

    @ripspaz

    4 жыл бұрын

    🤣🤣🤣🤣🤣😭😭😭😭😭😭😭

  • @k_dawg9935
    @k_dawg99355 жыл бұрын

    0:50 when your mom makes pizza rolls

  • @leeryalt4237

    @leeryalt4237

    4 жыл бұрын

    Why has nobody replied to this?

  • @satyman08

    @satyman08

    4 жыл бұрын

    Hilarious

  • @chamibrosnetwork7043

    @chamibrosnetwork7043

    4 жыл бұрын

    I actually laughed out loud when I saw this comment

  • @twisted.karmaa

    @twisted.karmaa

    4 жыл бұрын

    K_Dawg 993 GENIUS

  • @CoasterChamp

    @CoasterChamp

    4 жыл бұрын

    Kakakakakakakakakakakakakakakakakakakakakakakakakakakakakakkakakakakakkakakakakakakakakakakakakkakakkaakakakakakakakakakakakakakakak

  • @bernice3887
    @bernice38873 жыл бұрын

    I like watching him and always learn something new and find the topics interesting. I learned 2 things this time with regards to the napkin ring video; how much algebra starts hurting my head eventually, and nothing at all.

  • @philc2729
    @philc2729 Жыл бұрын

    If I could I would superlike this video. Stunning realization visualized in such a clean way. Thank you Michael!

  • @balazs7235
    @balazs72353 жыл бұрын

    0:50 I expected Michael to dance exactly like that

  • @aedan9227

    @aedan9227

    3 жыл бұрын

    same

  • @moderbash9684

    @moderbash9684

    Жыл бұрын

    Shut up we all know you did it (also I'm not trying to be mean by this I'm just sayin' we al know ya' lyin') Edit:why now does it seem like "ya'"and" lyin'"seem like good signs in math.

  • @KWGTech
    @KWGTech6 жыл бұрын

    I've noticed a trend. You started with interesting, general science topics, mixing in a little philosophy here and there to capture the viewers attention. Now you're moving toward more technical, more applicable knowledge. It's almost like you're trying to educate us.

  • @user-ft4pb5vb3e

    @user-ft4pb5vb3e

    6 жыл бұрын

    Well, he's failing on those who don't already know it, and succeeding on those who do, which is redundant.

  • @tdub6542

    @tdub6542

    6 жыл бұрын

    KWG he is

  • @BogdanHarasymowicz

    @BogdanHarasymowicz

    6 жыл бұрын

    @Na Zhao: Anyone who finished elementary school should be able to follow a proof like the one in the video and all of the Vsauce content (he doesn't even assume the viewer knows the Pitagorean theorem). To keep the content interesting, Michael can't afford to assume the viewer is even less educated (like explaining what a square root is and such).

  • @collanchavez

    @collanchavez

    6 жыл бұрын

    true

  • @noahlipsky6547

    @noahlipsky6547

    6 жыл бұрын

    Does the pitagorean theorem come with tzatziki sauce or hummus in it?

  • @MollyTheUkulele
    @MollyTheUkulele2 жыл бұрын

    Long time fan! (~13 years) and I’m finally grown enough to have my own curiosity box subscription! (Just subscribed) thank you for half a lifetime of amazing content ❤️

  • @TheSTallINNA
    @TheSTallINNA Жыл бұрын

    I just found this channel, like a week ago and I love this guy

  • @Hawkmenn
    @Hawkmenn3 жыл бұрын

    this legitimately helped me with a 3rd year applied calculus final in my mechanical engineering degree. question asked about the volume of a napkin ring of the determined height and instead of going through complicated calculus to find the answer i just found the volume if a sphere of the "same height" --- Very cool of you Micheal !:D (with teeth)

  • @EliteTeamKiller2.0

    @EliteTeamKiller2.0

    3 жыл бұрын

    How did you get that one right when the volume of a napkin ring is (1/6)pi h^3, which clearly is not the volume of a sphere? You had to do something fairly clever. Please elaborate.

  • @Mr.D.C.

    @Mr.D.C.

    3 жыл бұрын

    @@EliteTeamKiller2.0 If you have a napkin ring of height h taken from a sphere with radius R, the volume of that napkin ring will only depend on h. So you can just let h = 2r, so that the height of the napkin ring is the same as the height of the sphere, so then no volume is cut out of the sphere. (Edit: typo)

  • @keeyandameen1688

    @keeyandameen1688

    3 жыл бұрын

    @@Mr.D.C. I'm too stupid too understand whatever you just stayed

  • @vega0727

    @vega0727

    3 жыл бұрын

    @@keeyandameen1688 if the napkin ring of a sphere is as tall as the sphere... The napkin ring is the whole sphere. There's no middle cut out.

  • @DarkSheep_

    @DarkSheep_

    3 жыл бұрын

    @@vega0727 I'm still confused ;-;

  • @Adomas_B
    @Adomas_B4 жыл бұрын

    Soap: kills 99.98 % of germs other 0.02%: 0:49

  • @ChristineWang

    @ChristineWang

    4 жыл бұрын

    this had me in tears i dont know why

  • @zfloyd1627

    @zfloyd1627

    4 жыл бұрын

    It would actually be 😱😱😥😥😭😭😭

  • @mateusleal5943

    @mateusleal5943

    4 жыл бұрын

    Watching it on 1.5x speed makes this even funnier

  • @sifiso5055

    @sifiso5055

    4 жыл бұрын

    😂😂😂

  • @zfloyd1627

    @zfloyd1627

    4 жыл бұрын

    LMAO

  • @Ascertivus
    @Ascertivus2 жыл бұрын

    The transition at 3:04 is one of the coolest that I’ve seen in awhile.

  • @aerodaan
    @aerodaan Жыл бұрын

    This math lesson brought me straight back to my school days. Thanks Vsauce

  • @oldred9122
    @oldred91226 жыл бұрын

    So, taking this to it's logical limit, does this mean the exact volume of any napkin ring is equal to the volume of a sphere with a diameter equal to the height of the ring?

  • @ZeldakingZ11

    @ZeldakingZ11

    6 жыл бұрын

    Well that comment was better than this whole video.

  • @MajkelKerman

    @MajkelKerman

    6 жыл бұрын

    Yes. Wow. The sphere is like a napkin ring with an infinitely small hole in it.

  • @Vsauce

    @Vsauce

    6 жыл бұрын

    yes! such a sphere is a 'napkin ring' with an infinitely narrow cylindrical hole through its center. Great for when you don't want your one-dimensional napkins to blow away.

  • @Corninthesky

    @Corninthesky

    6 жыл бұрын

    Vsauce lmao

  • @raybel322

    @raybel322

    6 жыл бұрын

    OldRed91 thats the smartest comment i have seen on youtube

  • @sneaks9150
    @sneaks915011 ай бұрын

    8:47 with teeth

  • @kevins9242
    @kevins9242 Жыл бұрын

    Hi Michael, 4 seconds from the video start and I’m smiling. I really enjoy your fun and informative videos. Than you!

  • @rocketeditor
    @rocketeditor6 жыл бұрын

    By the way, orange oil is F L A M M A B L E

  • @maxistired3325

    @maxistired3325

    6 жыл бұрын

    -patrick- *wOw*

  • @AntiNepotismAdvocate

    @AntiNepotismAdvocate

    5 жыл бұрын

    by the way, I'm a pyromaniac

  • @lelainemorato

    @lelainemorato

    5 жыл бұрын

    🅱️

  • @brandenbran

    @brandenbran

    5 жыл бұрын

    Is my orange juice flammable

  • @flamejuice9122

    @flamejuice9122

    5 жыл бұрын

    Yes

  • @oliveroates
    @oliveroates3 жыл бұрын

    0:50 when the invisible man whispers in your ear

  • @oliveroates

    @oliveroates

    3 жыл бұрын

    @maddy likes sloths thanks for replying to a 4 month old comment

  • @Amy-si8gq

    @Amy-si8gq

    3 жыл бұрын

    Bees

  • @russellmenezes3355

    @russellmenezes3355

    3 жыл бұрын

    I'm the one who gave you the 69th like, have fun.

  • @mariafe7050

    @mariafe7050

    3 жыл бұрын

    @@russellmenezes3355 Someone unliked it, but I liked it again! :)

  • @isuckatnamingthings5499

    @isuckatnamingthings5499

    3 жыл бұрын

    @@oliveroates hi

  • @sirpicklestien1436
    @sirpicklestien14363 жыл бұрын

    Really satisfying ASMR to play in background during tasks!!

  • @adityamishra7711
    @adityamishra77112 жыл бұрын

    Vsauce never stops to amuse me....

  • @connieulm9034
    @connieulm90346 жыл бұрын

    0:49 JESUS CHRIST MICHEAL CALM DOWN

  • @RandomVideos1411

    @RandomVideos1411

    6 жыл бұрын

    Hey dancing, Micheal Here.

  • @phoeben6291

    @phoeben6291

    6 жыл бұрын

    let him live

  • @cakeandicecream1582

    @cakeandicecream1582

    6 жыл бұрын

    Thank you, I can't believe I didn't notice that

  • @michaelc7014

    @michaelc7014

    6 жыл бұрын

    Michael*

  • @Obeliss

    @Obeliss

    6 жыл бұрын

    that's what I do when my fave song comes on

  • @Ryanhelpmeunderstand
    @Ryanhelpmeunderstand6 жыл бұрын

    1:32 “by the way, orange oil is flammable” 🤣

  • @ZepG

    @ZepG

    6 жыл бұрын

    heroperse. It was funny because of how Vsauce went off-topic, Tillamook wasn't denying orange oil is flammable. You seriously need to get a social life and learn how humans communicate with each other.

  • @abaxialo5878

    @abaxialo5878

    6 жыл бұрын

    ZepG He never said he was denying it

  • @wobbiewobbles

    @wobbiewobbles

    6 жыл бұрын

    Human Person *COMBUSTIBLE LEMONS*

  • @Ruthavecflute

    @Ruthavecflute

    6 жыл бұрын

    it sounds like dried orange peal might be a good fire starter. Probably more eco-friendly than lighter fluid for starting bonfires and BBQs.

  • @Hyrixous

    @Hyrixous

    6 жыл бұрын

    It came out of nowhere and was irrelevant to the video.

  • @notsuitcase
    @notsuitcase7 ай бұрын

    Such a great video! I love watching your content. So amazing! Keep it up Vsauce!

  • @seanmccaul3034
    @seanmccaul30348 ай бұрын

    Okay, I didn’t know what to expect from this video based on the title. This was awesome.

  • @sum9586
    @sum95864 жыл бұрын

    0:50 when your favourite song comes up in the party

  • @jlrjlr8053

    @jlrjlr8053

    4 жыл бұрын

    0:51 but now were talkin' about balls.

  • @onionvlogs5222

    @onionvlogs5222

    4 жыл бұрын

    AngleSum Doesn’t matter how many times I see the 0:50 Time stamp I laugh

  • @Quadrocephis

    @Quadrocephis

    4 жыл бұрын

    Octo Ringo I have here two napkin rings from very differently sized spheres

  • @keane6
    @keane65 жыл бұрын

    0:50 “I am an alpha male.”

  • @folly3288

    @folly3288

    5 жыл бұрын

    No, Sir. You're not an alpha male. You are considered to be a beta male. Just like Albano

  • @Andrew-gu8uw

    @Andrew-gu8uw

    5 жыл бұрын

    deadpoolbxm He didn’t say that tho

  • @qurimp6012

    @qurimp6012

    5 жыл бұрын

    Sicko mode

  • @Andrew-gu8uw

    @Andrew-gu8uw

    5 жыл бұрын

    yessir

  • @aidanfoley3263

    @aidanfoley3263

    5 жыл бұрын

    andrew 🤦‍♂️

  • @jpdalvi
    @jpdalvi3 ай бұрын

    A vsauce video with actual step by step math proof. Didn't remember at all about this one. Kinda different but quite the same as the others. I loved it.

  • @DMBVR4
    @DMBVR4 Жыл бұрын

    What if the smaller sphere has a proportionally much larger core taken out, while the larger sphere has a proportionally much smaller core taken out? I feel like the volumes would be massively different, unless i lost some information somewhere while thinking about flammable oranges.

  • @misha_stupidyttookmyname

    @misha_stupidyttookmyname

    Жыл бұрын

    Yes, this confused me too. I'd have to rewatch the video to be sure but i don't think he said anything about proportionally bigger cylinder for the bigger sphere. But i'm no good at math so maybe i'm missing something obvious

  • @silvermagpie1071

    @silvermagpie1071

    Жыл бұрын

    If the bigger sphere had a proportionally thinner core taken out, the napkin ring at the end would be taller than a proportionally bigger one. If a marble and the earth both had half their radius taken out, the earth would have more volume, but that's not the question were asking here. If you have any two napkin rings that are the same height, the bigger spheres will have bigger cores relative, which cancels out the wider radius

  • @jafetramirez7429

    @jafetramirez7429

    Жыл бұрын

    The only requisite for this to work is that both cylinders are the same height. If you want to take out a larger core, then you have to make the cylinder wider, but this also makes it shorter, so the two cylinders wouldn't have the same height and this property doesn't hold.

  • @FireBeam

    @FireBeam

    Жыл бұрын

    @@jafetramirez7429 Which means this is all stupid garbage math

  • @icystrangers5482

    @icystrangers5482

    Жыл бұрын

    It won't. You don't get to choose. You are constrained to a fixed napkin height.

  • @geremydunn4836
    @geremydunn48365 жыл бұрын

    0:50 me walking out of school on friday

  • @goned216

    @goned216

    4 жыл бұрын

    lul

  • @pradeepverse
    @pradeepverse6 жыл бұрын

    Nice transition at 3:04

  • @pigbenis4399

    @pigbenis4399

    6 жыл бұрын

    yeah that was pretty clean

  • @idly1549

    @idly1549

    6 жыл бұрын

    even this also at every topic

  • @robodoom24

    @robodoom24

    6 жыл бұрын

    Loved the vibraslap in the background, hardly anyone uses that instrument.

  • @natattacc99

    @natattacc99

    6 жыл бұрын

    IKR

  • @kainovember
    @kainovember Жыл бұрын

    First thing that allowed me to fall asleep for a moment tonight ✨️

  • @07gm
    @07gm2 жыл бұрын

    0:10 me: ... brain: dont say it me: ... *opera*

  • @mh6276

    @mh6276

    Ай бұрын

    What do you mean?

  • @justnoah2073
    @justnoah20735 жыл бұрын

    "It's gonna be busy. But right now we're talking about balls." - Vsauce, 2018

  • @mccreamyfan1239

    @mccreamyfan1239

    4 жыл бұрын

    Omg actually 2017 mate

  • @v0id_d3m0n

    @v0id_d3m0n

    4 жыл бұрын

    And -hard- coring ( ͡° ͜ʖ ͡°)

  • @tikkidaddy

    @tikkidaddy

    4 жыл бұрын

    Ouch!😂

  • @jessetheademan7087
    @jessetheademan70874 жыл бұрын

    *is discussing napkin rings* “By the way, orange oil is flammable” *continues discussing napkin rings*

  • @ahmed38247

    @ahmed38247

    3 жыл бұрын

    for real lmao, it's bizzare

  • @BrendonGreenNZL

    @BrendonGreenNZL

    3 жыл бұрын

    Yes, that's completely out of character for him. I was expecting a complete change of topic at that point 😞

  • @3l1t355
    @3l1t355 Жыл бұрын

    these shows are brilliant.

  • @charleswilson8975
    @charleswilson89752 ай бұрын

    For a second, I thought the solar eclipse mentioned at the end of the video was talking about the one about to happen in a few days, not the one that happened years ago. That was a bit weird lol

  • @Djenx-
    @Djenx-4 жыл бұрын

    This is a McDonald's drive through, Sir.

  • @verlax8956

    @verlax8956

    4 жыл бұрын

    *or is it?*

  • @MDHUSSAIN-li6pm

    @MDHUSSAIN-li6pm

    4 жыл бұрын

    Verlax noice!

  • @copter7013

    @copter7013

    4 жыл бұрын

    What if I make a burger and a fry a napkin ring? They would have to pay the same price

  • @RealMudSkipper

    @RealMudSkipper

    4 жыл бұрын

    this comment made my day @djenx CR

  • @dguy0386

    @dguy0386

    3 жыл бұрын

    I'll have a quarter pounder with fries and a medium Dr pepper please :P

  • @nauseaqueen
    @nauseaqueen6 жыл бұрын

    I really just want to know how he peeled that orange.

  • @javierolive105

    @javierolive105

    6 жыл бұрын

    kellieveltri magic

  • @parthpatel0012

    @parthpatel0012

    6 жыл бұрын

    with a napkin ring :)

  • @simonkimberly6956

    @simonkimberly6956

    6 жыл бұрын

    A knife

  • @dyl4nftp

    @dyl4nftp

    6 жыл бұрын

    he use his maths squared

  • @zfloyd1627

    @zfloyd1627

    4 жыл бұрын

    Black magic

  • @harrypogger5285
    @harrypogger5285 Жыл бұрын

    nothing like going back and watching Vsauces old videos

  • @pestilencetheplague7646
    @pestilencetheplague76462 жыл бұрын

    that shot of Michael dancing at brain candy live gives me life

  • @modocrisma2
    @modocrisma24 жыл бұрын

    This was the most interesting surprise math lesson I’ve ever had.

  • @schrutebuck

    @schrutebuck

    4 жыл бұрын

    (You heard a something rustling in the bushes) (It jumps out at you!) (it’s a surprise math lesson!) “ hey! Vsauce, Michael here “

  • @krashsytegaming9222

    @krashsytegaming9222

    4 жыл бұрын

    Modocrisma its actually geometry 9th grade 😉 im in 10th grade lmao soo

  • @halamadruuid2380

    @halamadruuid2380

    4 жыл бұрын

    KrashSyteGaming wait what? Are you in america? In my country we learn it at 7th grade

  • @neme7895

    @neme7895

    4 жыл бұрын

    Ikr, that's amazing, and somewhat useless in normal life means.

  • @josephpaterson8274
    @josephpaterson82746 жыл бұрын

    0:50 when u got a spider on u

  • @Boss-vd6di

    @Boss-vd6di

    5 жыл бұрын

    A M A Z I N G

  • @BMeiome13

    @BMeiome13

    5 жыл бұрын

    No one like this comment! That's an *ORDER!* Keep it like that ♋♋♋

  • @tarunchandra2865

    @tarunchandra2865

    5 жыл бұрын

    ☠️☠️

  • @onlisexyt

    @onlisexyt

    5 жыл бұрын

    Yea

  • @velocelot1652

    @velocelot1652

    5 жыл бұрын

    Damn you.... lol

  • @TorrentialSilver_47
    @TorrentialSilver_47 Жыл бұрын

    It’s interesting how Vsauce can make i video where even if I have a 1st grade education, I’d be able to understand almost everything

  • @mantacid1221
    @mantacid122111 ай бұрын

    I saw this video a long time ago but never forgot it. Now I’ma math tutor and I bring it up with my students every so often. Although I did forget this version of the explanation, and so I’d have to use calculus to prove it, which I imagine must have confused the younger kids.

  • @deiadied
    @deiadied4 жыл бұрын

    I want Michael to be my uncle and bring up these crazy facts at the dinner table.

  • @superidol4670

    @superidol4670

    3 жыл бұрын

    Dinner table forever

  • @babybeans1477

    @babybeans1477

    3 жыл бұрын

    Doesn’t everyone?

  • @lahavgafni2642

    @lahavgafni2642

    3 жыл бұрын

    I want Michael to be my uncle and do what mine does to me daily ;)

  • @thememeguy2135

    @thememeguy2135

    3 жыл бұрын

    @MarsoloX hey Vsauce! Michael here, what happens when a male reproducts with another male?

  • @iva837

    @iva837

    3 жыл бұрын

    I'm the crazy uncle

  • @apple3217
    @apple32176 жыл бұрын

    0:50 is the reason why I subscribed to Vsauce

  • @JManK113
    @JManK1139 ай бұрын

    "but were talking about BALLS"

  • @jakel.1724
    @jakel.1724 Жыл бұрын

    Idk how or why but this is actually the only algebra whatever I’ve understood. The sticker stack part of that really helped me visualize what was going on

  • @Yellow_Slug
    @Yellow_Slug4 жыл бұрын

    0:50: 4 year old me explaining how to beat someone in a fight.

  • @brynn3310

    @brynn3310

    4 жыл бұрын

    Yellow Slug w h e e z e

  • @Yellow_Slug

    @Yellow_Slug

    4 жыл бұрын

    Brynn C Is this sarcasm? (=

  • @brynn3310

    @brynn3310

    4 жыл бұрын

    Yellow Slug No....or is it? *vsauce music starts to play*

  • @glowingspacecow8980

    @glowingspacecow8980

    4 жыл бұрын

    “It’s gonna be busy.”

  • @QuicksolutionsOnline

    @QuicksolutionsOnline

    4 жыл бұрын

    PUNCH PUNCH PUNCH JUST PUNCH👊

  • @Cerrios
    @Cerrios3 жыл бұрын

    The most interesting part is thinking bout how he PEELED THAT FREAKIN ORANGE

  • @Thaction

    @Thaction

    3 жыл бұрын

    He probably used some kind of cookie-cutter or metal cylinder, because it didn’t seem peeled by a knife, unless he delicately pierced it first.

  • @piediepaab6837

    @piediepaab6837

    3 жыл бұрын

    Maybe that perfect peel is from another orange that he totally messed up 😄

  • @csatacsibe

    @csatacsibe

    3 жыл бұрын

    you cut the two circles to the peel, you pierce the peel from one of the circles to the other with a needle, push a small metal wire through the hole and pull it anround the orange.

  • @robertkinslow8953

    @robertkinslow8953

    3 жыл бұрын

    With his girlfriends tongue?

  • @CoolGamerGuyWhoMakesMusic
    @CoolGamerGuyWhoMakesMusic9 ай бұрын

    I dont know how but this man manages to make the most mundane things interesting

  • @sam_2alexander480
    @sam_2alexander4803 жыл бұрын

    This idea and the math just blew my mind

  • @arkhamsans3541
    @arkhamsans35416 жыл бұрын

    "Hey, Vsauce, Michael here." We were the Vsauce all along.

  • @dickmeatbootysack2165

    @dickmeatbootysack2165

    6 жыл бұрын

    Arkham Sans I noticed that not to long ago

  • @PekaCheeki

    @PekaCheeki

    6 жыл бұрын

    Michael confirmed dis

  • @zoeytrent115

    @zoeytrent115

    6 жыл бұрын

    Lol

  • @jaystarr6571

    @jaystarr6571

    6 жыл бұрын

    Here Vsauce. Hey Micheal.

  • @IfYouMeetAWolf

    @IfYouMeetAWolf

    6 жыл бұрын

    That took ya'll a while. Welcome.

  • @KitaFr
    @KitaFr6 жыл бұрын

    *BTW ORANGE OIL IS FLAMMABLE*

  • @Focusedone-yr9ci

    @Focusedone-yr9ci

    6 жыл бұрын

    DomAllStar is I'm going to go to school and bring an orange put it on a tAble then point at it and shout look out a bomb

  • @MYNAMACHEF

    @MYNAMACHEF

    6 жыл бұрын

    Vsauce, arsonist here

  • @qqqqqqqqqq7488

    @qqqqqqqqqq7488

    6 жыл бұрын

    Focusedone2325 not recommended

  • @schroonsjozef

    @schroonsjozef

    6 жыл бұрын

    Was looking for this

  • @RMJ1984

    @RMJ1984

    6 жыл бұрын

    Random!! fact.

  • @Coldplay_Covers
    @Coldplay_Covers8 ай бұрын

    I know it’s too late at night when I decide to watch a VSauce video. Nothing again you Michael, I just never wanted to do anything with math again in my life, and yet I somehow always end up back here.

  • @kingo_clubs9097
    @kingo_clubs9097 Жыл бұрын

    Let's say you're sitting at a table during a dinner party. Nobody has touched their utensils yet. Now, do you take the napkin ring on the left, or the napkin ring on the right?

  • @acertainkirakuin

    @acertainkirakuin

    Жыл бұрын

    M-Mr. President?

  • @rosinros

    @rosinros

    Жыл бұрын

    right because im right handed

  • @RafaelMunizYT

    @RafaelMunizYT

    Жыл бұрын

    none because the parties I go to probably don't have napkins let alone napkin rings

  • @Odog-Tbone
    @Odog-Tbone4 жыл бұрын

    Me: *Closes eyes in class* 3:05 Me: *Looks up* 8:45

  • @ripspaz

    @ripspaz

    4 жыл бұрын

    😭😭😭😂😂😂🤣🤣🤣🤣🤣🤣😭

  • @ripspaz

    @ripspaz

    4 жыл бұрын

    Why does this have no likes it's golden

  • @Odog-Tbone

    @Odog-Tbone

    4 жыл бұрын

    Nathan Escobedo thanks, I have no idea 😂👍

  • @kosmic_overlord

    @kosmic_overlord

    3 жыл бұрын

    it also sounds like he says "let's calculate area.... with teeth"

  • @nabongobong9155

    @nabongobong9155

    3 жыл бұрын

    Can relate 😂

  • @omega_jay4355
    @omega_jay43556 жыл бұрын

    "oh btw orange oil is flammable" 😂😂

  • @srepahzatulzzz9610

    @srepahzatulzzz9610

    6 жыл бұрын

    Yeah we watched the video too

  • @stanley7598

    @stanley7598

    6 жыл бұрын

    H A N N A if you're cross about something don't take it out on random commenters...

  • @dolphinboi-playmonsterranc9668

    @dolphinboi-playmonsterranc9668

    6 жыл бұрын

    Omega_ Jay I learned that from cocktail videos lol

  • @hoonteri1760

    @hoonteri1760

    6 жыл бұрын

    kzread.info/dash/bejne/pYx6l9iug9ewhps.html

  • @mementomori6838
    @mementomori68382 жыл бұрын

    You make math fun and understandable for me again

  • @rivalifritdarc2481
    @rivalifritdarc24812 жыл бұрын

    I don't believe it Vsauce's video with no existential crisis

  • @viviandarkbloom172
    @viviandarkbloom1725 жыл бұрын

    *”yay...... with teeth”* 😂

  • @jacobe.1651

    @jacobe.1651

    4 жыл бұрын

    *"But what's does this mean for you?"*

  • @WhatifAlyssaActually
    @WhatifAlyssaActually6 жыл бұрын

    the fact that he used a pen and made no mistakes

  • @ryanoceros9382

    @ryanoceros9382

    6 жыл бұрын

    Alyssa Martinsen or did he? *Vsauce music kicks in*

  • @hanakibret3389

    @hanakibret3389

    6 жыл бұрын

    The Round Earth Society *did

  • @savannaobregon3823

    @savannaobregon3823

    5 жыл бұрын

    His math skills are the tea

  • @patrickhodson8715

    @patrickhodson8715

    5 жыл бұрын

    You’re really gonna sit there and tell me the teeth on the “yay” face weren’t a mistake...

  • @ashmeetnar

    @ashmeetnar

    5 жыл бұрын

    You use a pencil for maths?

  • @trickvro
    @trickvro3 жыл бұрын

    9:36 The view of the eclipse from "Organ" was amazing.

  • @Owen_loves_Butters
    @Owen_loves_Butters9 ай бұрын

    And actually, if you go through all the calculus (which I did because calculus = fun), or if you just make the insight that h=2r if the height of the napkin ring is the same as the sphere (and therefore the same volume), you can find out pretty easily that the formula for the volume is simply (pi/6)*h^3.

  • @senif684
    @senif6846 жыл бұрын

    Everyone in the comment section saying "i learned this in 8th grade" or "this is pretty much high school geometry" while I'm here like "what the actual fuck is a napkin ring?"

  • @johncarter3797

    @johncarter3797

    6 жыл бұрын

    Its a ring you put around a rolled up cloth napkin to keep it rolled up.

  • @GJuice

    @GJuice

    6 жыл бұрын

    John Carter LOL

  • @Reploidx9

    @Reploidx9

    6 жыл бұрын

    It's the ring to keep napkins looking all fancy and such. You know, when you go to those high-end, expensive as fuck restaurants.

  • @julianmelillo

    @julianmelillo

    6 жыл бұрын

    Senif Your not alone Wtf is a napkin ring Until I looked at comments

  • @bothriolepis6744

    @bothriolepis6744

    6 жыл бұрын

    That is literally the only thing i understood about this video.

  • @cup_check_official
    @cup_check_official6 жыл бұрын

    Vsauce uploaded. Or did it? *Vsauce music kicks in*

  • @kabirahmed5808

    @kabirahmed5808

    6 жыл бұрын

    😁😀

  • @silversurf9831

    @silversurf9831

    6 жыл бұрын

    jesus christ you are everywhere :D

  • @DarthLore00

    @DarthLore00

    6 жыл бұрын

    Tell Me This *he

  • @Wilker_uwu

    @Wilker_uwu

    6 жыл бұрын

    Jace Chudnow music, actually

  • @DragonYeng

    @DragonYeng

    6 жыл бұрын

    Is math related to science ?

  • @Hackerisitic
    @Hackerisitic Жыл бұрын

    Wow you really made me understand this concept (which is not in my syllabus) before my geometry exam.

  • @alexalitton7148
    @alexalitton714810 ай бұрын

    Sometimes i wish micheal was my science teacher

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