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.
@diegovargas33775 жыл бұрын
It easy t is 50 % of the 5 of the
@Kernel155 жыл бұрын
"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.
@MAYOJAMESD5 жыл бұрын
@@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.
@mustafasoykut25105 жыл бұрын
Get 4000000 subscribers plz 3Blue1Brown
@atlas0dan5 жыл бұрын
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
@mgsquared52044 жыл бұрын
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!
@deldia4 жыл бұрын
Haha mental
@magica35262 жыл бұрын
yep! that's why it's powers of 100, to convert to base 10
@OriEy72 жыл бұрын
It actually does not work for base 7
@fedoraguy67742 жыл бұрын
@@OriEy7 it most certainly will
@OriEy72 жыл бұрын
@@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...
@gogl0l3865 жыл бұрын
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.
@aidanokeeffe79285 жыл бұрын
Amen! If I never found this channel, I wouldn't be a math major today.
@TheSkepticSkwerl5 жыл бұрын
I still don't know what theta is.
@notnilc21075 жыл бұрын
@@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.
@pedronunes30635 жыл бұрын
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.
@floridaman69825 жыл бұрын
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
@______68798 ай бұрын
This video has lived rent free in my head for 4 years now. I literally think about this every 2-3 weeks. Congratulations
@RegularFantaTheBest8 ай бұрын
Lmao
@vampy_noah1659 Жыл бұрын
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 Жыл бұрын
same. it feels more amazing when start understanding what's going on
@leastofmyworries971 Жыл бұрын
Once you take university calculus, this makes 100% sense.
@rando_guy Жыл бұрын
@@leastofmyworries971 yep and classical mechanics
@MeMyself_andAI Жыл бұрын
Mathematics is the language of our universe. The better you can speak it, the better you can communicate with it.
@yourbigfan1777 Жыл бұрын
Same 😎
@akshaytiwari93485 жыл бұрын
You experience ultimate happiness when you see the links between two completely unrelated topics.
@yourlordandsaviouryeesusbe29985 жыл бұрын
That is correct. Atleast they *seem* completely unrelated before we investigate further.
@PKIVV5 жыл бұрын
> Every conspiracy theorist
@yuvrajsinghraj5 жыл бұрын
Everything is related we cannot see that easily
@jaydonnell5 жыл бұрын
What do you know connection is the key to happiness
@1996Pinocchio5 жыл бұрын
@@yourlordandsaviouryeesusbe2998 By invastigating, we divide. Before investigation, everything is one experience.
@SimonClark5 жыл бұрын
This is one of the most beautiful educational videos I've ever seen.
@TMHUpNorth5 жыл бұрын
Oh look, it's Dr Simon Clark.
@TheSharkyBoyCostyn5 жыл бұрын
Dr physicist, atmospheric physicist
@niccy2664 жыл бұрын
Yooo Simon Clark
@denisfan10554 жыл бұрын
This is sooooooooooooooo confusing, Yet Amazing science/physics-wise.
@benjiboi69_vlogz874 жыл бұрын
Hi
@blakebodycote102411 ай бұрын
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_IT8 ай бұрын
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_stupid8 ай бұрын
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.
@shadowmancer70408 ай бұрын
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!
@austinhernandez27165 ай бұрын
@@shadowmancer7040Thank Republican Governor Sonny Perdue for that.
@Leto_04 ай бұрын
@@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 Жыл бұрын
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 Жыл бұрын
I didn't understand anyone
@Ar_sole_hair_fiddler Жыл бұрын
You've got that "listen to this tape in your sleep" technique
@henriquecoelho65945 жыл бұрын
Thank you kindly for existing.
@jokinglimitreached15035 жыл бұрын
Well, that's a comment you don't see every day. Gotta remember that
@batboyhood310 ай бұрын
I agree
@MilProductions10 ай бұрын
Oh comment= 4 years ago, latest reply=4 days ago
@sifilo3 ай бұрын
You too!
@rivertaig87035 жыл бұрын
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.
@jpe15 жыл бұрын
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-nl6pf5 жыл бұрын
@@jpe1 You're absolutely right to want to learn but I wish there was a better place than our broken system.
@bourgeoisremi97785 жыл бұрын
It's never too late.
@grinreaperoftrolls75285 жыл бұрын
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.
@ytkaci5 жыл бұрын
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.
@krishgarg2806 Жыл бұрын
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 Жыл бұрын
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 Жыл бұрын
ur in 11th studying for jee arent u?
@krishgarg2806 Жыл бұрын
@@Niganigaballsackboii 😂😂 yup
@gaquekk Жыл бұрын
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
@dasburstling Жыл бұрын
I am not at all interested in maths, but this is definitely one of the coolest videos I’ve ever watched
@funnyhackerman Жыл бұрын
realest comment ever
@JulianLudwig-uq8vq7 ай бұрын
Is´nt that a contradiction?
@jaiyank4 жыл бұрын
Didn't understand most of it but loved the sound of that collisionsss.
@daniilgrigoryev62044 жыл бұрын
Lol
@jacobwright46534 жыл бұрын
Have you set your calculator to base 10?
@kishorekumarsathishkumar15624 жыл бұрын
REEEEEEEEEEEEEEEEEE
@anyonegotasnickersbar4 жыл бұрын
Have you set your calculator to calculate mode?
@Cp.Chaos7074 жыл бұрын
Same?😂
@welovfree5 жыл бұрын
11:51 That ghzzzzzt!! sound is satisfying for some reason.
@user-cn5pm7zg1u5 жыл бұрын
Deja vu someone?
@VENOM-tx6gp5 жыл бұрын
11:52
@luucvinky21945 жыл бұрын
welovfree yes
@ericsbuds5 жыл бұрын
agreed :D
@_trupples5 жыл бұрын
10h ASMR blocks colliding yes please
@1500초 Жыл бұрын
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😢
@jacktheguy955519 күн бұрын
I love just listening to this in the background not hearing a single word just enjoying the frequencies of your voice
@adude65684 жыл бұрын
As Archimedes once said, "give me an infinite mass object and an immovable wall and I can compute all of pi" Wait...
@anveshkhode37944 жыл бұрын
Did he predict Joker and Batman tho
@aloysiusvo3183 жыл бұрын
Did he actually say that?
@Soarvivor3 жыл бұрын
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.”
@LukasAnell3 жыл бұрын
lol
@Win0909493 жыл бұрын
Finally, we know what happens when an unstoppable force meets an immovable object
@mohitkulkarni9435 жыл бұрын
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..
@mdtalhaansari10965 жыл бұрын
Hope this becomes a trend.
@jinjunliu24015 жыл бұрын
I honestly love both just as much
@fpereyra5 жыл бұрын
Seria interesante que haga un video acerca del problema de la braquistocrona en la esfera. La solucion, para nada trivial, es una epicicloide
@rokus11455 жыл бұрын
Oh yeah yeah
@poopcatapult26235 жыл бұрын
Okay I need to reinstall Deus Ex.
@iamkiubi8 ай бұрын
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!
@sonic5d9 ай бұрын
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.
@omooba005 жыл бұрын
i always though i loved math, college taught me that i didn't, videos like this remind me that i did
@joserafael99135 жыл бұрын
same here, the struggle is real.
@lordMaroza5 жыл бұрын
Where I'm from, kids work for the grades, not knowledge. That why we end up hating stuff that should be really, really fun.
@TechSupportDave4 жыл бұрын
@@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.
@ekremdincel15054 жыл бұрын
@@TechSupportDave Good! I made my own similation with python too. Did you see Code Train's video about that? He made it in javascript.
@nyeeeeeee93464 жыл бұрын
Same tbh, college is killing me atm
@bobtivnan5 жыл бұрын
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.
@JackRule165 жыл бұрын
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-one5 жыл бұрын
There is another way of geometry. Can be possible, that our entire world is just 11 dimensional geometry
@ploniofludrasco27055 жыл бұрын
Glad to read this, as I was stuck on this problem at the point just after drawing the circle and the lines 😅
@Zghost2765 жыл бұрын
Of course. Geometry is commonly applied to physics. Such as finding net forces can require you to use cosine or sine of angels.
@BlueyMcPhluey5 жыл бұрын
Mohr's Circle is another example of physics concepts visualised on a plane
@zeynolabedinsoleymani4591 Жыл бұрын
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
@Jonathan-ru9zl11 ай бұрын
Grant, your place in the great educators of all time is granted 🙌
@BigDan853 жыл бұрын
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
@mikefraser45132 жыл бұрын
I am always jealous.
@nahema9079 Жыл бұрын
True his voice is cute
@matheuscabral9618 Жыл бұрын
he is not “gifted” he is skilled, he learn all that
@r1pperduck Жыл бұрын
@@matheuscabral9618statistically, not everyone has the ability to aquire these skills if they tried. Its both.
@matheuscabral9618 Жыл бұрын
@@r1pperduck what is your point? Sure a lobster can’t learn physics, but anyone without a major disability surely can
@blackpenredpen5 жыл бұрын
Purely amazing!!
@redaabakhti7685 жыл бұрын
senpa
@Albkiller225 жыл бұрын
Heey blackpenredpen really happy to see you are a fan too!
@bapolino7335 жыл бұрын
blackpenredpen YAY!
@soufian27335 жыл бұрын
CHEN LU
@soumaknandi92185 жыл бұрын
Oh my god! All my favourite channels are here!
@lilcyolo Жыл бұрын
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.
@colinmacaro7224 Жыл бұрын
My jaw legit dropped hearing this thank you you just got me out of KZfaq shorts for awhile
@tom_something5 жыл бұрын
0:51 - If your Geiger counter makes this sound, take your iodine.
@arienkano60025 жыл бұрын
Not good not bad either
@KingHalbatorix5 жыл бұрын
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_KSR5 жыл бұрын
@@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)
@krozjr50095 жыл бұрын
3,141,592 collisions. Not great, not terrible.
@akasakasvault75975 жыл бұрын
hum. well i guess i need to get to my local drug store.
@silentexcorcist4534 жыл бұрын
3 strongest things in the universe: The old family computer A nokia phone That wall in the simulation
@eve_the_eevee_rh4 жыл бұрын
Lol
@villagernumber78824 жыл бұрын
the sideways gamer. What about bedrock.
@antonioandreigiani65324 жыл бұрын
nope the floor
@xenoduck31894 жыл бұрын
Those are in order
@NovaWarrior774 жыл бұрын
Meme worthy.
@erwingifslangАй бұрын
I love that you explain everything so well visually that I understand what you are talking about before you say it.
@anandramesh Жыл бұрын
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.
@user-hh4xs7ml7s5 жыл бұрын
Can't wait to listen to 15 minutes of that sweet sweet clacking
@hecko-yes5 жыл бұрын
[asmr] calculating pi
@viniciuslambardozzi43585 жыл бұрын
10 hours of blocks colliding
@cielvague5 жыл бұрын
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)
@JNCressey5 жыл бұрын
Come on 3b1b... give us a slower 15 minute simulation of clacking. :)
@jiffylou985 жыл бұрын
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.
@aditt.74753 жыл бұрын
3:14 - "We are on a hunt for PI" Notice the timestamp...
@high24073 жыл бұрын
I refuse to believe that's an accident lmao
@sabiti54283 жыл бұрын
This whole thing reminds me that everything is Pi, and therefore waves.
@Sparsh_052 жыл бұрын
Damn
@binarywizard694202 жыл бұрын
Ah ahhhggggggggb
@playboibcrazy32902 жыл бұрын
@@high2407 me too
@supermonkey6543 Жыл бұрын
There's got to be a circular explanation for this. *Circle plotted on a graph at 1:15. Yup this checks out!
@gamingbeastlol Жыл бұрын
Ah yes, watching these videos and pretending I understood every word of it is a great midnight habit
@diegokoivukangas64612 жыл бұрын
I have no idea what you're talking about but damn I love those collision sounds
@Liamfavorstheboweh6 ай бұрын
Amen
@NedInYaHead6 ай бұрын
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.
@Liamfavorstheboweh6 ай бұрын
@@NedInYaHead …circular shape?
@GMPStudios5 жыл бұрын
This video is mechanics, calculus, trigonometry, geometry, co-ordinate geometry all in a nutshell!
@Chungus675 жыл бұрын
Welp, you just summoned kurzgesagt.
@GMPStudios5 жыл бұрын
@@Chungus67 oh included "In a Nutshell" xD. But I don't think they'll do classical mechanics videos
@ganondorfchampin5 жыл бұрын
Kurzgesagt is only smart enough to under half the things said in this vidoe.
@GMPStudios5 жыл бұрын
@@ganondorfchampin Kurzgesagt is more of an inspiring channel than an educating channel.
@colinsoileau50335 жыл бұрын
And tbh if you think about it from an engineering aspect, vibrations and harmonics.
@crazydave5977 Жыл бұрын
Watching this at 3 AM hitting would hit different, gaining knowledge you’ve never even heard of before
@tennenyt5311 Жыл бұрын
my ideal world is definitely one where there's no friction, I will not stop sliding
@Shubham-qk8fw5 жыл бұрын
That clack sound is just from another world. So satisfying 👌
@aidanokeeffe79285 жыл бұрын
It sounds like a Geiger counter
@Shubham-qk8fw5 жыл бұрын
@@aidanokeeffe7928 Exactly
@baguettegott34095 жыл бұрын
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
@chloroplast86115 жыл бұрын
Baguette Gott ocd
@aslaksockcraft5 жыл бұрын
The clack violates the laws of thermodynamics.
@meeksource40475 жыл бұрын
I love the awkward wait for that last click
@jwadaow5 жыл бұрын
OOf... awkward
@the1jessebrown Жыл бұрын
This is an example of a title I’d never be searching for on purpose but absolutely happy to find
@stemcell72005 жыл бұрын
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 :)
@3blue1brown5 жыл бұрын
It was a great video, and you made it so quickly too!
@maximan335 жыл бұрын
@@3blue1brown thank you very much to explain many mathematical and physical problems deeply and out of box. Unfortunately many professors don't do
@AalapShah122975 жыл бұрын
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.
@kabivose5 жыл бұрын
Of course no one is going to like that comment any more!
@kabivose5 жыл бұрын
They did! :-( 314 was perfect.
@masskonfuzion5 жыл бұрын
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-smith77015 жыл бұрын
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_com5 жыл бұрын
Explain things as simply as possible..but do not oversimplify. :)
@akasakasvault75975 жыл бұрын
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))
@saketh123gaming94 жыл бұрын
Daaamn I'm in grade 10
@TechSupportDave4 жыл бұрын
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!
@unoriginalname4426 Жыл бұрын
It’s things like this that make me think that _something_ designed the universe. It just fits together so perfectly.
@hunchinrana2123Ай бұрын
it took a year or two but after finishing my first physics course this is now understandable and makes me feel like school really did its job in this instance
@theCodyReeder5 жыл бұрын
Now to figure how tau fits this better. ;)
@sdcard96495 жыл бұрын
What do Cody's lab and 3blue1brown have in common? Both have gold videos
@-_Nuke_-5 жыл бұрын
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.
@vinyak123rohatgi5 жыл бұрын
Love your videos
@LeoStaley5 жыл бұрын
@@-_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.
@NotaWalrus15 жыл бұрын
Well, the reason tau unironically fits better is that you are adding copies of 2theta to get to 2pi.
@JasonSun3865 жыл бұрын
"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
@soumyasishbhattacharyya28055 жыл бұрын
♥️
@henrikburdett90524 ай бұрын
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!
@fyntanshaw5624 Жыл бұрын
Returned here after the KZfaq short to watch this masterpiece again
@aidanokeeffe79285 жыл бұрын
The use of sound effects in this video makes it infinitely more fun
@thoughtpolease71835 жыл бұрын
The quality of this channel is insanely high
@largewallofbeans9812 Жыл бұрын
For those who care, this still applies for other number bases. For instance, in binary (base 2), the amount of collisions between 1 kg and 4^n kg computes the bits of pi.
@aspectaura Жыл бұрын
The next generation regarding mathematics is up for a treat
@shebahammy4 жыл бұрын
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
@slim5314 жыл бұрын
THANK YOU
@abc36314 жыл бұрын
@asdf hjkl 😀 really
@scott4203 жыл бұрын
Legend
@ghabsterlol77683 жыл бұрын
we have a fellow memer here i see :)
@jakechurcher58373 жыл бұрын
The 1kg and 10,000kg sounds the most satisfying
@LuxuryDigitalAgenci5 жыл бұрын
Whenever i watch 3blue1brown I realize my ultimate goal is to find this man and hug him!!
@ranbirroy46275 жыл бұрын
I would be surprised if that doesn't result in a pi.
@vaibhavsingh67605 жыл бұрын
@@ranbirroy4627 very very cheeky
@vaibhavsingh67605 жыл бұрын
@@ranbirroy4627 may result a pie
@grimsk8 ай бұрын
미쳤네요 운동에너지 보존 식을 보고 그것이 원의 방정식과 같은 형태라는 생각을 해본 적이 없었는데
@leosamontesdad8 ай бұрын
So I started to understand this, realized that I’m in middle school, then got confused.
@andresmorera64264 ай бұрын
Same. Except realized I have a PhD in the biological sciences and am a few decades past middle school. :)
@EricNicholsdesign5 жыл бұрын
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!
@QuantumPhyZ5 жыл бұрын
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.
@EricNicholsdesign5 жыл бұрын
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?
@anLTproduction5 жыл бұрын
I was about to write the exact same thing, thanks for doing it for me!
@elementsofphysics73245 жыл бұрын
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 KZfaq, 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.
@user-qo1cq4yn1p5 ай бұрын
Pi is like an uninvited guest in maths that shows up everywhere where you'd never expect it to.
@Ar_sole_hair_fiddler Жыл бұрын
My professional summary of this video: circle on grid, lines on grid make circle, silly looking letters make mad.
@Deadfish8310 ай бұрын
yes
@xdo38654 жыл бұрын
3:14 Pi people: Hunt for pi! Me: aren’t you just hunting yourselves?
@LongboardtTrail4 жыл бұрын
Was it a coincidence that you used 3:14 as a time stamp. It's the first three digits of pi
@VivekKumar-td3me4 жыл бұрын
@@LongboardtTrail pi is everywhere
@VivekKumar-td3me4 жыл бұрын
@@LongboardtTrail that's scary
@benjiboi69_vlogz874 жыл бұрын
@@VivekKumar-td3me i know
@rollingrocky36084 жыл бұрын
@@LongboardtTrail Santa Maria!
@AppliedScience5 жыл бұрын
Wow. My favorite video of yours yet! Very nice work.
@3blue1brown5 жыл бұрын
Thanks!
@odw325 жыл бұрын
Everyone: Check the Applied Science channel. This man is an absolute mastermind when it comes to engineering & high-end DIY science experiments.
@akilansundaram21815 жыл бұрын
@@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.
@hoomaneshghi2535 жыл бұрын
Perfect video Thanks
@amuzak90635 жыл бұрын
I wanted to like this comment, but it has exactly pi likes on it right now...
@Peter_1986 Жыл бұрын
Matt Parker has got to use this scenario in one of his annual "Calculate Pi" videos; he could perhaps use some kind of low friction tracks or something.
@steelcash2 жыл бұрын
So glad I discovered your channel. Your contribution to the understanding of science and math is priceless. Thank you.
@MarkLucasProductions5 жыл бұрын
I have no mathematical ability whatsoever but this video (like many others) is absolutely orgasmic. No wonder some people love mathematics.
@PhysicsHelps5 жыл бұрын
Most of mathematical ability is finding this kind of stuff orgasmic, plus patience.
@berkaykartopu5 жыл бұрын
it’s physhics
@navaneethsujesh8505 жыл бұрын
Hard work beats talent
@bobon1235 жыл бұрын
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.
@prozzezion5 жыл бұрын
i´m with you
@UseAfterFreee5 жыл бұрын
"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!!
@3blue1brown5 жыл бұрын
Looking forward to seeing you there!
@elementsofphysics73245 жыл бұрын
@@3blue1brown He won't be the only one back on your channel, trust me!!!!!!
@greasycheese19573 ай бұрын
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
@freescape08 Жыл бұрын
Ok, so why haven't we seen Matt Parker do this practically? Just set up a graphite air bearing, a small tungsten ball, a large tungsten block, and a larger tungsten wall, then record it with a mic, and analyze the data. We could even compute how much loss is due to inefficiency!
@evilotto92005 жыл бұрын
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.
@JorgetePanete5 жыл бұрын
rote?
@NolorW5 жыл бұрын
@@JorgetePanete "by rote" = "by heart", learn something without understanding it (or being required to), I think :D (not native)
@TheMan835545 жыл бұрын
@@NolorW Correct
@kuro13wolf5 жыл бұрын
@@JorgetePanete Is it really easier to leave a reply and look ignorant than to write "rote" on a new tab? Genuinely baffles me.
@mushroomcube6235 жыл бұрын
@@kuro13wolf He probably didn't think it was a word and was trying to correct OP
@roeisameach5922 жыл бұрын
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 Жыл бұрын
So…. You fully understand it yet?
@overfotu Жыл бұрын
@@aglassofwater8582 lol
@Cyba_IT8 ай бұрын
How about now?
@ontopofbottom8 ай бұрын
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
@pauls.4513 Жыл бұрын
I still always think of this story my physics teacher gave- explaining he was an atheist his whole life until graduate school. When he found how the entire universe was governed by these beautiful numbers so perfectly, he believed in a greater power.
@betaic Жыл бұрын
this comment is VERY underrated
@stevencraeynest77298 ай бұрын
that makes no sense
@NeotronHorxen Жыл бұрын
3b1b is the ultimate guy for all my homework problems
@jb42jb5 жыл бұрын
Just as I suspected in 4th grade everything is solved by pi
@vitalnutrients7445 жыл бұрын
Except finding a ratio for pi
@lukeallen28945 жыл бұрын
@@vitalnutrients744 The ratio of pi to one, oh yeaaaaaaahhh.
@jmbalingit5 жыл бұрын
I love Pi. e^iπ=-1
@cameronsmith30475 жыл бұрын
Anything that can't be solved by pi can be solved by pie
@TheAmazingL1nk3rz5 жыл бұрын
@@cameronsmith3047 anything that can be solved with pi can also be solved with pie Mmm pie
@tymofei85865 жыл бұрын
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..
@NetheriteMiner4 жыл бұрын
I should be doing Trigonometry homework rn. This is more interesting.
@chupasaurus3 жыл бұрын
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.
@icefyre8331 Жыл бұрын
Ngl, this channel is the reason I grew up loving math.
@Eisenbergsteve5 ай бұрын
Mr. Grant, congratulations on your 6 million subscribers.
@YouTubeTryingToBeTwiter315815 жыл бұрын
This video needs to have 3,141,592 views
@jbtechcon74345 жыл бұрын
...then one more guy watches it and everyone is like goddammit Kyle!
@preppen785 жыл бұрын
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.
@evanwilliams20485 жыл бұрын
Excuse me the 2 would round up to a 3
@ObjectsInMotion5 жыл бұрын
I think you mean 31,415,926 views.
@loresoong82075 жыл бұрын
@@ObjectsInMotion wouldnt the 6 round up to a 7?
@Beara-sd9vg Жыл бұрын
Solid memes, glad to hear you’re feeling okay. You just earned yourself a new subscriber my guy, can’t wait for future videos
@jimlast4422 Жыл бұрын
It would be cool if someone made a website with the block things, I would love to just fiddle around with different masses and see how much the blocks move
@Pseudify10 ай бұрын
This is not exactly what you had in mind, but this is a piece of code that can verify the claim in this video. It’s in Visual Basic, which if you know how to use the Developer tab in Excel you could just copy this in. Comments are wrapped in double slash marks, and can be removed. //The do loop condition checks for the final collision which is when both objects are moving in + direction and the larger particle is moving faster than the smaller one. 1 is the larger object. 2 is the smaller object. ‘i' is initial and ‘f’ is final // Do Until vi1 > 0 And vi2 >= 0 And vi1 > vi2 If vi2 >= 0 Then //is the smaller object moving away from wall?// vf1 = ((m1 - m2) * vi1 / (m1 + m2)) + (2 * m2 * vi2 / (m1 + m2)) vf2 = (2 * m1 * vi1) / (m1 + m2) - ((m1 - m2) * vi2 / (m1 + m2)) vi1 = vf1 //reset final velocities to initial velocities for next iteration// vi2 = vf2 Else //is the smaller object moving towards the wall?// vi2 = -vi2 //a collision with the wall inverts the velocity of object 2 but no change to object 1// End If count = count + 1 //increment the counter for the number of collisions// Loop MsgBox count //this displays a message box with the result
@jimlast442210 ай бұрын
@@Pseudify thanks, dawg. But how long did this take you?!
@pewdepie9955 жыл бұрын
I was so looking forward to this
@user_hat4 жыл бұрын
How to find *The End* Of Pi: Set moving block to INF mass.
@oliverfeuer93234 жыл бұрын
IUnderated coment
@ondrazposukie4 жыл бұрын
The end of pi doesn't exist. Nor can infinitely many collisions occur in that time.
@paulmccartney82933 жыл бұрын
@@ondrazposukie you tried to be smart but actually, dumb lol
@numbers46853 жыл бұрын
@@paulmccartney8293 lol
@AnkurKumar-yx5sq3 жыл бұрын
If you're homeless, just buy a home
@yoRichaard Жыл бұрын
after three years (without trying) i have finally found the OP of this vid
@666FUC6KER666Ай бұрын
a summary of the total amount of math I was able to understand on any level while watching this: video: "...tangent (opposite/adjacent)...." my brain: "I remember this!! Trippin' On Acid!"
@wellfolks90964 жыл бұрын
It's one thing to understand math But explaining and visualising it like you do is really something else Keep up the good work
@MathDM3295 жыл бұрын
When I was a little kid, I despised math. Your videos showed me that math is not some loathsome abomination, and now I am a mathematics fanatic. Thank you. Because of your videos, I have learned that math isn't just useful; it is beautiful.
@cheshire1 Жыл бұрын
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.
@Fitzeroniii8 ай бұрын
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.
@muzaffercaginipekoglu1052 жыл бұрын
Hello there from Turkey, being an x-mechanical engineer and now a private maths and physics tutor, this totally amazed me, thank you for this wonderful channel and all the explanations made...this is absolutely mind blowing. I'm not very good at maths and physics but I'm getting there :). I'd have been so happy if just math and physics were explained to me in high school and in my university years like this...applied mathmematics etc...not just by using the textbook and the board, but just like this via insight, real word applications...hope we can teach the youngsters or guide them after us how beautiful and amazing math is. Thanks a million for the channel Grant. Thanks to teacher Edria Murray from MEF Int. School of Izmir, Turkey for recommending this youtube channel to me and to her students.
@nesslam48324 жыл бұрын
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?
@nadavron54604 жыл бұрын
This isnt a very hard question in regard to physics, but it is a very elegant and nice looking presentation
@jonathanmartin23264 жыл бұрын
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 :)
@nesslam48324 жыл бұрын
@@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)
@sanchu63353 жыл бұрын
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
@albin181611 ай бұрын
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.
@giusepperesponte8077 Жыл бұрын
I have a feeling that there’s something really special about this. Definitely not just a coincidence. The chances that Pi would just pop out of such a simple interaction for no reason is effectively nothing.
@mdj_quint5095 Жыл бұрын
The reason isn't out of the blue, any time there's Pi, there's a hidden circle somewhere in there! You just gotta find it
@blup99978 ай бұрын
bro his damn voice is too calming, I just use a playlist of his vids to make me sleep
@kylecow19305 жыл бұрын
1:08 holy hell my thing got in the video
@dexterdev5 жыл бұрын
congrats :)
@yourlordandsaviouryeesusbe29985 жыл бұрын
Well done my friend.
@duckymomo79355 жыл бұрын
Which solution was urs
@solarnaut5 жыл бұрын
consider yourself to now have 1.5 M jealous friends ;-) and welcome to faceborg.
@kylecow19305 жыл бұрын
I made the p5* simulation @@duckymomo7935
@user-ur6dc8zy6y3 жыл бұрын
3.14millions of subscribers to this channel at this time.❗️
@TweekLudwig8 ай бұрын
Galaxy Brain Move: Make the larger cube an infinite times more powerful than the smaller cube, as long as it’s a power of 100, and get every digit of pi to exist and memorize it that way. All jokes aside, this is amazing!
@MegaJugganot Жыл бұрын
Rough guess would be that (when the masses align) the larger block's acceleration vector is sinusoidal, in which case pi is bound to show itself somewhere.
@coopzr5 жыл бұрын
I'm nodding my head and pretending I know exactly what he's talking about. Edit (≈a year later): holy balls 2.6k likes