The Galton Board

[@spencergerwing7946]

"if you have a pulse, and are breathing, I think we can all agree that binomial powers are one of your favorite things". I love michael

[@jazzieman9687]

Sorry dude he is already married.

[@negg7046]

jazzie man it wassa joke.

[@PostModernToast]

r/whooooshception

[@Azuriiee]

omg 666 likes when i commented this

[@Azuriiee]

@@PostModernToast wooooosh not whoooooosh

[@anti_MATT_er]

Vsauce video: Beginning and end: meme material Middle: content

[@DogBeef]

balls are a common theme on this channel

[@osimmac]

balls are a common theme in this entire universe ( ͡° ͜ʖ ͡°)

[@tenma628]

( ͡° ͜ʖ ͡°)

[@Nikola95inYT]

Michaels toys

[@jellejoo]

you can't have a DONG without balls

[@Jumulmer]

1.5mill balls reveal

[@magnusthomsen2309]

Vsauce is like the cool teacher at school

[@ismailzulqarni4977]

I had a teacher like him last year, I honestly have a feeling he watched Vsauce

[@bolson42]

He IS the cool teacher at school

[@ViratKohli-jj3wj]

But what is a cool? (Vsauce music intensifies)

[@BigSkyCards23]

But, what is a school?

[@playmaker.3596]

@@BigSkyCards23 what is a teacher

[@iBuyNewStuff]

Well I didn't know that the diagonals were Fibonacci. Gosh darn Pascal you rascal. He got me again.

[@SomeRandomDude821]

also, each row is 11^n, where n is the row. 11^0 = 1 11^1 = 11 11^2 = 121 11^3 = 1331 11^4 = 14641 (for 5+, if the number is 10, add 1 to the previous cell) and the sum of the numbers in each row is 2^n

[@eigenbasis4482]

There are hundreds of patterns one can find in pascal's triangle.

[@dkw9525]

@@SomeRandomDude821 Thank you!

[@upsidedownChad]

Lmao

[@Zelchinho]

Any bonus bonus bonus juice me beach juicers here? And say nothing! Putrid! Shameless!!

[@mrcomp1971]

I feel like michael is becoming more and more aware of the meme culture surrounding him.

[@darkfire2937]

He's always been a meme.

[@calinmihai2934]

mrcomp what made you feel that?

[@icebread9335]

mrcomp that's partially why he is great :D

[@Super.AmmarI0]

Have you seen the h3 podcast with him on? He literally admits that he likes being a meme.

[@mrcomp1971]

Prime Number Theorem I've seen it yeah. But his videos at the time had a way more serious tone to it if that makes any sense.

[@Jombo1]

ok but why the spooks :(

[@dchsj]

randomness

[@ThomsBP]

I’m guessing it’s a reference to the joke of normal and paranormal distribution

[@jonathanthompson4734]

Thank goodness someone else saw them

[@lulf1304]

Why tho

[@RusZugunder]

what spooks?

[@itsastikbotparty8149]

knock knock knock knock knock knock knock knock knock knock knock knock "whos there?" fibbonaci

[@daffy6489]

ItsAStikbotParty! Jacksfilms

[@dumbblondehairbrush]

@Slap Happy Pappy imagine caring about what other people comment on

[@getintheoven5515]

@@dumbblondehairbrush imagine

[@ItsRubyGD]

@@dumbblondehairbrush ikr that would be crazy, imagine if you did that

[@xr.3102]

@@Samm-vf6ti cry harder

[@wyattc6572]

dude its one in the morning and the intro jumpscare was not okay. specially without an explanation.

[@dashiellleigh6137]

i know right

[@attoblaze3395]

*happy tones continues* Micheal's Toys

[@sahidcm]

And there was one at the end as well which I wasn't expecting

[@jubooty27]

Correct

[@beyse101]

The "normal" Michael never came out of that isolation chamber

[@Riftley]

Proof Michael is actually Tim from Grand Illusion.

[@azaz129]

Toys from the Nile.

[@rafaeligmpraciano4123]

Is this a conspiration

[@121dan121]

Heh

[@supernovatryceratops6026]

Yes definitive proof

[@jkrai9684]

No he is How2Basic

[@zeldamax4741]

The intro is one of the best I ever saw. The music, the random jump scare, you can see him standing still in the reflection of the glass. I love this kind of humour.

[@aidenrobinson495]

I think the music comes from the soundtrack of a ps3 game called Eufloria.

[@karineaudet6270]

He is awesome. Heal all sadness... Hes incredible. Smart. Funny. Thanks. Keep up.

[@frenchvanilla343]

When he revealed Fibonacci’s sequence I lost it.

[@eugenesagan212]

TheMysteryMan spoiler

[@brianwalendy3735]

Black, Then White are All I see In my infancy Red and yellow then came to be Reaching out to me Let's me see There is So Much More that Beckons me To look through to the Infinite possibilities

[@cloudyo_o2792]

Same

[@KSR3]

the what sequence

[@davidholmes2932]

@@KSR3 *chuckles in high school math*

[@lawrencecalablaster568]

Why you gotta scare me like that, Michael?

[@spiritwatcher8880]

No replies on this comment ? Only me ?

[@JJTheDev]

Check the description : starring Hannah... Guest appearance : Micheal Stevens (I'm on my phone I can't check it. It's probably different) Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

[@NorwayDuck]

JJ The θwθ You can't read the description on your phone?? Wtf

[@JJTheDev]

NorwayDuck while typing, I don't want to have to go back and then find this comment again

[@NorwayDuck]

JJ The θwθ Ah, gotcha.

[@rachelmorrow9042]

It's so fun to just watch Michael talk about something he's interested in.

[@ultravidz]

Wish I knew that binomial trick in middle school

[@Catmomila]

AlphaOmega why tho

[@Whovian1029]

Yeah, that was awesome!

[@adaptiveplexus]

cnow can I use this for the lotto?

[@zyadmohamed5360]

I am at middle school tho /:

[@hakivin]

I knew it when i was in high school

[@bondfool]

Michael’s passion for educating is so heartwarming.

[@MrWazzup112]

Living meme/legend

[@AnimeLawyers]

Imagine the one timeline where all the balls fell down the same path while filming this

[@benthomason3307]

they'd just do a second take.

[@conifyre]

Ben Thomason But there would also be that one universe where both takes would go down the same path.

[@benthomason3307]

@@conifyre then do a third take, duh.

[@AnimeLawyers]

@@benthomason3307 You don't get it, there exists a universe where every take will make them all fall in the same path. Is your plan to just keep recording until the end of time?

[@mbrusyda9437]

@@AnimeLawyers there may exist universe wherein quantum mechanics was never developed because all coin flips resulted in heads

[@soltanikian]

We literally were forced to learn everything in this video in algebra. It was so confusing. If only this vid was out back then

[@Shampoid]

Have you ever watched a vsauce episode

[@CaveyMoth]

This video reminded me of when I used to be smart.

[@larlwheezer2334]

im in algebra 2 honors right now why didnt they teach me pascal's triangle and binomial expansion like this

[@facebook9yearsago646]

I know what he is talking about, but I have no idea what kind if scenario would make the last equation useful.

[@larlwheezer2334]

@@facebook9yearsago646 its used in economics and architecture usually, and also apparently its used to distribute ip addresses or something like that

[@villand2235]

Also, the sum of each row equals the corresponding power of two. For example, the 4th row is 1+4+6+4+1 which equals 16. 16 is also equal to 2 raised to the fourth.

[@SimplyMavAgain]

It feels great to watch a Vsauce video about something you already knew and understood and still learn something new.

[@muhammedhussain8090]

Yes!!!

[@jaidynbelbin4863]

This is utterly beautiful.

[@jamesjackson3810]

less beautiful when you realise its named after the father of eugenics but

[@StickMaster500]

Is this The Ring sequel?

[@AarPlays]

For those wondering why this comment is relevant, watch the entire video.

[@kieubasiarz]

Can I see your subs list? Would recommend you some channels.

[@fykz489]

What is wrong with you and justin wtf

[@StefanST]

I saw exactly the 1.100.000 subscribers!!!!

[@pategustavo4392]

StickMaster500 hai boss!

[@ericli4948]

7:10 me during my school presentation in front of my whole entire class

[@HYDO.0]

🤣🤣

[@aidenr3310]

XD

[@small_SHOT]

lmao 😂

[@catwithshotgun1571]

Confusion is coming tho...

[@equaius893]

a- uh eh- uh

[@StefanST]

Got a mini heart attack at the beginning thanks to Michael's toys... 😂

[@calinmihai2934]

Stefan ST i got a mini heart attack at the ending

[@tenma628]

nah didn't scare me at the beginning or end, but i got to say i wasn't expecting that!

[@brandonmohammed9092]

same. anyone know who it is tho?

[@RaoDGuitar]

Brandon Mohammed I think it's Hannah Canetti. Just a wild guess though.

[@outsidethepyramid]

what was the point of that woman at the beginning?

[@matthewjamestaylor]

Stats professor here. . . hey, you're giving away all my best magic tricks. Stop it. Okay, just this once. Cheers.

[@cynthiaaaa5204]

Matthew Taylor Curiosity here. Would you mind showing me the long hand version of how (x+y)^4 gets to the answer he gave? I don't doubt his accuracy, I just would like to see it done so I can wrap my mind around it.

[@matthewjamestaylor]

You start by multiplying x+y by x+y taking each element in the multiplicand and multiplying those with each term in the multiplier (x times x, plus x times y plus y times x plus y times y - AKA FOIL, firsts-outers-inners-lasts). You take that product and multiply that by x+y. Then that product by x+y. After combining terms you get the distributed form of x+y to the fourth. What he showed. Need a big whiteboard to show my work, sorry.

[@linsleyboxill6863]

Matthew Taylor You just got some free education my friend and he wasn't even paid for it. World needs more teachers like this

[@andvil01]

When I worked as a math/science teacher in highschool, I showed Pascals triangle to tie different parts of math together. Binominals, combinatory, distribution, Fibonacci numbers, golden ratio. All in one figure. Now I work as a brewer. Less students, still alot math, chemistry, biology and physics.

[@wooferjr169]

I take statistics and that triangle thing looked familiar.

[@JWhitePWC]

Me: “The Galton Board can also be called a quincunx.” Friend who wasn’t paying attention: “What did you just call me?”

[@johnballentine8915]

Lol, I miss the soundtrack from Vsauce. It's the only thing missing from DONG.

[@ericstoverink6579]

Actual DONGs have been missing from DONG for quite some time.

[@gabechristian2022]

Petition to make Michael a new email so he can log back in to vsauce

[@kooshades25]

What’s dong? Never heard of it never existed.

[@diptipanat793]

What's DONG?

[@CaveyMoth]

Or is it?

[@steliostoulis1875]

I like numberphile's new Professor.

[@red__guy]

He's the lost brother of the blond one.

[@gryphon885]

t's interesting to see VSause do a video about something that we are currently working on in my Math class. It's quite cool, honestly.

[@pka696]

smh thats right, same here lol

[@willbe_human]

I wonder what my friends and family would think of me if they knew how excited I get every time a channel called "DONG" uploads

[@BluntforceJ]

They'd probably think you're a real quincunx.

[@frama1122]

Imagine they click on the past couple of vids to just see balls, density balls, small balls, big balls... Just... Balms

[@rafaeligmpraciano4123]

The dong expands

[@Supergn0me]

I feel like Michael is going to wake us all up from the Matrix one day.

[@uwuifyingransomware]

The December Challenger

[@johnsalamii]

and now that has an entire different meaning lol

[@LoganSlinkard]

He all ready did

[@jehugarcia]

noooo! Why Am I Watching a video about math and not hating it?

[@zer0bre]

Why would you?

[@reenapandey8433]

jehugarcia becos u r not asked to solve questions

[@LucasGarrow]

Hi jehu!

[@maximthefox]

The combination of performance enthusiasm and occasional phrase like "ooh this is going to be fun"

[@RuLeZ1988]

Renna Pandey No, its because of the way it is presented. His fascination for it, which drives him, catches you.

[@bendingsands87]

I'm curious to know how the result would look if only one ball were falling at a time without other balls behind it forcing it down. It is videos like this that can make kids fall in love with math. It is amazing the things you can predict with math.

[@joaoliduario]

I had the same thought. And they are not falling from exactly the same spot.

[@tsaszymborska7389]

Exactly. The opening should be narrower. But then it would often be clogged, so this is probably the best compromise.

[@brucebeverly2629]

bendingsands87 - You may see it in the Plinko pricing game on the TV show "The Price is Right." Drew Carey, the host, always instructs the contestant to drop only one puck into the pegs at a time. Interestingly, contestants choose differing drop points while trying to find the "lucky" spot. If they understood the normal distribution, they would only drop the puck from the center position directly above the $10,000 (highest) result.

[@EpicFishStudio]

and what interests mathematicans? questioning why all this works like it does, why would it be arbitrary...

[@vakusdrake3224]

If anything you ought to expect things to look more like a normal distribution without other factors like the balls hitting each other and messing with things.

[@vofenn]

Wasnt expecting the jump scares in the beginning and the end o...o

[@whatonearthamito]

Yeah. What was with that?

[@Wyvernnnn]

It's just Michael getting weirder and weirder. He's beginning to trust us so he's revealing his true nature.

[@davidcook4823]

Normal and paranormal

[@Geheimnis-c2e]

I wasn't expecting the jumpscare at the beginning but it kind of made me aware of how Michael will do the ending so I was ready for it. I was right.

[@marianafiorin8703]

I dont like those and im making it very clear

[@gdnautilus9075]

When your friend Galton is bored

[@luminousfractal420]

unfortunately when francis galton got bored he spent his time trying to wipe out the general public. galton was a eugenicist :/

[@Datboichannel]

nah my friend is called xuincunx

[@ninadmilindjoshi]

Hey Dong, you have missed that Pascal's Triangle also gives powers of 11. Starting from the 0th Row, 11^0 = 1 11^1 = 11 11^2 = 121 11^3 = 1331 And so on...

[@RAyLV17]

doesn't work after 11^5

[@simone3042]

Ninad Joshi tartaglia

[@garx0]

Rafay Alvi it works if you substitute numbers from triangle instead of digits in another representation of decimal number: 1*1000+3*100+3*10+1=1331=11^3 1*100000+5*10000+10*1000+10*100+5*10+1=11^5 or do transformations: 1,5,10,10,5,1 ->1,6,0,10,5,1 ->1,6,1,0,5,1 161051=11^5

[@LudwigvanBeethoven2]

Base 10?

[@Quasarbooster]

One could say he implicitly covered it since 11^n = (10+1)^n

[@MrPoeTrolling]

I wish he can be my teacher

[@евграфломов]

he cant. he is just a person who is interested in scince the same as you. correct me if i have a mistake) Eng isnt my 1st language

[@NationalPK]

Андрэ Баханов I forgive you (sorry for Anglish)

[@SilvonYT]

You like math? I thought you were more into Poe-a-tree.

[@евграфломов]

National Pornographic lol thanks

[@Alaska1925]

could*

[@NataliePate]

I think I saw a Japanese ghost there. From a haunted Pachinko perhaps? Some kind of warning?

[@Tinyflower1]

yeah that sh't scared me..

[@jongyon7192p]

Quantum effects on Michael?

[@666Tomato666]

> haunted Pachinko yeah, after Konami started killing its franchises using pachinko machines, they are roaming the world

[@Moon8241113]

that scared me to

[@Aakraos]

I just love how Micheal goes, at every mathematical/phisical/scientific thing "Oh oh oh, alright this is gonna be suuuuuperfun" AND THATS ACTUALLY SUPERFUN

[@the_real_Kurt_Yarish]

There were diagrams of Pascal's Triangle in several of my math classes back in High School, yet not once was I ever taught what it was or what it tells us. At least, not to any note-worthy degree. Thanks, Michael, for filling in where the education system did not.

[@EarthScienceEnjoyer]

Kurt Yarish education system in my highschool covered it in first month

[@KimonoSuki]

I'm a freshman in highschool rn and we covered it pretty much straight away in my Algebra 2 class

[@leardvr]

I'm with you Kurt, I learned it when I asked one of the kids in class how he was getting the answers so easily. He told me his engineer dad should him. I wrote it down for test and went from a D to a B.

[@samueljackson3512]

Piggy and Bunny You used it for binomials?

[@leardvr]

Samuel Jackson just like Michael showed. Solving for "to the power of" FOIL works for to the power of 2, but larger then that it confused me. That was 30 years ago. In my line of work I used trig and geometry not algebra. Which is good, because I hated algebra.

[@LolForFun422]

This brought back so many memories from high school maths... Thanks for the throwback Michael! Great video!

[@hiimapop7755]

Michael is returning to his original state 6 years ago. Ps: Michael please don't shave that majestic beard of yours.

[@dhruvdakshgargi]

Spoke too early lol

[@BlielPol]

Oh boy, did he listen!

[@LionsYouth]

One of my all time favorite videos on this channel. Thanks Michael and thanks to the whole crew. You guys are awesome!

[@joeyebeling7681]

That's crazy! A natural way of finding the coefficients of powered binomials is mind blowing. I had no idea about this. Does this mean that if we did this triangle in 3-dimensions that we would be able to find the coefficients of a trinomial? None of your videos has every made me this excited. Thank you!

[@abhishekmewar671]

Any trinomial can be further categorised into a binomial for instance.(a+b+c)^n=(x+c)^n; x=a+b; and so on. And as far as a triangle in 3D is concernedit would be a pyramidal shape with each of the four planes along the sides would be represented by a Pascal triangle consisting of the combination of one of the ordered pairs of (x,y),(y,z) and (z,x)

[@treees420]

Abhishek Mewar don't you mean a triangular prism?

[@ethanjensen661]

Yes! It's called Pascal's tetrahedron. I came up with a way of finding coefficients at any triangle layer

[@Sollace]

What the hell was that at 10:30!?

[@robertkiss2350]

It was randomness.

[@Monkey-l8s]

Also watch the Galton board

[@Monkey-l8s]

And he might have flipped the black board over

[@Monkey-l8s]

Which had his wife

[@Sollace]

Huh. Now I see it. I slowed it down an it definitely looks like the back of a woman. Before I just saw something that looked like a gorey mophead creature.

[@aherprasad]

Pewdiepie- MEME REVIEW👏👏 Vsauce- Michael's Toy Reviews.

[@widescreenproductions9346]

Prasad Aher how dare you compare these two

[@santerirautamaa9479]

Pewdiepie, aka. Felix and Michael are both quite awesome. Chill, intelligent guys and both very entertaining. :)

[@mattygmtg9755]

pen island

[@jesusthroughmary]

5:50 Going along fine, thinking, "this video is OK" 6:00 YOU DEMON, YOU SORCERER

[@madmanpecos]

What?

[@JustinY.]

You almost gave me a heart attack from that intro

[@jeffreycanfield1939]

You give me a heart attack every time I see you. Get off KZbin for a couple minutes, plz

[@thorhagen295]

Justin Y. I have seen you all over the internet today 😂

[@thorhagen295]

Sayori i was going to sat that

[@Jakallax]

One day he’ll go blind from watching so many videos

[@brecknichols3010]

First idubbbztv2 now this

[@fen4554]

Mathematics summons information out of ether.

[@EtherBotGames]

you called?

[@arkaus8888]

Luminiferous aether

[@grandolddrummer]

Not really. Mathematics kind of IS the ether. All of the math that exists wasn't created; it was discovered. The structure of our universe caused mathematics to be the way that it is. It's been there all along waiting for someone to find it. There's plenty more out there too.

[@gabrielabraga7624]

^ Yep

[@vc2702]

Its crazy thats how most of us were taught at school. And that makes most math boring as hell. They teach us the math with out teaching us how and why they got the math problem. If teachers did it the other way around im sure most kids would think of math as fun and interesting.

[@ImSkully]

so are we not going to talk about the awkward way he holds a marker to write on the board

[@sarahkrzywicki1886]

Skully I would guess he's keeping his hand out of the way of what he's writing.

[@ZomBeeNature]

It's so secret that, if we talked about it, then someone would have to eliminate us... 😳

[@connortoenail]

Maybe so he doesn't erase his hard work with his palm

[@connortoenail]

These are all good guesses fam

[@HuyV]

How else would you hold it? Look at every teacher ever holding chalk to write on a blackboard. This is a black board using some more modern type of "chalk". Why would anyone hold differently...

[@shawnbrando6145]

“Out of chaos, comes order” . Great closing, Michael!

[@ignemuton5500]

*leaves math lesson to watch Vsauce, Michael does a math lesson* gg

[@UnderscoreZeroLP]

yeah because real maths is actually cool and interesting, but schools aren't motivated to make students interested in maths, they only want grades, and mistakenly think rote memorisation is how to get good grades from their students.

[@jonahnichols2158]

Underscore Zero - YES! EXACTLY! THANK YOU!

[@shubhamkhare8749]

The end of the video is the thumbnail This man is a Legend

[@Cj-lu3pl]

SHUBHAM KHARE or the thumbnail is the end of the video...

[@shubhamkhare8749]

Courtney Henry 🤔 hmmm...

[@Greennoob2]

I love this one especially. I can understand the maths and relate to this. Pretty cool

[@TheRealSamSpedding]

Oh yeah the maths is cool, but it’s seriously not coincidences. Have a look at the proofs for all these results and you’ll see why they’re all connected. That’s where the true beauty of maths lies, in the connection between seemingly unrelated ideas.

[@aP1atypus]

"I can understand the maths" "coincidences" gtfo

[@JdotCarver]

_"Pretty cool coincidences"_ .... Just no.

[@larryscott3982]

Relevant Games You didn’t stand a chance of getting away with coincidences and math together. It’s good that you like the subject matter.

[@olivetom1599]

Any one can link or explain why this happens ? This blew my mind ....

[@dylandreisbach1986]

Man, Michael is really making the matrix work hard today to simulate those balls.

[@js2010ish]

:)

[@MrBomberman11]

Wtf this is the most fascinating math video I've ever seen.

[@peeweevle2238]

U scare me. And hurt my head. And make my loins warm

[@vsauce4678]

Peeweevle what a wonderful comment

[@faked9963]

This isn't something that I can do online now guys.

[@AndrewPRoberts]

You just did learning

[@Schoko4craft]

FakeDeath and its the internet. I think there will be a video where someone is turning this over and over 10 hours streight. Perfect random

[@fotwen]

What's with the spooky female at the beginning and the end?

[@outsidethepyramid]

some trick to get people talking

[@Brunoenribeiro]

That was scary as hell

[@AlwaysCheckmateNeverStalemate]

The Ring

[@BradyAus]

You mean Samara?

[@theproindagames9387]

Samara? No that was Hannah the destroyer

[@МаркВоеводин-ж6м]

6:33 quick maths

[@okayge_]

Stop.

[@twistedgwazi5727]

This meme is unfunny and dead. It never was funny.

[@Suamere]

Lol, this joke is hot.

[@twistedgwazi5727]

TheEyeKing Use commas, "darling."

[@AlternateRye]

GD MCB_Blazar There was no need for a comma in his statement, darling.

[@marccolten9801]

"This man belongs in a straight jacket" - Max Bialystock, The Producers.

[@asho4821]

6:35 quick math!

[@ksp6091]

One other spooky thing about the pascal triangle is how each row is a power of 11 : so you have 11^0 = 1, 11^1=1, 11^2=121 and so one

[@RunstarHomer]

This is a result of the binomial theorem which Michael goes through at 7:00, using x=10 and y=1

[@elyazidasri2968]

10:44 That's some quality meme material.

[@InsanePorcupine]

I'm pretty sure he's fully aware at this point and just doing the random stuff to fuel the memes.

[@samuelgonzalez4196]

Call Dolan dark!!

[@carjohnson9729]

Michael is legit a legend. Memes aside, the Vsauce channels are some of my favorites on the entire youtube platform. Keep on teaching Vsauce, you guys are the best!

[@jixaw9383]

I’d love to say “If only teachers taught it like this...” but that’s not true. You and I clicked on this video. It was us that said “I want to learn something”. In schools, unless it’s a class you are really passionate about, you won’t want to learn it because you aren’t asked to learn it. It’s just in our nature to do the opposite of what we’re told

[@SternLX]

Math class was the only class all through Jr High and High School I was always in a hurry to get to. I was one of those kids that worked far ahead in the Text book and outpace the class. Actually got in trouble for doing History Homework in Geometry class one day because I was so board. Rather fround upon to get ahead of the syllabus apparently.

[@加州猫主席]

SternLX Oh, trust me, where you excel in mathematics you make up for in English. Even if it's an ESL case, at least learn it well before you actually use it.

[@memoboy4141]

my math teacher actually taught us this

[@加州猫主席]

memo boy "Teached" What are you, a caveman? Learn English, jeez.

[@memoboy4141]

Na Zhao o jeez, no offence fam, i fixed it for ya

[@PJB4453]

I live when you find things related in math, like how the Fibby can be derived from a Pascal's Triangle. It's amazing

[@wishiwasabear]

Michael is evolving into Water from the Nile. And I'm thirsty for it

[@supra107]

Grand Illusions from the Nile

[@richardl1708]

Kuma lmfao

[@DAraas-m4g]

Vsauce is the second coming

[@Peewee0413]

Now that's a vsauce video....

[@XLatMaths]

Showed this to my A-Level Statistics class for Binomial approximations to the Normal Distribution and Central Limit Theorem, great stuff.

[@ninnus12]

0:09 the one and only

[@ohboy1113]

3:11 my brain did this thing where when I heard it the first time I swear he pronounced it Beeeautiful, but after listening again I realized that it was just my brain highlighting a good pun and Michael really didn’t say it any different than normal. My brain is literally hard wired to make puns so much that I hear them even when they’re not there.

[@foreman_spike]

congratulations !

[@foreman_spike]

CONgratulations

[@foreman_spike]

conGRATulations

[@foreman_spike]

congratulaTIONS

[@foreman_spike]

congratuLATions

[@JustAGiraffe]

Wow, something I'm actually learning in school except it's not boring or frustrating , thanks Michael.

[@RichGreene1]

Dude...where where you when I was in school. I struggled with this stuff my whole life (graduate, post grad, and doctoral degrees). Finally, at 58 this is so clear. Cant wait to watch your other videos. Thanks!

[@rahulsubramanian3417]

Pascals triangle also represents the powers of 11 in each of its row. Eg, first row is 11, second row is 11^2, third row is 11^3 and so on...

[@rahulsubramanian3417]

transylvanian oh yeah.. i didn't check it that far. But hey this is cool too

[@BK01012]

0:08 i can see the memes

[@_dannybove]

Enjoy the Vsauce Grand illusion crossover

[@danielgebert4556]

I would love to see how Michael would make and teach a high school math curriculum. I think the way he relates math to many other things might help some of that procedural math stick better in young minds, and maybe help with correlative thinking in other classes.

[@commentforthealgo5383]

that light + black board is so fun to look at.

[@infoweeb4634]

They should use Pascal's Triangle in math classes to teach all of this stuff. It's such a simple and tangible representation of these concepts that take weeks of class time.

[@justanutellajar]

I want that blackboard

[@sebastianzaczek]

nutella you certainly don't want to have a jumpscare blackboard

[@dellconagher8121]

I want that Michael

[@tristanmartin5455]

Michael you are such a good teacher you make me want to learn more, I remember learning the concept of squaring binomials in 11th grade and I absolutely hated it; but worse, didn't understand the concept so I kept failing my tests. I actually learned the concept by watching your video, it just clicked! What I previously dreaded to do is now it's such a fun little math trick to me. Thank you so much :)

[@alphastronghold4425]

and i've just noticed that nearly everything written is in comic sans XD

[@gok7393]

That intro almost gave me a heart attack

[@jean-pauljouet3407]

Man I just learned about binomial distribution and the central limit theorem how cool

[@irfanlone9032]

Nicely demonstrated

[@Crostil]

quincunx

[@Felhek]

Crostil exactly what I wanted to say

[@iagreebut6813]

Man that's deep, almost brought a tear to my eye. You addressed the issues of our time so well, with such great prose.

[@felixhultman8410]

tf you calling me huh

[@azeemazoom3976]

Why the heck my math teacher never taugh me Pascal's triangle.. I could have had a better present while understanding maths equations...

[@VoltisArt]

I am a firm believer that everyone would have an easier time with math if teachers learned to teach the many ways to explore, play with, and solve given problems, rather than the one boring way the textbook writer decided was "the way this should be taught." There's always multiple and often weird ways to do things with numbers, and this video includes beautiful examples of the relationships between different types and uses of math. One of my recent favorite examples of interesting math: A phone or keyboard number pad can be used for memorizing times tables up to 9. This is kind of like Jaime Escalante's finger trick for 9's, from the movie Stand and Deliver. Try it, count off the first few numbers and continue the pattern to see the next unit digit. Everything from 1 to 9 has a specific repeating pattern, you just have to fill in the tens digit. On a keyboard number pad, 1's go right, then up. 9's go left, then down. 3's go up, then left. 7's go down, then right. 2's, 4's, 6's, 8's, all go in a clockwise pinwheel of diagonals, for their first pair: 2,4; 4,8; 8,16; 6,12. (Note the odds all make a counter-clockwise pinwheel with their first three digits.) 5's step between 5 and 0, nothing else. 0 is the last segment in every pattern before repeating. Phone pad layout is reversed for top/bottom row, but the same patterns are there. Pass this along to friends and kids starting multiplication - there's a good chance they'll have one of these two devices around that can help them practice.

[@stefthorman8548]

i remember hearing it, but don't remember learning it because it was boring.

[@TheChiptuner]

My teacher taught us about pascal’s triangle but not how to produce it. She just told us to memorize it

[@alicebloch6396]

Maybe he did and you forgot lol.. here in Brazil se learn it.

[@KevinSZebua]

Here in Indonesia, we learned it in grade 6 LMAO

[@WorstZedTW]

This is the only episode I watch so far that I know, from everything from beginning to the end

[@badlula]

I would love to have you as maths teacher!

[@jacksonschumacher175]

Vsauce please stop, your giving me flash backs to my math class Algebra II trig

[@zer0bre]

"Next episode, we practice spelling!"

[@theeiwryuhuihdfulriegbe6177]

You should also mention about alternating sign changes when it’s (a-b)^n.

[@Tr1Hard777]

Its like a playoff bracket. The winner has to win the most games which makes it rare or in this case the ball has to hit right or left on the peg every time to make it to the outside.

[@Treeko13]

statistically, it will be tomorrow in less than a day, statistically of course.

[@matthewbertrand4139]

Treeko13 Statistically, tomorrow is ALWAYS in less than a day. Only at exactly 12:00:00.00000000000... AM is tomorrow in one day. An immeasurably small amount of time later, tomorrow is now calculably less than a day away, and will remain so until the next time it's 12:00:00.00000000000... AM. The window of time in which tomorrow is a day away, and by extension the probability that a randomly selected time will be in the window, is so ridiculously small that it takes on the property of negligibility: it's so incredibly close to zero, we can just call it zero and calculations involving this figure won't change at all.

[@want-diversecontent3887]

Matthew Bertrand A planck time?

[@matthewbertrand4139]

@@want-diversecontent3887 If you would argue that in a single Planck time, time has passed, you then also argue that one Planck time after exactly midnight, tomorrow is less than a day away.

[@peteypablo09]

Could someone explain what's up with the jump scares?

[@696969yolo696969]

It's just kinda funny cuz its completely unexplained and never talked about.

[@InsanePorcupine]

I have this theory that it's because of all the vsauce memes, and at this point Michael has embraced the memes, and is just doing this stuff to help them with their content. It's so meta.

[@DPZmusic]

Possibly related to "paranormal" distributions, or just a meme

[@corvus418]

Paranormal distributions

[@sebastianzaczek]

Paranormal disturbance

[@cr5678]

The specific Galton board he’s using, made of nothing more than basic metal and plastic, costs $65 on amazon

[@kyanovp1915]

*The more you know*

[@rapmastac1362]

@JoexCool Yeah, but software is on it too.

[@keagster31]

RapMastaC1 last time I checked software wasn’t the main thing raising the price of a computer...

[@dlol.]

It’s because of the small balls, the paint (minor), and the tolerances for the plastic Also the wood would cost some Also they need some profit

[@justhasan8423]

Dlol. Change the word some for 'a stupidly large amount of'

[@mandylatimer1607]

I just learned all of this in math class and I feel so smart for understanding all of this because I usually have absolutely no idea what Michael is talking about.

[@ezra6094]

I would really love it if there was one bright red ball in there, so people could bet on which column it landed in :)

[@dreysantillan]

Ezra Bernstein some people with OCD won't think that's a good idea

[@ezra6094]

Yeah, probably.

[@zeliumite]

Yeah it would really annoy me unless it lands in the middle all the time.

[@dr.hawkraps8457]

Pretty easy to figure out what kind of odds you could get on that kind of action.

[@cheesecakelasagna]

yes!