e (Euler's Number) - Numberphile
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Dr James Grime discusses "e" - the famed Euler's Number.
More links & stuff in full description below ↓↓↓
A bit extra from this video: • e (Extra Footage) - Nu...
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"Don't put that in the video"
_Puts that in the video_
they had ONE job
absolute M A D L A D
+HalcyonSerenade
Kinda reminds me of that scene in Monty Python And The Holy Grail, where King Arthur got annoyed by a scene and then ran in front of the camera and screamed "Cut that out! Cut that out!".
r/madlads
Savage
Math is just all about who can pronounce Euler the most correct
The football team at one of my hometown high schools was the “Oilers.”
I have a tattoo of Euler’s identity and just now found out it’s pronounced “Oy-ler”
the edmonton hockey team is called the oilers (don't even ask me about hockey alr)
Germans: You dare challenge us mortals
@@PMT17 fax
Pride x humility = "I would not have called it g, I would have hoped that someone else would have called it g and I would have accepted that."
Teacher: In what year did the defeat of the Spanish Armada occur?
Me: Euler or Gauss.
e's decimal expansion is random, so the likelyhood of finding a four integer sequence in it that coincides with the year of the attack by the Spanish Armada is equal to 1.
@@hammerth1421 WRONG
There's no proof of e being a normal number
So, unless you prove that or find the year itself, you can't say that
@@chanderule605 Even though e is not a normal number, it's digits are still random. While you can't find any sequence of any length in it, you are pretty much guaranteed to find every four digit sequence, also the year of the Spanish Armada.
@@hammerth1421 There's no proof of that other than "it's kinda likely"
And I dont think it's proven to be random either
HammerTh its digits are not random. Now I'll have to wait and see if you reply with what I expect you'll reply with.
Main Theme - e
Main Theme - e
Main Theme - e
YTSunny Main Theme - e
Main Theme - e
Main Theme - e
December 31st 2019, 3:52 AM GMT
2.718.281 (e million) views
:)
Wow
What about e^e?
Today on February 71st,1828, 1:82 e'clock
01/01/2020 15:45pm.
@@HenryTheTodd hahahahahah
My Business Calculus professor at the University of Southern Maine was a big Euler fan. All of the classrooms Mainville used had a bit of graffiti; the Euler number, its square and its cube (all written out to five or six places) were written above the blackboard in magic marker. Since we used natural logs in the class, it was like an authorized cheat sheet during exams.
"Everybody knows this anyway. If you don't, now you do."
not knowing the values of it to a few decimal points is crazy anyway😭 or just using a calculator but i presume it was a non calculator paper
I can't believe Euler predicted the meme.
no he didn't
@@terrariaman8454 wooosh
Terraria Man r/woooosh
@@tipstyx1867 r/ihavereddit
You fool. The man made the oldest shitpost
1:29 Said no-one ever...
xD
Zahlenteufel1 I mean, maybe in sarcasm...
That was hillarious, I'm dying lol
Republican$ and Democrat$ in Congress say that all-the-time...
No, _everyone_ said this...
in a sarcastic manner.
Thank you! There are lots of discussions of e on TH-cam, but this is by far the most lucid I have seen. I learned calculus 55 years ago, never used it in real life (I became a soldier and later a lawyer) and am returning to re-learn it at my own pace. This video has been a tremendous help in my understanding of this important concept.
Your story is interesting
Is not it such a treat? It is analogous to discovering classical music later on in life, when you were once exposed to it as a child, but strayed from it to listen to contemporary music in the interim.
The relation and usefulness of e, I, and trigonometry melted my mind.
best title - 10/10
2.7182818284/2.7182818284
i r8 e/e
e/π
A solid 5/7.
Please don't ever stop making maths videos. I truly appreciate your explanation (history and reasoning). Love your work and truly admire what you are doing.
If they stop making math videos they would stop making videos, the channel is numberphile
BA in Maths I presume.
eeeeeeeeeeeeeeeeeeeeeeeeeeeeee
@@granvillebarraclough8846 Why though? because at day 1 MA he'd be bound to be sick of it already or have moved on to another area of studies altogether? hehehe :D
Sorry, I had to reply, even 2 years late :P
I love the videos as well, gotta say.
Euler was such a fit guy
He worked everything out
I'm a complete mathematical moron, and yet I've always been fascinated by higher level maths. The idea of calculus, even geometry is just amazing. I've never in my life found anybody who could get me through a college level algebra course. I get close, but have never been able to finish it. I feel as though I've always sat outside the sun, watching other people achieve and understand this. I'm a sort of "Flowers For Algernon" guy. In any case, this is really interesting.
8:58 when they say Infinity War is the most ambitious crossover in history
What?
I don't get it
Lol
@@sticks9757 e , π and i(√-1 if you don't know) are the most iconic constants (except i) in Math. So in this equation they powered e to the power of π multiplied by i and added them with 1 which is equal to 0 (bizzare actually. How e, π and i are really complex numbers in math somehow combine into making a simple number which is -1) So in summary all the iconic constants(except i) in 1 equation.
@@78anurag That's literally not what I asked
what is up with all these clickbait titles
VSeve I know right, they didn't even put the thumbnail in the video. Fockin clickbaiters😂😂😂
VSeve they need more arrows and circles
How is it clickbait? The video is about... e.
Andrew anon its an ironic comment
ApplicationBot Technically, since he obviously knew what he was talking about, it wasn't ironic, it was just a joke.
Wow SiIvagunner
yea
5:50 Do you add 1 to the denominator and then divide by 2 or do you add 1+1/2? I'm confused to as to how the sequence of the operations is with such a fraction. Can anyone help me?
@@EbonyPope It's an infitie fraction so there is no end. It's more like the 2nd option you have. You would basically say when you want to stop writing down the fractions and then solve for it going backwards from down up.
It is a beautiful equation. I had it on my birthday cake when I was 18.
If you graph x^y=y^x, you get two simultaneous graphs. One is x=y, and the other is some variation of y=1/x. They cross at the co-ordinate (e,e)
Nice
I tried to eyeball what the y=1/x -like function might be, and the closest I can seem to get is y=((e-1)^2)/(x-1) + 1. It matches the asymptotic behavior of x^y = y^x and passes through (e,e), but it doesn't perfectly match. The true function has something to do with the fact that ln(x)/x has two different x values that give the same y value for any positive y less than about 0.368, but for the life of me I can't figure it out.
@@adamkotter6174similarly the graphs a^x and loga(x) intersect at coordinates (e,e) when a = e^1/e
not really sure why that is but it’s neat.
@@adamkotter6174 that "about 0.368" number is actually 1/e. I don't know why though.
@@davidiv4915 it's pretty satisfying if you sub in x=e to both equations.
a^x = (e^(1/e))^e = e^(e^e) = e^1 = e
loga(x) = log(e^(1/e))(e) = e (because of the line above)
e
No one cares
Sari Masu yea haha I look in subscriptions and was uploaded 3 second ago :D
e
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Liwo Jima you forgot a couple digits
i love siivagunner
I legitimately believe this will help when I try to do a college calculus class again. No one bothers to explain what’s going on with new material. When you understand why you use symbols and how, it makes it easier to solve things. Thank you.
I've been trying to understand the relevance of this for days, but you made it so damn simple to understand. Truly the best channel for maths content.
e^(i*pi) = -1 is very useful in electrical engineering phasor notation and complex impedance. It essentially allows equations that would need calculus to solve to be easily solved algebraically.
The complete Euler formula tho for every angle, not just the Euler identity everyone knows
You can thank Laplace and Fourier for that too!
It’s also used in Controls engineering, and vibrations
Also useful in digital signal processing.
It's also used in computer science for writing various algorithms and making them efficient wrt complexity
I remembered when I first watched this video. It was like 2 years ago and I barely understand what’s going on. Now I watched it again after the previous 2 years and I found myself turned super focused. I understood everything
Thanks for your explanation
I can relate... I was 13 when I watched it... Now I'm 16 and I understand this lol. This is what I study loool
One might say you had continuous interest
@@MrInsideEye
Underrated comment.
You said the same thing on the Cardano's formula video
I’ve recommended Numberphile to various young students having trouble with maths. It is an excellent motivator for cultivating an interest in maths.
I think this is the first numberphile video I ever watched and I come back to rewatch it every once in a while. I just love it.
the thumbnail haunts me in my dreams
e^(i*pi)+1=0 not only brings together the most important constants, but also the basic arithmetic operations addition, multiplication and exponentiation.
And is the most tatooed formula among maths nerds.
Yet it works only because of some semi arbitrary definitions, such as the extension of powers of e along the imaginary axis.
@Clumsy Jester Exactly 👌🏻🎯😌.
Whats this, A Numberphile video, about a real number!? I never thought id see the day.
It also happens to be a complex number.
Thomas Eding um, no it isnt.
Complex numbers encompass the reals. It is complex with imaginary part = 0.
Thomas Eding e is totally on the complex plane.
All real numbers are in the set of complex numbers. If that seems odd, just consider also that all integers are in the set of reals...etc.
Continuous fractions are amazing, the most simple of them all already gives the golden number.
this is E-silly that fun E haha High Qualit-E ripper siivagunner, cause of the E-vent
uh huh
GHOST AND PALS FAN?! Rare find!!
yep@@Alexizhereee
@@Xavier13swag Eyyy bro whats ur fav ghost song lemmie guess distortionist. Frl frl.
yes, ong no cap fr fr no joke@@Alexizhereee
Isn't this channel called "Numberphile"?
Not "Letterphile".
Kappa.
It is a number represented by a letter. Kappa
Kappa means he didnt mean it seriously
It's funny, since kappa is also a letter (κ).
Letterphile would end rather quickly, wouldn't it?
They already talked about all the numbers, so now that there are no more numbers to talk about, they have to start with letters.
Otherwise, there wouldn't be any content, so I am ok with letterphile.
pi > e
tau > pi > e
Gramm's number > e
3 > e > 2
colox97 tbh i before e except after C :)
τ > π > e > φ > √2 > 1/φ = φ-1
this content is timeless thanks for all the enthusiasm and clarity
This video just made me extremely excited about math. For the first time, i actually enjoyed learning this.
The TH-cam video with the shortest title?
John Thimakis no vsauce holds that title with no title
John Thimakis yet it doesn't terminate
there's a vsauce3 video with an infinity symbol as the title... so no, not quite
e
John Thimakis Vsauce also has a video with no title, its about nothingness
8:58 Biggest crossover in history.
Heckk yea
I love how everything comes together, especially in the end..
love your videos, also the happiness you obviously have from talking about the math! i enjoy numbers immeasurably, part of my job, and these videos are so pleasing!
This is my new favorite channel; it's so well-explained, interesting and fun even when dealing with complex topics, and yet somehow really adorable and nerdy at the same time.
Watch ted ed
It isn't nerdy.
"Euler, he works everything out!"
Well does he work out?
He's having a break now. Stay tuned for the next iteration of the Universe.
Does he even lift bro
He skipped everything but head day ... wait, that sounded kind of dirty!
@@Raptorman0909 It did didn't it?
@@Raptorman0909Calling it brain day would work
This is perhaps one of my favorite videos of all time. Thank you.
3:51 let’s just take a moment to appreciate his hard work
Crikey Bluey, there was a flamin' Ozzie 10c piece in there!
+picknikbasket ;)
A U.S. dime, as well :)
?H$lllllaaA
What a lovely title. Captures the essence of this video quite well. Fully encapsulates and proves the quote by the "not-so-well-known-outside-his-circles" Victor Tran, "A letter says an entire video!" :)
clik bait title
badman jones how tf is 'e' clickbait?
Prediator X makes ya curious. "what the heck? its just an e?? gotta look at this"
not enough to classify as clickbait though!
Merlin Brennt But this is a mathematical channel. As soon as I saw the title, I knew that they were going to do something with Euler's constant. :)
But I suppose the logarithmic graph and James Grime on the thumbnail helped too :)
Victor Tran oh you must be very smart!
An absolute masterpiece, I have not seen a better explanation historical or logical before.
Well done.
the amount of passion and love for math makes the points go straight to ur heart and brain
Lord Farquad wants to know your location.
Owen Lewis you mean Lord MARKquad
Markiplier wants to know your location.
uhh...
Lord Farquad *E*
I can switch this between 2k likes and 2.1k likes imao
smooth e
309 likes and still no answers
e
Nice mix.
And here we are, the letter e used to be a running jokes on siIva’s rips and now a lord farquaad meme.
So siIva is now a normie meme?
*TASTE E*
Real ones remember when this video was just titled 'e'.
I love this video very much!
Does saying "Don't put this in the video" ever work?
we will never know because there can never be recorded evidence, because that would mean putting it in the video
badman jones Perhaps memoirs would recollect how a courteous editor obeyed the request?
Pablo Griswold you could put it in a separate video and thus you wouldn't be putting it in the video the person's telling you not to put it in
Why don't you ask Schrodinger?
Revan Sith'ari ahah imagine like a whole "dont put that in the video" compilation
Happy e day! (2/7/18)
What about 27 January?
Woowowowowowowowowowowowowowowowowowoeowowowow
I late. Waiting for 27/18/28
The next is 2718-2-8
Oh my gosh... there can only be one e day a century🤤
Lovely lecture! thanks a lot for explaining it so well!
I was just doing doing calculus and knew the value of e was 2.7..... and it kept coming in many different things like derivative of e^x is e^x and many more things like that , after watching this video I found how really how interesting it is!!
y = 0
gradient is 0, area under the graph is 0
lol that's actually true xD
says person with a pony icon
Yeah but that function is boring and useless :(
Is this for e^x? Or all functions? Both don't work because n^x=0 is undefined except for n=0, and there are plenty of functions where the gradient at y=0 is not 0? or am I misinterpreting the idea? Haha
OriginalPiMan Nevermind, just got it. "f(x)->0". Mind you, this is kinda cheating seeing as the x value has no effect on the gradient anyway ;)
A little bit extra: th-cam.com/video/uawO3-tjP1c/w-d-xo.html
And thanks to The Great Courses Plus for sponsoring this video: ow.ly/tKWt306Gg7a (give them a look)
Numberphile could you make a video explaining aleph-nul! (Factorial)
As a recently graduated actuarial science major, this video is speaking my language :D. Great stuff, love the content.
Numberphile f 💀
Hooray! New Numberphile!
Dr. Grimes is my favorite Numberphile personality. I love the way he pronounces "tortoise."
Random User If only he wasn't so happy. I'm sorry but it makes me feel depressed. Sorry
The history of discovery those constants is amazing, thanks.
As this video approaches pi million views, it occurs to me that I would love for Numberphile to revisit Euler's other number -- gamma -- from a mathematician's perspective. I enjoyed Tony's video on the subject, but I would be very interested to learn more about the mathematical underpinnings of gamma, including its connection to the Gamma and zeta functions, and given that James has discussed Riemann before, he seems to be the logical choice for such a video. I've been waiting for 3Blue1Brown to do something on gamma tying in with their videos on Riemann and the prime number spirals too. Maybe because we know so little about it, but I find gamma to be a far more interesting number than either pi or e... which are still the second and third most interesting numbers, with the golden ratio coming in at #4.
"Don't put that in the video" *puts it in the video* typical!
We can not know how many times they actually say that, and it is actually not in the video. So you can't say if it is really typical.
Koen Looijmans ಠ_ಠ
I gave you 200
"Wow thanks a lot, bank!"
😂😂😂🤭🤭
Great explanation. How have I never been taught this before, it took just 10 minutes and I totally get it.
That's fascinating especially the bit where the area = the value = the gradient.
How Euler would publish it now: e prank (TH-cam 2016) (GONE WRONG) (GONE SEXUAL)
Euler wouldnt be that much of a misleader when it comes to promoting his work, he actually had brains unlike most youtube slaves today.
DatK9
E prank (TH-cam 2016) (GONE WRONG) (GONE SEXUAL) (ALMOST DIED) (COPS CALLED) (HOW MUCH MONEY DO I MAKE FROM YOUTUB?!)
We're gonna talk about...
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E and e is not the same
domjanabi yeah, one is capital, the other is lowercase
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2:07 'β, it's β!'
Your thumbnail is mine now.
Makoren Why does your pic look so familiar
Essem because it's the same pic as in Ur identity card.
f(x)=0 also has that property... but not as useful.
Jay Chan isn't the gradient of X=0 infinity?
f(x) = 0 is not synonymous with x=0, but y=0. At any point on the function, the output (y) is equal to 0, the slope is 0, and the area under the curve is 0.
I've just starting considering this number extensively because of calculus one. This is wondrous. Thank you for the video
Great Job! Well explained!!! Thanks for the excellent and cool explanations.
1:29 "Wow, thanks a lot bank!" made me laugh more than it should have
I knew i wasn't alone😂
Five minutes in to math and chill and he gives you this look 5:18
Fantastic explanation, building it from the foundations! Thank you.
Thanks for this enthusiastic explanation! :)
I find the use of e very useful in complex analysis, where we can write e^(it) instead of cos(t) + i sin(t).
Which of those expressions would be easier to evaluate? I suppose I could plug in some dummy values and figure out myself but im lazy.
Personally I think the latter expression but I like how the first expression is more compact.
e is such an interesting number. I came up with the strangest function that approached e as x approached infinity.
y = 1/((x^(x+1)/(x+1)^x) - ((x-1)^x/x^(x-1)
It’s pretty cool.
ex: (56^57 / 57^56) - (55^56 / 56^55)
Take a reciprocal of this number and be amazed
great job!
What about this
Y^D=Y
So tell me What numbers the letters are ok
e shows up in very interesting places. x^y=y^x is an unusual graph that shows 2 lines, one linear and one curved, intersecting at the point (e,e). the graph of x^x also contains some e-related information; the minimum value for f(x) is at x=e^-1, or decimal 0.3678... so the lowest point in the graph of x^x is (e^-1,(e^-1)^e^-1)) or (0.3678,0.6922). It all has to do with exponential and logarithmic growth.
Nice work bro, I like these types of persons
Just use (1 + 1/x)^x like normal people...
Ok it's a joke, don't get offended
I mostly like how passionate and excited he is while talking about this math's stuff
I can't listen to the intro without hearing the SiIvaGunner cover
Thank you sooooo much. Your explanation was excellent and now I almost fully understand the use of Euler's number. 😊
Thank you so much for this, I’m learning logarithms right now, and I couldn’t understand what the natural logarithm was about and wanted to know. This helps a lot!
The Pythagoreans have never forgiven Euler for this....
Why?
Pythagoreans hated irrational numbers
😂...
@@mace1230 . So does Professor Wildberger.
I love this channel so much.
I truly enjoyed the video with the passion and brilliant approach of explanation from James Grime! Thanks a lot!
e^iτ = 1
Melthornal
*-1
+Lucas M
He was using Tau.
e^iτ = wau
It's funny how our brains see what's written and decide to interpret it as something else. Today I assumed a multiplication was addition, because the symbols look similar and the majority were addition.
But this doesn't have the most important number 0. Which is why I think π is more essential for the Euler identity than tau.
I really need to clean my monitor. It seemed especially Grimey during this video.
He seemed high in this video, like he'd just done an e.
"Euler, he works everything out."
Nice to know he didn't skip leg day
I grew up in sciences being inspire by this kind of Channel, learning more daily! Now I started mine to, thanks for the inspiration!!
BRING BACK JAMES
-A big numberphile fan, August 2019
e^x is not the only function to have the same area, value, and gradient. f(x)=0 also has that property.
MOOSEWHISKER so does 2 * e^x :O
That's true of all functrions on the form f(x) = ke^x, where k is a constant. Your is a special case where k = 0
Chrischo1997 finally someone who knows what there on about
That's trivial
+marche45
Here's how I think about your comment. Zero could be considered a trivial multi-variable function, with a well-defined gradient. That gradient is zero. If you say, "0 does not have a gradient", doesn't that mean you're implicitly saying that 'having the value zero' is the same thing as 'not having a value'? Little bit pedantic, but that's the spirit of this thread anyway.
Finally an explanation of Euler's number that tells me how it fits into the workings of the real world. Thanks.
Great video. This guys has a gift for teaching.
this is why you pay your mortgage every 2 weeks, and make one extra payment a year, and a 30yr mtg = ~15 yrs. the interest kills you.
xrisku yet with inflation that changes
It's still calculated p.a.
Many banks simply hold the partial payment until the complete monthly payment is received.
I don't think a bank gives you any credit for paying multiple times within the month.
I always understood e using limits in Calculus however this is a great, practical view that should be taught in class. Great video!
I would never have understood this concept if it wasn't for this video.
I haven't been to a STEM university course (yet) but I think this video, plus 3Blue1Brown's video about e covers as much as a newbie to this topic could possibly want to know! Thanks for this great content
You've explained this so much better than anyone else
guys im just starting to expand my maths knowledge after an undergrad in politics and a post grad computer science (focussed on ontology) These videos are amazingly helpful for letting me continue to expand and combine my knowledge of disciplines, so big heartfelt thank you for posting such useful and accessible content.
whenever I get bored with a concept I just go here and watch a video and it instantly makes it more fun
e is also used for log or Ln bases like e^ln(2) or log based e.