Apéry's constant (calculated with Twitter) - Numberphile
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- Опубліковано 3 тра 2017
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Tony Padilla is an associate professor of physics at the University of Nottingham. Here he discusses the zeta function and Apéry's Constant.
More Tony videos: bit.ly/Padilla_Numberphile
Tony's Tweet: / 828527018081918976
Roger Apéry pics courtesy of François Apéry
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Man, you messed up the joke. It goes "What is that? Are you armed?"
"No, I am legged"
Really??! Then he butchered it hard..!;)
@@mienzillaz unlikely that he would have been speaking English
@@rad858 that was about joke, that story can't be true..:)
That makes no sense in French though. Not in German either.
That certainly isn't a leg of humor
Euler seems to have been involved with every dam constant in his days.
I wonder what Euler would do if he had access to MATLAB.
he died, so he can't be a constant
Robb V. Constantly involved
@Pedro Marinho: If Euler had access to MATLAB, we would be enjoying the Star Trek Transporter by now...
Wouldn't that make right almost half of the time? ;)
My garden is too small to include the proof
Heliocentric otro argentino viendo numberphile?
Nicolás Torchia tres
quinto por aca
Heliocentric I have a fantastic little proof, but there isn't enough room in my garden to write it down
"I'm gonna do a pro-Fermat move"
And the Gestapo shot Apery on sight because although he wasn’t armed he was legged.
I heard his mate was so upset about the shooting he got legless to drown his sorrows
This is alleggedly what happened that night
Exactly and may be "growing in my garden" means he needed sheets and sheets to lay out on the ground for evaluating the expanding formula, lots of papers all with written numbers, sums and digits on them for calculation and approval. Such a genius brain, too bad his garden was just big enough to evaluate Zeta of 3.
More like LEGEND.
You could not have been closer in 87 trials:
87 / 71 - 1.20205 = 0.02330
87 / 72 - 1.20205 = 0.00628
87 / 73 - 1.20205 = -0.01026
To get no error: 1 / (1.202056903 / 87) = 72.3759 expected number of primes.
epic
Thank you for doing this. Amazing. 😂
Not only that, but it could not have been closer with 72 co-primes.
86/72 - 1.20205 = -0.00760,
87/72 - 1.20205 = 0.00628
88/72 - 1.20205 = 0.02017
1/(constant/87) can be simplified to 87/constant, because (1*87)/(constant/87*87)=87/constant
This is pretty fantastic
You missed the most important part...
WHY DO THEY GROW IN HIS GARDEN???
I wanna know too!
Now proofs don't grow on trees do they?
"Apéry's quite an interesting character, he's French" yes... very interesting...
+
×
/
^
666th comment.
6:03 - Matt Parker's reply always the best :)
Oh, Matt...
IIARROWS such a parker square
69
420 blaze it
last one is over 9000
XD
There has to exist some number base where the numbers would have fit. Might have had to use emoji.
I'm a birdplane
When he said "They grow in my garden" I thought he was going to go on to say that he found that the formula modelled the growth of mushrooms or leaves on a branch or something like that...
Me too!
Why would he tell the truth? He was not talking to Gestapo.
Literally got the closest possible result with that sample size. Well done!
With a sample size of 87 you can't actually get any closer to the actual constant than this, can you?
I think he might mean if he counted more of tweets, thus increasing the sample size?
I know. I was merely pointing out how well the experiment went for such a small sample size! Just one set of numbers going the other way would have made things worse. If it was me I wouldn't tempt fate by increasing my sample size - job done with just 87!
Tom Blakeson I agree
i know right...
I don't think so it's like Euler's number the thing if you get interest every second from the bank ... for example if you use 25 samples 25% close 50 samples 37.5 % closer, 75 samples 40% closer ...
69,420 and 9001 what a meme..
why?
In case anyone needed further explanation: 69 is a sexual move (double oral), 4/20 is a pothead's favorite day and 4:20 their favorite time, and "over 9000" is a Dragon Ball Z reference (hence 9001).
shouldnt we consider cloning euler if we can get dna from his remains
Who says maths is boring?
Columbine happened on 4/20 too
That's fabulous. I actually burst out laughing when he ran that fraction through the calculator and pulled Apery's Constant out of the hat. My eldest daughter thinks I'm loony. Well done!
You know it's a good Numberphile video when you already know the maths behind it and you are still both entertained and enlightened.
I mean, you kinda know it's a good Numberphile video when you get the notification, but still.
Given how often Padilla claims that Apery was "good but not great" I get a strong vibe that he is just lowkey jelly he didn't get to solve it.
I think the point is to show why Apery wasn't taken seriously by his colleagues and why it was so surprising in general that he solved the problem, when people like Euler could not.
I don't sense any jealousy here at all.
Cobalt Hey, get back to the PUBG series
this is the last place i would expect to see other nlss fans
Nice name
Not great as in, he solved only one major mathematical problem of his time instead of dozens like Euler or Gauss.
10:09 : "makes sense?" Complete silence from Brady XD
One of my favorite numberphiles. Tells good story with plot, personalities and suspense. Fun.
Well wait, hold on. What did he mean by "they grow in my garden"? It was never explained in the video!
Dry sarcasm by Apery when he was asked from where he got the formula as it was in disbelief on the part of the audience that seemingly couldn't imagine Apery succeeded where Euler failed.
@@at7388 I know all of what you said and much more. Specifically I appreciate the magnitude of Euler's intelligence so that If Euler did not solve it after concentrating for a week, then it might be difficult for ordinary mathematicians to do it in years of work.
@@nahidhkurdi6740 i was thinking maybe he does math outside in his garden.
This mathematical relations are so astonishingly beautiful. It's like watching the source code of the universe being shown to me.
As an engineering student I found this channel amazing, I have seen every video on this channel and every single one of them teached me something. Loving Numberphile ❤️
At 2:47
Gestapo: "Is that your firearm?"
Apéry: "No, i'ts my friend's _leg_!"
Gestapo: "Oh"
*gets notification*
Oh boy a new Numberphile video, gonna solve that 'unsolvable problem' with my extraordinary intelligence...
*watches video*
Yea, I definitely understand some of these words...
Ibrahim Fadhil Senjaya LOL
This is some of the first use of Monte Carlo i've seen in Numberphile which I think has been a real missed opportunity for the channel as MC is such an interesting topic. I think it could make an interesting video to talk about how we can approximate other constants like pi and e or solve integrals etc. using random numbers.
the buffons matches video uses a monte carlo method to calculate pi
Wow, I'm impressed... Tony does a video related to the Riemann zeta function without mentioning a certain negative rational number.
10:09 Uhmm yea... sure..
When I try to explain maths to my sister
Watch Mathologer's video on the Riemann Zeta Function! It helped me understand the coprime part
You don't need to understand what the Riemann Zeta function is, the crux of this video is just some basic statistics.
6:02 Matt Parker: "I tried..."
The numbers could almost fit. You could say it was a bit of a
Parker square! hahaha im funny validate me
0:52 Of course!
1:43 Of course!!
1:56 Of course!!!
2:01 Right.
2:10 Of course!!!
2:12 Of course!!!!
Of coarse!
If we divide the total number of interjections by the number of "of course" occurrences we get 6/5 = 1.200. Great Apery's constant approximation!
If you pause the video at 4:45 you can read some part of the demonstration (in French). The 6th point starts with "si on a de la chance.." means "if we are lucky" which is kinda funny in such a paper
"That's why it worked.... Make sense?"
Amazing! Maybe it made sense to Euler, but not to me.
Quantum electrodynamics sounds quite intimidating.
7:00 respect the dedication
Big applause !
Love this kind of videos, where something relatively simple but not known is explain, like how calculate zeta function of integers with twitter.
Love it !
Every Tony video I watch, I wonder why he's not a mathematician. He seems to be very passionate about mathematics and numbers!
FINALLY! I've been wondering for 3 months what you wanted these for
8:00 quite a ... Parker Square
Brotcrunsher 😂😂😂
That's what Matt tends to say too..."not bad"
(first digit comes out and is correct)
Matt : Not bad , look at that
How is doing exactly what he set out to do a Parker square?
I can imagine Matt's voice: LOOOOK AT THAAAT!!
"We recognize that, of course, as the riemann zeta function"
Me, stuffing another handful of cheetos i my mouth: "Yeah, of course"
It really bugs me that he doesn't write 1/1^s
He did, you just don't see it =)
@Furrane yes, it's like the invisible motorcycle meme.
1/1^s equals 1 for all complex numbers, so 1:38 is correct afaik
As a layman, I appreciate the way you warn me that you're about to cite some historical mathematical gobbledegook I've never heard of by prefacing it with the words "Of course"
0:37 "It's a *crazy* number."
Twitter... Crazy... Yep, it fits
PlayTheMind lol so true
true
Didn't think I'd see you here PlayTheMind haha
Playthemind ,when is your next video ? :D
I'm no mathematician but that was amazing.
Fascinating! I like Padilla very much
So far, the best Numberphile video to me.
i love Tony! more of him please
Fascinating. Though, Matt Parker have done this for his Pi day video for ζ(2) to estimate π.
Very clever and a great way to demonstrate how it generalizes to the real world. Thanks!
Absolutely wonderful, thanks.
(6:03): This is the moment in this video that earned my thumbs-up!
His estimate is actually the closest he could have got with only 87 random triads of numbers! Makes it even more impressive!
i always read Oiler in my head when someone mentions Euler and think they're some sort of specialized bike mechanic who goes around oiling things
I used to pronounce Euler like "Ferris Bueller"
@@elietheprof5678 I still pronounce it like that, and just to really rile up the mathematicians, I also pronounce Euclid as "Oiclid".
amazing stuff for non mathematicians. Great divulgation, thanks!
"not a great mathematician but just good"
goes on to solve something the brilliant Euler himself couldnt solve
...ha, im sorry but that should *instantly* place you in the great category, even if you failed all other things
indeed , that was an inappropriate and disrespectful remark and in fact to this day many mathematicians have tried and failed to generalize apery's proof although his proof got them closer to it , which indicates his impact.
No wtf?
I believe he was referring to him prior to having solved this
Yup, kinda disrespectful from Tony Padilla....
Consistency over luck I recon
We missed you Professor
Wow man. This video made my day.
Tony is back!
8:07 really mind blown. Explanation is even better.
That roundabout demonstration using Twitter was super cool.
An open ended question of integers usually results in a logarithmic distribution.
I love you. Please continue.
The probabilistic interpretation of the inverse zeta function at integer values was really clever! Never thought of it that way.
I like this type of video keep it up
This was so beautiful!
I've already seen it. Brady uploaded the live stream of the editing. Great editing Brady!
He's like so happy in the end :)
These are priceless gems for the grand archives. Brady keep 'em hot like this.
"OK. how...? why?" his excitement is my favourite part of this video. Like a child that really wants to show something he or she learned at school. this kind of enthusiasm for maths is what needs to be introduced to children and students imo.
Great video
Breathtaking
6:03 - what a Parker square of a reply
Fascinating!
That's an amazing result!
This was beautiful math!
I like his happy little face at 10:09.
Gotta love the one they kept on the screen longest was 69, 420, 9001 XD
Great stuff.
This is just like Matt's video he did for Pie Day, I wonder who they got this idea from!
I was just going to say the same thing. He looked at pairs of numbers instead of sets of three, which give an estimate for ζ(2) which Euler shows was equal to π²/6, and so it gives an estimate of π.
I like how Google reads my mind recommending videos. I have a math clock, and just saw the 1 on the clock (which in my case is apery's constant).
THIS is why I watch Numberphile
This guy is amazing!
Somebody needs to photoshop Euler dabbing.
"69, 420, 9001"
What a spicy meme
Brilliant!!
This stuff goes way over my head.
"the chance that any random number is dividable by p, is 1/p", i learned something :O
NIST: "so where did you get these huge elliptic curve numbers, P and Q, from?"
NSA: "they grow in our garden"
NIST: "perfectly acceptable answer, standard approved !!!"
Alice: " wtf ? "
Bob: " fml :( "
Bruce: " ffs !!! "
This is essentialy what Matt Parker did on pi day. But it's nice to see how this generalizes to other values of the zeta function
Great, impressive!
When I saw Tony and ζ in the same video I got so on edge waiting for that -1/12 to appear out of nowhere.
Woah that's amazing!
-be born 150-200 years ago
-make a convergent series with a bunch of low digit numbers
-call the constant after yourself
-???
-get remembered at great mathematician
-be immortal in the memory of people
-profit
Underpants!
Actually, others named it after him.
dat iz ossome !
nice vid :)
bruh the ending of this video blew my mind
Note that the letter pi in the latter part of the video is an upper-case pi (means product). The pi at the beginning is lower-case (the constant pi). Both of them are discussed in the context of Euler though...
When Padilla writes the word prime I can't stop seeing the word prune.
Damn, this was a great video!
Wonderful :-)
You here...
Cool
I was looking at another tab when he mentioned Euler, and I immediately knew that Brady put that picture up.
On a completely different note, I did find a simpler way of representing the ceiling function with an infinite sum of the sign function (or my version which is x/|x|) and moving it around, it might simplify the collatz conjecture or something
"Is that a gun?"
"No it's a leg"
insane.. love it!
so awesome , he is so clever
Beautiful ending! :D