3Blue1Brown - 2018-03-02
A most beautiful proof of the Basel problem, using light. Home page: https://www.3blue1brown.com/ Brought to you by you: http://3b1b.co/basel-thanks And by Brilliant: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Get early access and more through Patreon: https://www.patreon.com/3blue1brown The content here was based on a paper by Johan Wästlund http://www.math.chalmers.se/~wastlund/Cosmic.pdf Check out Mathologer's video on the many cousins of the Pythagorean theorem: https://youtu.be/p-0SOWbzUYI On the topic of Mathologer, he also has a nice video about the Basel problem: https://youtu.be/yPl64xi_ZZA A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here. https://ggbm.at/yPExUf7b Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details. 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: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Other mathematicians: QED
3Blue1Brown: Badaboom badabing
@Kings Cross 😂😂😂
I wonder if he got that from Beakman's World
C.Q.D.
@Kings Cross 😂😂😂
@Kings Cross because he was passing time watching π creatures videos on YouTube!!😂😂
Pi is like an uninvited guest who shows up at every party where he isn't supposed to be
Except ... he actually IS supposed to be there, he was simply uninvited.
pi is the party host.
😂
Don't forget e
Alon Amit explains why. They are related by another function you all have seen before.
https://qr.ae/p8EQu9
"I'm so tired of studying, guess I'll just watch some funny videos on youtube"
Me 30 seconds later:
Maria Cecília This is fun
Yeah, this is really fun if you know enough to understand :)
Maria Cecília you’re not tired of studying. You’re just tired studying the conventional stuff the conventional way
exactly definition jajajajaja
why these subjects are so interesting only when i'm preparing midterm exam
what term is at its mid point in May? just curious.
@facite non victimarum seems China stuff
@Tech Made Easy
Thank you.
Tech Made Easy
No, because
a) the Chinese Spring term goes from Feb to Jun
b) the OP's name is Korean
Lol
I want to nominate 3Blue1Brown the noble peace prize for year 2020. Thanks.
because of his wife having cheated on him it can not be))))
It's nobel prize not noble just a correction
but for mathematics FIELDS MEDAL
Абдаллах Муслим wow im ruski look Im making cringy jokes using bad English))))))) so funny right?))))
15:11 "the number line is kind of like a limit of ever growing circles" - i've been thinking of a number line like this since forever, i thought i was insane, but it makes sense now
DUDE SAME this video blew my mind with that statement
12:57 that circular right angle kills me to this day
@Divas verma I live in Europe and I see "circular" right angles all the time
Yeah i live in Europe and we use only circular right angle with dot
Pac-Man
In this particular step that angle is 90 degrees, but the analogous angle in subsequent steps it will be smaller. I think it makes more sense to keep it circular.
omg same
0:40 challenge posed in 1644 first 4 digits of awnser 1.644 coincidence I think not!
Just wow.
Nice observation man
Next digit is 9 (for 90 years when problem was unsolved) and 34 (for 1734, year before Euler solve this problem). It can't be coincidence
1.644*9* so actually yeah
Now I understand how wizards draw a magic circle: MATH!
Mathic thircle
I am still in high school but love watching these videos,even tough I didn’t understand 95% of what he was saying.
I am still 1 and I don't even understand the words but still i love these
I am at high school too at seven grade in colombia
@Virat Kohli Galat channel pe aa gye bhai
I am doing my masters and still didn't understand this
I am 2 years old and I still goo goo ga ga
0:00 "okay I'm not English so i hope it won't be so so hard to understand c:"
Rip my poor brain, i loved u
Did the captions help?
"What is pi doing here?" Can be said to be the greatest question is math!
This is beautiful man!!
I wish the whole world can see and appreciate how amazing your explanations and representations in your videos are.
You're showing the true beauty of maths
takes one look at tumbnail
Riemann Zeta, my old nemesis, we meet again!
ζ(3)=?
Wonderfull!!!!!!!
Marvelous!!!!!!!!!!
Excellent!!!!!!!!!!
Brilliant(Not The org Though)!!!!!!!
I Don't have more Adjectives So....................
Great Video.
I found some more:
Superb
Magnificent
@Pi What is pi doing here?
@Sharda Bishnoi This needs more likes
@Sharda Bishnoi Sen-pi
After every amination
Me: Wowww!!!
I've been wondering how this equation related to Geometry for more than 20 years since I first saw it in college. THANK YOU!
11:30 what kind of math witchcraft is this?!
There are already so many mathematical results named after "Euler", that if they had called this "Euler's Problem" or something, it would start getting confusing...
Go get a reuler
Theorems mathematics have to be named after the second person who discover them, otherwise they'd all just be called "Euler's theorem".
It is said that every maths problem should be named after the 2nd person who solves since Euler probably already solved it 1st
Euler had too many problems
@Aleph Null 1. i love ur username mr. א
2. wtf why is there a wiki page on things named after euler
I just submitted my final year paper on the Basel Problem, I kinda wish I'd seen this video a few weeks ago!
That was the most exciting math lesson I've ever been to.
Thank you for making math so fun.
That's the Magic of Mathematics. A non-sense idea of LightHouses solving a weird problem like that.
13:53 instantaneous cardioid!
Explaining lighthouse placements 11:28
Accidentally draws a pentagram
A wild morningstar appears
the luc in lucifer DOES mean light..
Amazing, this is how math works with physics. The video, of course, fantastic!!!
At the beginning you said, "You've never had the experience of your heart rate increasing in excitement, while you were imagining an infinitely large lake with lighthouses around it. Well, if you feel anything like I do about math, That is gonna change by the end of this video." And that does. I literally had goosebumps at the end!
did anyone hav those "aha" (more like holy sh*t) moment when watching 3B1B videos?
Mine is at 10:00 for this one
it's fascinating and frustrating at the same time to see how super-abstract concepts can be linked to some weird geometrical ones, like honestly wtf ?!
they are just numbers, and we human find a way to map number to 2d and 3d plane, and thus the geometry, they're not that fundamentally different.
The most frustrating thing in it is I am not intelligent enough to figure out the concepts myself. I clearly see it just requires way higher IQ than I have. And it seems like nothing that could be learned anyhow. Either you brain sees and processes such relations between super-abstract concepts, or it doesn't. You can learn about the relations, you can even barely understand what happens here, but... I don't really believe that problem solving skill can be learned, at least not by an adult person. Well, not by me anyway.
äähhhmm ... yeah - i mean math is ofc not restricted to eucledian space but like physics and math are still different things: like math can deliver the geometric framework wherein the physics happen... (for example how in general relativity the gravitational field would have an effect on spacetime itself and therefore change its metric continuesly (which remains a big problem still to quantifiy as far as I understand it).... (so 1 meter would at a given distance from a center of mass would not equal one meter at another distance from the same center of mass in relation to a refernce fram of meters that does not underly the effects of the gravitational field)... and so on... so yeah 1+1 would still be 2 but since thered be a dimension added to each "1" like 1meter for example at given at a certain distance from the center of mass and added another meter at a different distance from that center it would add up to two meters with a different lenght in relation to a reference frame than two meters lenght for example starting at a different distance from said center of mass... like I think thats what he ment.. (lets say physicall geometry is "weighed) by its dimensions and than in general relativtiy compared to a reference frame where spacetime is not affected by physical effects!
I thought that was only me who felt that way.
Not sure if Euler came to his answer using this method at all or just is for pedagogic porpouses only... It's fascinating that things that seem have not relation between them at all actually have it. Notice that there are some basic concepts involved: right angle in a circle and other more obscures: inverse Pythagorean theorem, and especially the property of those "bacons' light". The most frustrating thing must to be that there are many other hidden relationships out there but not many are able to see them.
This is absolutely amazing. How do you even change your perspective and think of that!
Watched during 2018-2019 (10 pm to 1 am) until I understood it. Thanks for new years gift
When you first mentioned light sources I was like "ok, where's he going with this?" Then you them along a number line and immediately realized "holy crap, that's the inverse square law!" I needed the rest of the video to get the things with triangles and pi, but I was pleased when I was able to figure out for myself where the squared part of the summation was coming from before you explained it.
I ain’t never seen no lighthouse emit no light from its base before.
Wow! This proof is so beautiful and not that complex.
I was worried the channel will go down hill when I heard more people were going to join. But now I have no doubt in my mind that it's going to be GREAT!
Good job Ben for the awesome video!
michael einhorn sadly,I believe sum of any other higher powers is impossible for a human to compute,since the extension would need higher dimensions than 3,which we are unable to properly imagine,on our own
jayasri ganesh Currently we can do some really cool maths in the 4th spacial dimension, even if its near-impossible to visualize. So while Im not sure if it will work, I wouldn't rule it out
I have seen sums for up to a 6th degree p series, and only evens
http://www.math.drexel.edu/~tolya/p_series.pdf
Awk Werp nvm,it may be possible, (An relation equivalent to the inverse Pythagoras theorm may exist in higher dimensions,which enables us to distribute some quantity in the order of required sum), however ,I believe the computation would be Cumbersome (Note:Although it may be impossible to solve through this method ,we can find the power sums through other methods, so a solution exists,although it may not be enlightening)
still going downhill. But underground now...
Mindblowing stuff, presented by the most soothing voice imaginable. Awesome
6:02 RIGHT >:(
This is one of the best YouTube videos I've ever seen so far and I've seen much <3 It makes you think about life, my reaction is just "wow"
8:58 I wasn't buckled up.
15:11 "The number line is kind of like a limit of ever-growing circles"
MY MIND IS BLOWN
My mind exploded so hard that my round skull became straight
संख्या रेखा एक प्रकार की सीमा है जो कभी बढ़ते हुए वृत्तों की सीमा होती है
Me: oh I totally understand
Brain: no u don’t
Hi! I am struggling to understand how you connect the amount of brightness to 1/a^2 + 1/b^2 ? It is clear that 1/a^2 + 1/b^2 equals 1/h^2 and that those angles correspond to each other when you scale down and transform the big rectangle into a smaller one. But 1) how do you prove that each of those angles covered by each of the lighthouses A and B equal to the original brightness from a lighthouse at the distance h and 2) where do you use the fact the all 3 lighthouses emit the same amount of light?
Why am I here? And why is this in my recommendations?
Whatever the reason, I’m glad it was
This was amazing
this is awesome my dad is clapping with joy nobody can make him clap so much : ) : 3
this channel's quality is unmatched
This visualisation couldn't be so beautiful without BADABOOM BADABING!
Wow this has blown my mind. Seriously
I love that moment where it just clicks
11:31 he almost summoned satan for a moment there.
This is wonderful! As I said in my paper, it's based on proofs by Yaglom & Yaglom, Hofbauer, and others, and I added some of my own ideas. I thought of the light sources as stars revolving around a common center of gravity, but light-houses are arguably easier to move around! :) I hope the "light-house proof" now becomes folklore, and I'm happy to have contributed to that!
you can have double the usual percentage off the top.....20 percent@josematias2010
we can have our attorneys hash out the future intellectual rights and patents on software and applicability ....lol....is that easy enough for you and your fantasy youtube conversation?@josematias2010
@the therorist 3 million sounds good, you did not specified the currency, I took the liberty to define it as Zimbabwe dollars, we should meet. Hope I can bring your knowledge to the crypto community, I am excited
Don't go all Grigori Perelman on me!
he didn't accept the money...........@josematias2010
Kexmonster - 2019-11-11
"In honor of Basel" or rather "We had to find something other to name it than 'Euler'"
Tri Kỷ - 2019-12-15
Too many Euler mathematical things 😂
Miguel! I Draw! - 2020-02-25
@Tri Kỷ Euler's little theorem ( ͡° ͜ʖ ͡°)
Ayman Jameel - 2020-03-04
Euler number = e = 2.718281828 ..........
mr.1n5an_e - 2020-03-07
Haha, thats probably what happened, that legend had his name all over mathematics😂