Why do colliding blocks compute pi?

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Even prettier solution: • How colliding blocks a...
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An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/clacks-thanks
Home page: www.3blue1brown.com
Many of you shared solutions, attempts, and simulations with me this last week. I loved it! You all are the best. Here are just two of my favorites.
By a channel STEM cell: • A solution to 3Blue1Br...
By Doga Kurkcuoglu: bilimneguzellan.net/bouncing-c...
And here's a lovely interactive built by GitHub user prajwalsouza after watching this video: prajwalsouza.github.io/Experi...
NY Times blog post about this problem:
wordplay.blogs.nytimes.com/20...
The original paper by Gregory Galperin:
www.maths.tcd.ie/~lebed/Galpe...
For anyone curious about if the tan(x) ≈ x approximation, being off by only a cubic error term, is actually close enough not to affect the final count, take a look at sections 9 and 10 of Galperin's paper. In short, it could break if there were some point where among the first 2N digits of pi, the last N of them were all 9's. This seems exceedingly unlikely, but it quite hard to disprove.
Although I found the approach shown in this video independently, after the fact I found that Gary Antonick, who wrote the Numberplay blog referenced above, was the first to solve it this way. In some ways, I think this is the most natural approach one might take given the problem statement, as corroborated by the fact that many solutions people sent my way in this last week had this flavor. The Galperin solution you will see in the next video, though, involves a wonderfully creative perspective.
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
Timestamps
0:00 - Recap on the puzzle
1:10 - Using conservation laws
6:55 - Counting hops in our diagram
11:55 - Small angle approximations
13:04 - Summary
Thanks to these viewers for their contributions to translations
German: Greenst0ne
Hebrew: Omer Tuchfeld
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with RU-vid, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
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Website: www.3blue1brown.com
Twitter: / 3blue1brown
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Facebook: / 3blue1brown

Опубликовано:

17 июн 2024

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Комментарии : 5 тыс.

@3blue1brown 5 лет назад

Some added notes (copied from the pinned commend to the next video): 1) Some people have asked about if the tan(x) ≈ x approximation, being off by only a cubic error term, is actually close enough not to affect the final count. It's actually a very interesting answer! I really went back and forth on whether or not to include this in the video but decided to leave it out to better keep things to the point. This difference between arctan(x) and x could be problematic for our final count if, at some point when you're looking at the first 2n digits of pi, the last n of them are all 9's. It seems exceedingly unlikely that this should be true. For example, among the first 100 million digits of pi, the maximal sequence of consecutive 9's has length 8, whereas you'd need a sequence of 50 million for things to break our count! Nevertheless, this is quite difficult to prove, related to the question of whether or not pi is a "normal" number, roughly meaning that it's digits behave like a random sequence. It was left as a conjecture in Galperin's paper on the topic. See sections 9 and 10 of that paper (linked in the description) for more details. 2) A word on terminology: I tend to use the word “phase space” to describe any space like the ones described in this video and the last, encoding some state of some system. You should know, though, that often in the context of mechanics, this term is reserved for the special case of a space which encodes both the positions and the momenta of all the objects involved. For example, in that setting, the “phase space” here would be four-dimensional, where the four coordinates represent the position and momentum of each pair of blocks. The term “configuration space”, in contrast, just refers to one where the coordinates describe the positions of all the objects involved, which is what we do next video.

@diegovargas3377 5 лет назад

It easy t is 50 % of the 5 of the

@Kernel15 5 лет назад

"For example, among the first 100 million digits of pi, the maximal sequence of consecutive 9's has length 8, whereas you'd need a sequence of 50 million for things to break our count!" As pi is irrational, doesn't that mean that every possible number can be found in there as there is no point at which the digits of pi would start to repeat? Sure, it would probably be too far in to matter by then, but yes, the last n digits of pi being 9 would be true at some point.

@MAYOJAMESD 5 лет назад

@@Kernel15 I'm not sure how true this is. Just because a sequence of numbers is infinite does not mean that it contains every imaginable combination of numbers. For example, there is an infinity of numbers between 1 and 0. There's .0001, there's 1/3, you got pi over ten, etc. Yet, even given the infinite count of numbers you get between 0 and 1, you can never get any number larger than one. There is an infinite number of numbers, yet not all numbers are included. So even though Pi is irrational, I don't think it necessarily means that you get every possible combination of digits. In fact, since by the very definition of it being infinite we can never create all of its digits, there will always be some combination of digits that we cannot give a proof for being included in pi.

@mustafasoykut2510 5 лет назад

Get 4000000 subscribers plz 3Blue1Brown

@atlas0dan 5 лет назад

I'm wondering whether there is a relationship between the next digit of pi and the momentum of the two blocks after reaching the maximum number of collisions

@gogl0l386 5 лет назад

Grant I don't know if you're aware of this, but you're actually changing the world. The next generation of mathematicians will be a bunch of people inspired by you. You're absolutely a master of presenting and visualisinh beautiful proofs without the need of advanced mathematics.

@aidanokeeffe7928 5 лет назад

Amen! If I never found this channel, I wouldn't be a math major today.

@TheSkepticSkwerl 5 лет назад

I still don't know what theta is.

@notnilc2107 5 лет назад

@@TheSkepticSkwerl Wait til you hear about different counting systems. I questioned my understanding of numbers for a whole year after I seeing the base 12 counting system video on numberphile.

@pedronunes3063 5 лет назад

I was in the Brazilian Olympic Week (Semana Olímpica) where who won a medal in the OBM (Brazilian Mathematics Olympics) go to a place to have classes and meet other medalists (actually I didn't won a medal but I got so close that I was called) and there many people knew 3b1b's channel. So I guess... greatings from Brazil.

@floridaman6982 5 лет назад

I littererly got interested in higher maths by his videos and just searching the web. It amazes me how this stuff was discovered before computers

@mgsquared5204 4 года назад

It’s interesting to note that in the 64 kg example at 0:28 it actually computes the first 5 digits of pi in binary. 2^(6-1) gives the first 6 digits of pi in base two! This method works for all bases!

@deldia 4 года назад

Haha mental

@magica3526 2 года назад

yep! that's why it's powers of 100, to convert to base 10

@OriEy7 2 года назад

It actually does not work for base 7

@fedoraguy6774 2 года назад

@@OriEy7 it most certainly will

@OriEy7 2 года назад

@@fedoraguy6774 My comment wasn't very detailed. It only give the wrong digits when you only calculate a few (1 or 2 maybe?). But then it works like in does for base 2 and 10. I did simulate it a long time ago. This basically happens, because Pi in base 7 has a 'long' run of 6s: 3.06636...

@______6879 6 месяцев назад

This video has lived rent free in my head for 4 years now. I literally think about this every 2-3 weeks. Congratulations

@RegularFantaTheBest 5 месяцев назад

Lmao

@vampy_noah1659 Год назад

Tbh I watched this vid like 2 years ago and did not quite understand the equation. Now that I am older and almost done with high school, I understand the conservation of energy and momentum and we literally just had it in our recent physics class. This is why I love physics, it always has a relation to something. Whether it is mathematical or irrational and just a fun fact. It blows my mind everyday

@rando_guy 11 месяцев назад

same. it feels more amazing when start understanding what's going on

@leastofmyworries971 11 месяцев назад

Once you take university calculus, this makes 100% sense.

@rando_guy 11 месяцев назад

@@leastofmyworries971 yep and classical mechanics

@MeMyself_andAI 11 месяцев назад

Mathematics is the language of our universe. The better you can speak it, the better you can communicate with it.

@yourbigfan1777 10 месяцев назад

Same 😎

@adude6568 3 года назад

As Archimedes once said, "give me an infinite mass object and an immovable wall and I can compute all of pi" Wait...

@anveshkhode3794 3 года назад

Did he predict Joker and Batman tho

@aloysiusvo318 3 года назад

Did he actually say that?

@Soarvivor 3 года назад

No, the real quote is “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.”

@LukasAnell 3 года назад

lol

@Win090949 3 года назад

Finally, we know what happens when an unstoppable force meets an immovable object

@jaiyank 4 года назад

Didn't understand most of it but loved the sound of that collisionsss.

@daniilgrigoryev6204 4 года назад

Lol

@jacobwright4653 3 года назад

Have you set your calculator to base 10?

@kishorekumarsathishkumar1562 3 года назад

REEEEEEEEEEEEEEEEEE

@anyonegotasnickersbar 3 года назад

Have you set your calculator to calculate mode?

@Cp.Chaos707 3 года назад

Same?😂

@blakebodycote1024 9 месяцев назад

if there's anything I've learnt from my maths, statistics, computer science and data science courses is that visualisations of the relationships between numbers is most definitely the future of teaching mathematics. It's videos like this that show how describing concepts with visual elements make teaching mathematics exponentially easier and I cannot wait to see how much more it becomes integrated with learning.

@Cyba_IT 6 месяцев назад

Yup, totally agree. When I was at school decades ago there would be a diagram in the textbook and they'd explain the equation but it was hard to visualize exactly how it worked. Now kids have this.

@these_handles_are_stupid 6 месяцев назад

Agreed, I am terrible at math and finished high school only just after visual elements started to become a thing, so it was not easy for me at all. A visual means of explanation makes math not only easier to understand but easier to appreciate and wonder at. It really is kinda cool sometimes. I wish I had this sort of thing in school. It would have made it feel so much less of a chore.

@shadowmancer7040 6 месяцев назад

Sadly politics and lawyers and other worse things have instead derailed our education system into a glorified day care and we end up with high school graduates that can barely read, can't write, and can't do math. Woo common core!

@austinhernandez2716 2 месяца назад

@@shadowmancer7040Thank Republican Governor Sonny Perdue for that.

@Leto_0 2 месяца назад

@@shadowmancer7040 I say half the reason is the baby boomer generation's _wonderful_ hip new idea of "hands off parenting", where they sit back and let he television raise their children, and "give them the freedom to make their own mistakes". So nice of them to give us that freedom. Who needs a parental figure to teach them the value of education? Oh and while we're talking about role models... how do we expect teachers to inspire and educate students if they're paid so little that the only teachers left are bitter, apathetic, and generally not super intelligent? Just like with public servants, we NEED them to better, so we must pay them better and demand better standards.

@SpiritmanProductions Год назад

I'm not a maths expert but I do love these videos because I get an intuitive sense of understanding, even when I don't quite grasp all of the proof's finer points. And the animations are amazing. Great work, and thanks for posting.

@Lolo_Antonio-FryEmUpFan 11 месяцев назад

I didn't understand anyone

@Ar_sole_hair_fiddler 10 месяцев назад

You've got that "listen to this tape in your sleep" technique

@SimonClark 5 лет назад

This is one of the most beautiful educational videos I've ever seen.

@TMHUpNorth 5 лет назад

Oh look, it's Dr Simon Clark.

@TheSharkyBoyCostyn 4 года назад

Dr physicist, atmospheric physicist

@niccy266 4 года назад

Yooo Simon Clark

@denisfan1055 4 года назад

This is sooooooooooooooo confusing, Yet Amazing science/physics-wise.

@benjiboi69_vlogz87 4 года назад

@henriquecoelho6594 5 лет назад

Thank you kindly for existing.

@jokinglimitreached1503 5 лет назад

Well, that's a comment you don't see every day. Gotta remember that

@batboyhood3 8 месяцев назад

I agree

@Milxfanta 7 месяцев назад

Oh comment= 4 years ago, latest reply=4 days ago

@sifilo Месяц назад

You too!

@iamkiubi 6 месяцев назад

I understood precisely none of this, but it got me so interested that it makes me want to learn maths beyond what i did in high school. Great video!

@sonic5d 6 месяцев назад

I remember the humble beginnings of this channel vividly, with Euler's identity being the spark that first guided me here many years ago. Your adorable pi mascot has continually played an indispensable role, often unexpectedly appearing in the most surprising places. I'm incredibly grateful for the consistently stunning visual content you produce, which has succeeded in shedding light on complex ideas in an extraordinary way. Thank you for your tireless efforts in bringing such high-quality content to your viewers.

@welovfree 5 лет назад

11:51 That ghzzzzzt!! sound is satisfying for some reason.

@user-cn5pm7zg1u 5 лет назад

Deja vu someone?

@VENOM-tx6gp 5 лет назад

11:52

@luucvinky2194 5 лет назад

welovfree yes

@ericsbuds 5 лет назад

agreed :D

@_trupples 5 лет назад

10h ASMR blocks colliding yes please

@omooba00 5 лет назад

i always though i loved math, college taught me that i didn't, videos like this remind me that i did

@joserafael9913 5 лет назад

same here, the struggle is real.

@lordMaroza 4 года назад

Where I'm from, kids work for the grades, not knowledge. That why we end up hating stuff that should be really, really fun.

@TechSupportDave 4 года назад

@@lordMaroza i'm pretty sure it's like this everywhere. people never do it for the knowledge. i did, and now i'm having the time of my life programming math-related software at home. and at first i hated maths. but the reality is, only the beginning is tedious. once you get into the intermediate or advanced mathematics, things start to become awesome even if you can't do much with that knowledge alone. it's videos like these that remind me that i love programming. this video even made me get back to doing what i used to constantly do. i'm currently recreating the collision program they made in this video and i'm looking forward to finishing it.

@ekremdincel1505 4 года назад

@@TechSupportDave Good! I made my own similation with python too. Did you see Code Train's video about that? He made it in javascript.

@nyeeeeeee9346 4 года назад

Same tbh, college is killing me atm

@krishgarg2806 Год назад

I watched this video a year ago, when I didn't know anything about, equations of circle and straight line, conservation of momentum and energy, and collisions. Now I have covered all the above topics, so I can finally say that I understood the video.

@jeffreyleonard7210 Год назад

You came a long way in one year. That is excellent. Your progress + the value of sharing information + mentors + ethics = hope for a positive future. Yes, you can be that important.

@Niganigaballsackboii Год назад

ur in 11th studying for jee arent u?

@krishgarg2806 Год назад

@@Niganigaballsackboii 😂😂 yup

@gaquekk Год назад

Yeah, i am in second grade of high school on brazil and i don't undertand almost nothing of the math but i hope i undertand onde day lol

@steelcash Год назад

So glad I discovered your channel. Your contribution to the understanding of science and math is priceless. Thank you.

@akshaytiwari9348 5 лет назад

You experience ultimate happiness when you see the links between two completely unrelated topics.

@yourlordandsaviouryeesusbe2998 5 лет назад

That is correct. Atleast they *seem* completely unrelated before we investigate further.

@PKIVV 5 лет назад

> Every conspiracy theorist

@yuvrajsinghraj 5 лет назад

Everything is related we cannot see that easily

@jaydonnell 5 лет назад

What do you know connection is the key to happiness

@1996Pinocchio 5 лет назад

@@yourlordandsaviouryeesusbe2998 By invastigating, we divide. Before investigation, everything is one experience.

@aditt.7475 2 года назад

3:14 - "We are on a hunt for PI" Notice the timestamp...

@high2407 2 года назад

I refuse to believe that's an accident lmao

@sabiti5428 2 года назад

This whole thing reminds me that everything is Pi, and therefore waves.

@Sparsh_05 2 года назад

Damn

@binarywizard69420 2 года назад

Ah ahhhggggggggb

@playboibcrazy3290 2 года назад

@@high2407 me too

@lilcyolo Год назад

More teachers need to use you. I tried studying using my teachers method and got nowhere. I watched a couple of your videos and now I feel like I actually understand it.

@chimkinnugget7134 Год назад

Im going to be a physics major this upcoming year, and your videos are so interesting to me, and part of what inspired me in the first place. Love your videos! Thank you!

@tom_something 5 лет назад

0:51 - If your Geiger counter makes this sound, take your iodine.

@arienkano6002 5 лет назад

Not good not bad either

@KingHalbatorix 5 лет назад

that's when you take out your 9mm You do NOT want to end up like the japanese guy who got lethal radiation poisoning and lived for almost 3 months with his organs literally melting

@Kasser_KSR 5 лет назад

@@KingHalbatorix Wasn't that guy kept alive by doctors who wanted to do some experiments on him or smth (his name was Hisashi Ouchi btw)

@krozjr5009 4 года назад

3,141,592 collisions. Not great, not terrible.

@akasakasvault7597 4 года назад

hum. well i guess i need to get to my local drug store.

@silentexcorcist453 4 года назад

3 strongest things in the universe: The old family computer A nokia phone That wall in the simulation

@evetheeevee2977 4 года назад

Lol

@villagernumber7882 4 года назад

the sideways gamer. What about bedrock.

@antonioandreigiani6532 4 года назад

nope the floor

@xenoduck3189 4 года назад

Those are in order

@NovaWarrior77 4 года назад

Meme worthy.

@zeynolabedinsoleymani4591 10 месяцев назад

Watching your content reminds me good memories of my high school when I was preparing for math Olympiad. Very good days with lots of joys with solving challenging problems

@dasburstling 10 месяцев назад

I am not at all interested in maths, but this is definitely one of the coolest videos I’ve ever watched

@funnyhackerman 9 месяцев назад

realest comment ever

@JulianLudwig-uq8vq 5 месяцев назад

Is´nt that a contradiction?

@GMPStudios 5 лет назад

This video is mechanics, calculus, trigonometry, geometry, co-ordinate geometry all in a nutshell!

@Chungus67 5 лет назад

Welp, you just summoned kurzgesagt.

@GMPStudios 5 лет назад

@@Chungus67 oh included "In a Nutshell" xD. But I don't think they'll do classical mechanics videos

@ganondorfchampin 5 лет назад

Kurzgesagt is only smart enough to under half the things said in this vidoe.

@GMPStudios 5 лет назад

@@ganondorfchampin Kurzgesagt is more of an inspiring channel than an educating channel.

@colinsoileau5033 4 года назад

And tbh if you think about it from an engineering aspect, vibrations and harmonics.

@rivertaig8703 5 лет назад

What I really appreciate about this channel - and it's so well exemplified in these last two videos - is that through the creative use of animation, geometry, and well thought out naration, you can spark in a non-math major like myself not just understanding of what would otherwise be esoteric and unapproachable concepts, but genuine excitement. I'm turning 50 this week, and I'm finding myself wanting to go back to college and get a degree in mathematics. This was superb. Thank you 3,141,592,653 times.

@jpe1 5 лет назад

River Taig I turn 50 in three weeks and feel similarly. I’m not unhappy how my life has gone so far, but watching videos like this reinforces the fact that the only reason I dropped out of math classes was because they were poorly taught, not that I was stupid, and I imagine I will feel satisfaction if I go ahead and return to college to succeed in math classes where I previously failed. Good luck with your efforts.

@Tony-nl6pf 5 лет назад

@@jpe1 You're absolutely right to want to learn but I wish there was a better place than our broken system.

@bourgeoisremi9778 5 лет назад

It's never too late.

@grinreaperoftrolls7528 5 лет назад

It's not too late to go back to school! DO IT! I am a physics major. I'm still deciding what I want my 2nd major to be.

@ytkaci 5 лет назад

I can vouch for you about how this guy allows us to see stuff which at first seem so complex yet shown so concisely and logically. I'm 15 and this made almost perfect sense to me.

@ABCDCBA1 Год назад

Hello! I'm a Korean student who loves your videos! I don't know how many times I've seen this video of you. When I was in the 3rd grade of middle school, I memorized it without any understanding. It was fun even though I didn't understand it at the time, but now that I'm in my second year of high school, I think I understand the principle a little bit, so I'm very happy If I learn a little more math, one day I can understand all the math videos in your videos, right? Your video is healing for me. Thank you for posting this video There may be misinterpretation using a translator I'm sorry😢

@flyingbirds6794 8 месяцев назад

This is truly one of the BEST videos on RU-vid, maybe the best one!!! Thank you so much!!! What an excellent explanation

@blackpenredpen 5 лет назад

Purely amazing!!

@redaabakhti768 5 лет назад

senpa

@Albkiller22 5 лет назад

Heey blackpenredpen really happy to see you are a fan too!

@bapolino733 5 лет назад

blackpenredpen YAY!

@soufian2733 5 лет назад

CHEN LU

@soumaknandi9218 5 лет назад

Oh my god! All my favourite channels are here!

@user-hh4xs7ml7s 5 лет назад

Can't wait to listen to 15 minutes of that sweet sweet clacking

@hecko-yes 5 лет назад

[asmr] calculating pi

@viniciuslambardozzi4358 5 лет назад

10 hours of blocks colliding

@cielvague 5 лет назад

Agreed. We need to organize in order to get our hands on that stuff. I only see 2 options : 1. Find out where 3Blue1Brown lives and kidnap him to some overseas basement where he would be forced to make colliding blocks animations for the rest of his life in order to satisfy our now insatiable addiction for high-frequency clacking 2. Get a similar sound file and actually code and upload the damn thing on github. Anyone volunteering for option 2 ? (or option 1 if it's more to your fancy)

@JNCressey 5 лет назад

Come on 3b1b... give us a slower 15 minute simulation of clacking. :)

@jiffylou98 5 лет назад

ahh, I remember going down into my grandmother's irradiated childhood basement in Nagasaki and hearing that oh so satisfying sound on the geiger counter as rogue hadrons pierced through my DNA. now I have a tail.

@DylBilch 5 месяцев назад

I Can’t explain how amazing these videos are. I failed precalc in college and wrote off mathematics completely but somehow I can understand was you talking about and I can follow in your videos. I’m having epiphanies just watching.

@Beara-sd9vg 11 месяцев назад

Solid memes, glad to hear you’re feeling okay. You just earned yourself a new subscriber my guy, can’t wait for future videos

@bobtivnan 5 лет назад

The most brilliant part of this is making the connection between a physics formula and geometry. I'm a geometry teacher, and it makes me smile to see so many rich geometry concepts applied in a totally new way.

@JackRule16 5 лет назад

Mean while my geometry teacher was out there clubbing during my high school days. Your kids are lucky to have someone who still wants to learn.

@antares-the-one 5 лет назад

There is another way of geometry. Can be possible, that our entire world is just 11 dimensional geometry

@ploniofludrasco2705 5 лет назад

Glad to read this, as I was stuck on this problem at the point just after drawing the circle and the lines 😅

@Zghost276 5 лет назад

Of course. Geometry is commonly applied to physics. Such as finding net forces can require you to use cosine or sine of angels.

@BlueyMcPhluey 5 лет назад

Mohr's Circle is another example of physics concepts visualised on a plane

@meeksource4047 5 лет назад

I love the awkward wait for that last click

@jwadaow 5 лет назад

OOf... awkward

@Fitzeroniii 6 месяцев назад

I’m not sure why this popped up on my shorts, but I’m in love with it. I love learning though and especially learning stuff I would’ve never bothered to try and learn on my own.

@the1jessebrown 10 месяцев назад

This is an example of a title I’d never be searching for on purpose but absolutely happy to find

@diegokoivukangas6461 2 года назад

I have no idea what you're talking about but damn I love those collision sounds

@LiamList7 4 месяца назад

Amen

@NedInYaHead 4 месяца назад

Which is funny, because the reason it's so satisfying probably has something to do with the fact that the frequency results in circular shape, exactly what 3b1b is explaining.

@LiamList7 4 месяца назад

@@NedInYaHead …circular shape?

@Shubham-qk8fw 5 лет назад

That clack sound is just from another world. So satisfying 👌

@aidanokeeffe7928 5 лет назад

It sounds like a Geiger counter

@Shubham-qk8fw 5 лет назад

@@aidanokeeffe7928 Exactly

@baguettegott3409 5 лет назад

Nooooo the sound is horrible! It's fine if it plays just once, but if a lot of these clacks play very fast it makes me really squirmy and uncomfortable, I hate it

@chloroplast8611 5 лет назад

Baguette Gott ocd

@aslaksockcraft 5 лет назад

The clack violates the laws of thermodynamics.

@samuelcrawford8055 7 месяцев назад

Thank you very much for this Grant. Phase space is often indecipherably defined by places like wikipedia so this was incredibly helpful and clear.

@Peteboi64932 6 месяцев назад

I don’t care about pi just let me listen to the beep

@theCodyReeder 5 лет назад

Now to figure how tau fits this better. ;)

@sdcard9649 5 лет назад

What do Cody's lab and 3blue1brown have in common? Both have gold videos

@-_Nuke_- 5 лет назад

Clever comment but I won't give it to you and here's why. All you people that like Tau more than Pi don't even know how to pronounce Tau correctly and as a Greek it pisses me off. The letter " τ " is not pronounced "Tau" that's just another thing that was lost in translation from Ancient Greek to latin and then to English. The Greek letter " τ " is pronounced " Ταυ " see the resemblance? T = τ A = α U = υ That's why you pronounce Tαυ as Tau though just because u = υ doesn't mean that in Greek the letter " υ " is pronounced as a " u " every single time. In some occasions the Greek letter " υ " is pronounces as an " f " sound. And in this case we have Ταυ = Taf *T H E R E F O R E* Tau should be pronounces as *Taf* because that's the correct Greek pronunciation of the name. Calling "Taf" as "Tau" is horrible and can only be done by people that have no idea of the Greek alphabet. I'm so mad that people call this beautiful " τ " letter as "tau" that sounds horrible and makes me wanna vomit. Now maybe you in particular do know the correct pronunciation of the word so I apologise if that's so, but anyway, I'm leaving this comment here for other people to stop calling τ as Tau. yikes.

@vinyak123rohatgi 5 лет назад

Love your videos

@LeoStaley 5 лет назад

@@-_Nuke_- **NO**. That "F" isn't an F. it's a DIGAMMA. en.wikipedia.org/wiki/Digamma. you pronounce a digamma as, basically, a w sound, except when it is functioning as a vowel, in which case you pronounce it very much like a u. So YES. "TAU" is the correct pronunciation. I took 4 years of ancient Greek. Pedants like *you* who have no idea what you're talking about, but ACT like you do, are the reason the world sucks.

@felipe970421 5 лет назад

Well, the reason tau unironically fits better is that you are adding copies of 2theta to get to 2pi.

@BigDan85 3 года назад

I am always stunned when I see such content. You must be so gifted, when you - are able to understand this physics stuff - are able to talk about it in a way that others can understand it AND still keep it at a high level - are sooo good at animating and editing - have a great voice that people like to listen to IHML

@mikefraser4513 2 года назад

I am always jealous.

@nahema9079 Год назад

True his voice is cute

@matheuscabral9618 11 месяцев назад

he is not “gifted” he is skilled, he learn all that

@r1pperduck 11 месяцев назад

@@matheuscabral9618statistically, not everyone has the ability to aquire these skills if they tried. Its both.

@matheuscabral9618 11 месяцев назад

@@r1pperduck what is your point? Sure a lobster can’t learn physics, but anyone without a major disability surely can

@greasycheese1957 Месяц назад

Im pretty proud of myself for actually getting this, I hope you know you are an amazing teacher and the internet is lucky to have you

@chezlizzle Месяц назад

Highly recommend for any classical mechanic enthusiasts. Great video.

@mohitkulkarni943 5 лет назад

I like this idea of giving a problem and then introducing the corresponding topic. Thinking about the problem and then watching the solution actually interests me more than watching a video on a random topic. I really hope you continue this..

@mdtalhaansari1096 5 лет назад

Hope this becomes a trend.

@jinjunliu2401 5 лет назад

I honestly love both just as much

@fpereyra 5 лет назад

Seria interesante que haga un video acerca del problema de la braquistocrona en la esfera. La solucion, para nada trivial, es una epicicloide

@rokus1145 5 лет назад

Oh yeah yeah

@poopcatapult2623 5 лет назад

Okay I need to reinstall Deus Ex.

@stemcell7200 5 лет назад

Thanks for mentioning me! Your videos are beautifully explained and if I had remembered the inscribed angle theorem I would have been saved a lot of trouble in my solution :)

@3blue1brown 5 лет назад

It was a great video, and you made it so quickly too!

@maximan33 5 лет назад

@@3blue1brown thank you very much to explain many mathematical and physical problems deeply and out of box. Unfortunately many professors don't do

@AalapShah12297 5 лет назад

I faced the same issue. I got stuck after I moved to the phase space and and represented the collisions as points along a zig-zag line. I was trying to get to pi somehow using area but the solution using inscribed angles is pure elegance.

@kabivose 5 лет назад

Of course no one is going to like that comment any more!

@kabivose 5 лет назад

They did! :-( 314 was perfect.

@these_handles_are_stupid 6 месяцев назад

They’d teach us about graphing stuff like reflections and translations or how to make a circle in school but never really applied it in an understandable, non-abstract way. It made math frustrating. This demonstration puts a face to the name of so many concepts I learned. Very nicely done 👏

@GeorgeZoto 10 месяцев назад

Beautiful, just beautiful 😊 The connection between dynamics and geometry is beautiful 😍

@shebahammy 4 года назад

All the good collision scenes Comment if I missed anything 0:20 64 kg 11:04 10 thousand kg 9:26 10 thousand kg 11:48 1 million 14:28 1 million 0:32 1 million kg 0:50 1 trillion kg

@slim531 3 года назад

THANK YOU

@abc3631 3 года назад

@asdf hjkl 😀 really

@scott420 3 года назад

Legend

@ghabsterlol7768 3 года назад

we have a fellow memer here i see :)

@jakechurcher5837 2 года назад

The 1kg and 10,000kg sounds the most satisfying

@jb42jb 5 лет назад

Just as I suspected in 4th grade everything is solved by pi

@vitalnutrients744 5 лет назад

Except finding a ratio for pi

@lukeallen2894 5 лет назад

@@vitalnutrients744 The ratio of pi to one, oh yeaaaaaaahhh.

@jmbalingit 5 лет назад

I love Pi. e^iπ=-1

@cameronsmith3047 5 лет назад

Anything that can't be solved by pi can be solved by pie

@TheAmazingL1nk3rz 5 лет назад

@@cameronsmith3047 anything that can be solved with pi can also be solved with pie Mmm pie

@ThorHC11 Год назад

This is sickeningly beautiful. Grant, your content is fabulous.

@theresamclaird1572 6 месяцев назад

What a wonderfully surprising way to find pi! And so interesting to dig into the explanations.

@aidanokeeffe7928 5 лет назад

The use of sound effects in this video makes it infinitely more fun

@masskonfuzion 5 лет назад

I'm not sure what I can say here that hasn't already been said.. but I'll try 😁 I studied computer engineering in college - some of my 3rd & 4th year classes covered the calculus of electricity (AC circuits and such), which dealt heavily with phase diagrams, phase angles, etc.. Never, at any point in my education, did any teacher come anywhere close to explaining any of that math as clearly and concisely as this (or any other 3Blue1Brown video, for that matter), that I can recall. This seriously is on another level.

@chriscatto-smith7701 4 года назад

masskonfuzion I agree totally. Seven years it took to gain a BSc in Maths, double masters in engineering and post graduate aerodynamics. I have never had something as complex described in such an understandable and interesting, concise manner.

@Pawbreakers_com 4 года назад

Explain things as simply as possible..but do not oversimplify. :)

@akasakasvault7597 4 года назад

agreed (lol i was taking a test and it was so annoying i came over to this video instead (i'm in home education so i can do this))

@saketh123gaming9 4 года назад

Daaamn I'm in grade 10

@TechSupportDave 4 года назад

This is exactly what happened to me. I take Engineering and we too are dealing with AC electricity and trigonometry, phasor diagrams and such. It feels so nice and refreshing having someone teach these topics to you so well and in such a satisfying manner. i'm definitely subscribing and cannot wait to see more of his videos!

@Jonathan-ru9zl 9 месяцев назад

Grant, your place in the great educators of all time is granted 🙌

@henrikburdett9052 Месяц назад

Civil engineer here so I am usually more interested in the real-world application of physics/math BUT…this geometric solution to a physical system was incredibly satisfying! Math can really be beautiful and elegant sometimes. The presentation and how you explained it was fantastic as well. Awesome video!

@LuxuryDigitalAgenci 5 лет назад

Whenever i watch 3blue1brown I realize my ultimate goal is to find this man and hug him!!

@ranbirroy4627 5 лет назад

I would be surprised if that doesn't result in a pi.

@vaibhavsingh6760 5 лет назад

@@ranbirroy4627 very very cheeky

@vaibhavsingh6760 5 лет назад

@@ranbirroy4627 may result a pie

@JasonSun386 5 лет назад

"Most notably, the conservation of energy plants the circular seed that ultimately blossoms into the pi we find in the final count." - this sentence is like poetry

@soumyasishbhattacharyya2805 5 лет назад

♥️

@flyingwhale157 6 месяцев назад

Why am i finding myself watching this video every few months? And find it interesting and mesmerizing each time again and again

@hrz6di 8 месяцев назад

This is the most beautiful video I've watched this year. I love it.

@thoughtpolease7183 5 лет назад

The quality of this channel is insanely high

@EricNicholsdesign 5 лет назад

I've said it before on your videos but seriously... my career path, and life for that matter, would have been radically different if my visual learning mind was taught math with videos like this. Its amazing how instantaneously I can comprehend ideas that would have taken hours from just a textbook or verbal explanation. Thank you for your videos, they're fantastic!

@QuantumPhyZ 5 лет назад

Psychologists have been saying things like that forever. Not everybody have the same learning style. School systems all around the world could be way better, but the thing is things like this are common in private schools.

@EricNicholsdesign 5 лет назад

Was commenting directly to the content creator. But in response - of course they have, exactly my point, duh, and sorry I went to public school?

@anLTproduction 5 лет назад

I was about to write the exact same thing, thanks for doing it for me!

@ledgerlinelife 10 месяцев назад

I don't usually understand the reasoning behind problems like this, but I think I get this one, and it's pretty cool. Thanks 3Blue1Brown!

@Fitzeroniii 6 месяцев назад

I can’t tell you why this popped up for me on my shorts page, but I love this.

@YouTubeTryingToBeTwiter31581 5 лет назад

This video needs to have 3,141,592 views

@jbtechcon7434 5 лет назад

...then one more guy watches it and everyone is like goddammit Kyle!

@preppen78 5 лет назад

I'd need an explanation for why Pi unexpectedly shows up in the youtube count if that happens. Preferably in a geometry lesson with clacking noises.

@evanwilliams2048 5 лет назад

Excuse me the 2 would round up to a 3

@ObjectsInMotion 5 лет назад

I think you mean 31,415,926 views.

@loresoong8207 5 лет назад

@@ObjectsInMotion wouldnt the 6 round up to a 7?

@user_hat 3 года назад

How to find *The End* Of Pi: Set moving block to INF mass.

@oliverfeuer9323 3 года назад

IUnderated coment

@ondrazposukie 3 года назад

The end of pi doesn't exist. Nor can infinitely many collisions occur in that time.

@paulmccartney8293 3 года назад

@@ondrazposukie you tried to be smart but actually, dumb lol

@numbers4685 3 года назад

@@paulmccartney8293 lol

@AnkurKumar-yx5sq 3 года назад

If you're homeless, just buy a home

@c4p4c1t1v3 4 месяца назад

Your animations are something else... I wish I had access to this when I was in high school and college

@CrazyGaming-ig6qq 3 месяца назад

Very fascinating. Ending at the step just before the step that would increase the value beyond pi. What an amazing and funny way to approximate this constant.

@evilotto9200 5 лет назад

Maths I had to power through by rote memorization, you are able provide with meaningful understanding. Thank you. You are great. I want my tuition refunded.

@JorgetePanete 5 лет назад

rote?

@NolorW 5 лет назад

@@JorgetePanete "by rote" = "by heart", learn something without understanding it (or being required to), I think :D (not native)

@TheMan83554 5 лет назад

@@NolorW Correct

@kuro13wolf 5 лет назад

@@JorgetePanete Is it really easier to leave a reply and look ignorant than to write "rote" on a new tab? Genuinely baffles me.

@mushroomcube623 5 лет назад

@@kuro13wolf He probably didn't think it was a word and was trying to correct OP

@AppliedScience 5 лет назад

Wow. My favorite video of yours yet! Very nice work.

@3blue1brown 5 лет назад

Thanks!

@odw32 5 лет назад

Everyone: Check the Applied Science channel. This man is an absolute mastermind when it comes to engineering & high-end DIY science experiments.

@akilansundaram2181 5 лет назад

@@3blue1brown Awesome video. You really need more subscribers. Every single video of yours is so good for understanding mathematical concepts. Especially the animations, they are just godly.

@hoomaneshghi253 5 лет назад

Perfect video Thanks

@amuzak9063 5 лет назад

I wanted to like this comment, but it has exactly pi likes on it right now...

@rowanscheunemann6733 5 месяцев назад

Why was this so much more entertaining and easier to learn and follow then any math I ever learned?

@user-fp9kz6xv6l Год назад

Amazing! This is your first video I have seen and it is definitely not going to be the last.

@MarkLucasProductions 5 лет назад

I have no mathematical ability whatsoever but this video (like many others) is absolutely orgasmic. No wonder some people love mathematics.

@PhysicsHelps 5 лет назад

Most of mathematical ability is finding this kind of stuff orgasmic, plus patience.

@berkaykartopu 5 лет назад

it’s physhics

@navaneethsujesh850 5 лет назад

Hard work beats talent

@bobon123 5 лет назад

If you like this video, it is simply not true that you do not have mathematical ability. You have been probably just exposed to mathematics in the wrong way.

@prozzezion 5 лет назад

i´m with you

@coopzr 5 лет назад

I'm nodding my head and pretending I know exactly what he's talking about. Edit (≈a year later): holy balls 2.6k likes

@hadjerboi5805 5 лет назад

The same here 🤣

@FryingPan76 5 лет назад

@whitewalker608 5 лет назад

What part you did not?

@zinsy23 5 лет назад

Same here.

@lindsaytang1017 5 лет назад

@@whitewalker608 Everything

@demi_ryka1306 11 месяцев назад

I love videos like this- for some reason I can't learn well (Especially physics my god) in school- but videos like this where I'm actually interested in the stuff and equations and whatnot just holds my attention really well- makes me wish education could be more personalized

@crazydave5977 11 месяцев назад

Watching this at 3 AM hitting would hit different, gaining knowledge you’ve never even heard of before

@xdo3865 4 года назад

3:14 Pi people: Hunt for pi! Me: aren’t you just hunting yourselves?

@LongboardtTrail 4 года назад

Was it a coincidence that you used 3:14 as a time stamp. It's the first three digits of pi

@VivekKumar-td3me 4 года назад

@@LongboardtTrail pi is everywhere

@VivekKumar-td3me 4 года назад

@@LongboardtTrail that's scary

@benjiboi69_vlogz87 4 года назад

@@VivekKumar-td3me i know

@rollingrocky3608 4 года назад

@@LongboardtTrail Santa Maria!

@pewdepie995 5 лет назад

I was so looking forward to this

@danielthemaniel3856 Год назад

What a whimsical and inviting nature!

@rainidrops 11 месяцев назад

This is so fascinating, i love this connection. Super described man!

@tymofei8586 5 лет назад

what tf im shocked as mechanical engineer,literally how this is possible and even more interesting who might have thought of this ? Linking pi to dynamics,geometry,trigonometry,mathematics at the same time..I mean its really different point of view. Brilliant channel deserves to be subscribed..

@NetheriteMiner 4 года назад

I should be doing Trigonometry homework rn. This is more interesting.

@chupasaurus 3 года назад

Mechanics has the tightest link to mathematics, even models in geometrical optics (which is basically made of geometry and trigonometry) are just describing the mechanics of photons.

@elementsofphysics7324 5 лет назад

I am an astrophysicist, and I can say that this video is one of my favourite maths video of all time. I hope the future will show that people with such a talent will have the opportunity to have a lifelong career as "teachers" on RU-vid, with their videos available worldwide, instead of being stuck in a job they don't like. Some researchers are wonderful teachers (and some are not...) transmitting to a handful of people in a specific university. Some genius teachers won't get a researcher position. This can be the future.

@gamingbeastlol Год назад

Ah yes, watching these videos and pretending I understood every word of it is a great midnight habit

@kylecow1930 5 лет назад

1:08 holy hell my thing got in the video

@dexterdev 5 лет назад

congrats :)

@yourlordandsaviouryeesusbe2998 5 лет назад

Well done my friend.

@duckymomo7935 5 лет назад

Which solution was urs

@solarnaut 5 лет назад

consider yourself to now have 1.5 M jealous friends ;-) and welcome to faceborg.

@kylecow1930 5 лет назад

I made the p5* simulation @@duckymomo7935

@roeisameach592 2 года назад

I remember watching this a year and a half and ago going "oh, I don't get it, but cool" now after being halfway into high-school physics and finishing with geometry I think I got some of it, see you in a year when I actually understand everything and can fully appreciate it.

@aglassofwater8582 11 месяцев назад

So…. You fully understand it yet?

@overfotu 10 месяцев назад

@@aglassofwater8582 lol

@Cyba_IT 6 месяцев назад

How about now?

@ontopofbottom 5 месяцев назад

You won’t ever understand all of it. Get your PhD and you still won’t understand all of physics. We know the answers to many things, but some reasons for why things are stay a mystery

@darciestimpson8904 6 месяцев назад

thankyou for inspiring and fueling the spark of excitement i get from maths ! you've built a truly wonderful community

@Isaak.4 6 месяцев назад

I use u to learn in the background while I’m doing other things and I learn so much

@UseAfterFreee 5 лет назад

"And if this solution leaves you feeling satisfied... It shouldn't" Well there goes my excitement ... "Trust me I've saved the best for last so I hope to see you again in the next video" And my excitement just came back doubled ! Thanks 3B1B you are awesome!!

@3blue1brown 5 лет назад

Looking forward to seeing you there!

@elementsofphysics7324 5 лет назад

@@3blue1brown He won't be the only one back on your channel, trust me!!!!!!

@anandramesh 11 месяцев назад

I'm watching this at 3am in the morning. It's been 5 whole years since I was THIS interested in math. Thank you kind sir.

@tennenyt5311 11 месяцев назад

my ideal world is definitely one where there's no friction, I will not stop sliding

@wellfolks9096 4 года назад

It's one thing to understand math But explaining and visualising it like you do is really something else Keep up the good work

@hiteshkumar3442 5 лет назад

Mathematics + Physics = heaven

@shivimish9962 5 лет назад

mathematics+physics=everything

@etepeteseat7424 5 лет назад

We found the Platonists.

@creepergames6547 5 лет назад

mathematics x Physics = 3blue1brown is awesome 😎

@WaveOfDestiny 5 лет назад

Physics is already mathematics

@physics-guy3164 5 лет назад

@@WaveOfDestiny Yeah but Maths with cool space pics. Do Mathematicians have cool space pics? I doubt it

@prawnydagrate Год назад

When I was in fourth grade, a guy who worked at my school (not sure if he was a teacher, but I don't think he was a janitor) told me about this problem knowing I liked math. I was fascinated. I love that guy.

@cheshire1 11 месяцев назад

There's another nice way to see why all the arc lengths are the same. We get arc 2 as a mirror image of arc 1 across the x-axis, so it must have the same length. Then arc 3 is a mirror of arc 2 across the diameter through the midpoint of arc 1. And we continue like this, at each point mirroring across one of these two lines.

@fiveoneecho 3 года назад

I routinely forget about drawing the relations when solving a system of equations in physics like momentum and energy, but it really is an awesome trick for understanding a system. Sometimes when doing a quick solve by hand, it can be very helpful to just sketch the relations and see where they are equal. I love this channel because no matter how many times I watch a video or how well I understand a topic, there is always some humbling reminder of something SUPER helpful I have forgotten.

@nesslam4832 3 года назад

I understand everything in this video but I can't wrap my head around how they all fit together perfectly, like wow... how did anyone figure this out?

@nadavron5460 3 года назад

This isnt a very hard question in regard to physics, but it is a very elegant and nice looking presentation

@jonathanmartin2326 3 года назад

First of all, thanks for asking this, Second of all, this is less of figuring anything out specifically, but more so explaining how certain concepts relate to one other. In other words, when working with equations, or concepts it is sometimes important to look at the information from another perspective, this is similar to a lot of university physics equations tie in circles to things like spring constants and pendulums. You can solve problems without the other perspective, but the ability to see it from another, may allow you to solve even more problems down the line, hence why we have standard quadrant system, spherical coordinates, and that other one I don't remember anymore :)

@nesslam4832 3 года назад

@@jonathanmartin2326 damn thanks for that in depth reply! I do see the purpose of translating scenarios into different mathematical concepts. My comment was more of an emotional "WOW" moment than anything, mostly because I've never seen mathematics presented in such a way in school before. (Also regarding coordinate systems I think you mean polar and cylindrical. I kind of see how that analogy translates to these systems too, but on a much narrower scale since they mostly still deal with the same scenario except with a different "notation" with the way you perceive the dimensions, I guess? In this video it relates a system of colliding bodies with circular "phases" which I found to be much more impressive haha)

@sanchu6335 3 года назад

So lets say there is an infinite amount of universes that go by the butterfly effect, our universe is the one that discovery happens in, also by the same logic everything and anything can happen

@albin1816 8 месяцев назад

idk much about math (I suck at it). But I can intuit that the small mass and an immovable wall is equivalent to a perfect spring when returning the large mass, which means it will have a curvature of a perfect circle. And the larger the ratio between the small and large mass, the closer to perfect it is.

@diy_wizard 8 месяцев назад

This is the best thing I’ve seen for a while, thank you!😮

@fyntanshaw5624 11 месяцев назад

Returned here after the RU-vid short to watch this masterpiece again

@rmclean3 5 лет назад

Your explanations are so clear and pleasant, even someone like myself with virtually no math background beyond highschool, can understand it... mostly ;)