@robjohn The larger diagonal of a parallelogram of area $8$ must have length: a)at least 4 b)equal to 8 c)at most 4 d)equal to $\sqrt8$

I straightaway rejected $\sqrt8$ as there are infinite parallelograms with area 8

@Sawarnik hi, you could do that problem?

@Hawk Oh, wait.

@Sawarnik why?

@Hawk there is only one possibility using that logic

@Hawk the minimum is attained with a square of side $\sqrt8$.

@robjohn I used that there are infinite parallelograms with same area with a fixed base and a parallel line to the base...will that be applicable or is that wrong?

@Hawk that tells you that the longer diagonal is unbounded... there is only one choice that is in agreement with that.

@robjohn yes, you are right...the first one...

@Hawk if you can have as long a diagonal as you wish, look at each choice...

I miss Ethan. He should come to chat more often.

@robjohn But, how do I mathematically prove that?

@Hawk does the question ask you to prove it?

@Hawk I think the choices are wrong. We can produce examples for <4 and>4.

@robjohn No, it doesn't...it's me feeling curious.

@Sawarnik how do you get an example of a parallelogram with area 8 and longer diagonal shorter than 4?

@Hawk okay... the area is the $bh$

@robjohn yes, it is...

@robjohn Sorry, I get it now. Both the diagonals can't be smaller than 4, but if one of them is bigger than 4 then the other one can be smaller than 4. Right?

@Hawk say the sides are $a$ and $b$...

@Sawarnik yes

@robjohn Ok :) We can prove it quite easily using $16=d_1 d_2 \sin\theta$.

Multiple punctuation and boldface is so annoying. I wonder why. Is it just me?

@robjohn yes...

It makes me. Want. To. Punch.

I did not see the word larger, that's why the confusion. @Hawk Sorry.

@Sawarnik No prob

@Hawk Can you prove it now?

@Hawk the diagonals are $\left(\sqrt{a^2-h^2}-b\right)^2+h^2$ and $\left(\sqrt{a^2-h^2}+b\right)^2+h^2$

@robjohn yes...

@Hawk which is the larger?

@robjohn the second one...

@Hawk If both the diagonals are smaller than 4, then it obviously doesn't satisfy $16=d_1d_2\sinθ$.

@Sawarnik Where does this formula come from? I don't remember this... :(

@Hawk so find the minimum

@MattN. I am annoyed by overformatting. There is a high rep user on this site that always annoys me with overformatting and overpunctuating.

@robjohn Don't you think that would be brutal?

Oh no! Don't you know the formula that the area is half the product of diagonals into the sine of angle between them @hawk Its verrry easy to prove, do you want it?

@WillHunting What is "overformatting" and "overpunctuating"?

Multiple unnecessary edits?

@Hawk Use my approach ;)

@DanielFischer What is your take on multiple punctutation???

@Hawk square it and get $a^2-h^2+b^2+h^2+2b\sqrt{a^2-h^2}=a^2+b^2+2b\sqrt{a^2-h^2}$

@MattN. For example, putting commas and ellipses in places where they should not be. Using lots of bold and italics unnecessarily.

@WillHunting I see. The punctuation doesn't annoy me, it's just a mistake. Whereas the rest is intentional.

@Sawarnik yes...

@MattN. $(2n+1)!!$ isn't multiple punctuation, it's the double factorial.

Shorthand for theorem is thm, what is shorthand for lemma?

lma ?

@DanielFischer : )

@N3buchadnezzar Lemma. That's short enough.

@MattN. I have resolved never to upvote this user, lol.

@DanielFischer Really I need it shorter in a refference see [lemma.~4.4 , 1] is too long =(

@Hawk Draw the diagonals of the convex quad. Its divided into 4 triangles. Sum their areas using $2A=ab\sin C$. Done! Its quite a useful formula, you should remember.

@WillHunting I think that is a good resolution.

@MattN. A particular reason for the complaint at this point?

@MattN. Do you think you know who I am referring to?

@Hawk and $a^2+b^2+2b\sqrt{a^2-h^2}=a^2+b^2+2\sqrt{a^2b^2-64}$

@Sawarnik ok...

@N3buchadnezzar reference*

@robjohn yes...

@Hawk Any more questions of my type? ... :)

@DanielFischer It's been bothering me for some time and I can't seem to get over it. Every time I see boldface it just annoys me. I can understand that some undergrad new and low rep users might use "??" to put emphasis on their question but when it is used in comments by established users... it really annoys me. And that's an understatement. Does it not bother you?

@Sawarnik Are you done with the one I gave you?

@WillHunting No, actually. No one comes to mind when I think of incorrect punctuation.

@Hawk How can we solve it?

@MattN. There is one thing worse than bold, many many colors.

@MattN. I sometimes use boldface to emphasise some particular item.

@Sawarnik Should I tell you the solution?

@Hawk so to get a minimum we could just keep decreasing $a$ and $b$ except that we need $ab\ge8$.

@N3buchadnezzar Ah, yes. They think colour is nicer, but it looks stupid.

@Hawk Yes, please! At least some detailed hints.

@robjohn ok...

@Hawk Where did you get a geometry question btw?

@Hawk so we can assume $ab=8$ and find the minimum of $a^2+b^2$

@WillHunting Likewise with bold, it can be used effectively and subtle. See many of robjohn answers for some delightefull examples.

@N3buchadnezzar Yeah, I can't stand that either.

@robjohn Yes, so we can...

Whilst Felix is on the opposite side of the scale..

@robjohn so, we are done?

@robjohn so loong.. this algebraic approach.

@Hawk that is pretty easy, we get $a=b=\sqrt8$

@Sawarnik Previous year test papers...

@robjohn Yes, I can do that...:)

@Hawk WAt! You told you didn't have geometry questions!

@robjohn Thank you so much!

@Sawarnik These are too previous...

Okay, I apologise in advance for picking a particular user. But for an example: Are two question marks necessary? @WillHunting and @DanielFischer

@Sawarnik We don't have geometry now...

@hawk Oh no :(

I would have written it with only one.

@N3buchadnezzar : D

What?

@robjohn as you can see...Sawarnik is now eating my head...I will ask you my questions a little later...

@Sawarnik the solution to the question I gave you...

Let me find a different user for another example.

@Hawk Ok -- Keeps quiet --

@MattN. He uses 2 because there are 2 sentences, if I read correctly.

lolwat?

$|f(x)-f(y)|<99(x-y)^2 \implies -99(x-y)<\dfrac{f(x)-f(y)}{x-y}<99(x-y)$

@Sawarnik can you do now?

@Sawarnik No, I will ask him later on...you keep on...

Ah... my random downvoter has returned :-(

@Hawk I had done that much.

@MattN. I was referring to the question itself, which is what I see when I click on the link.

@Sawarnik You did? and still couldn't do it?

@Sawarnik you know MVT?

@WillHunting No, the link points to one particular comment.

@Hawk No, I like to miss the obvious things.

@robjohn that is really sad...and that user should be banished from this site

@Hawk Yes, I hope.

@Hawk The problem is we don't know who is that user.

Another one is this one here. Almost every single comment contains boldface, italics or even both. Plus a decent amount of typos.

@MattN. Not for me. But anyway, one should never ever use ??, that is for sure.

@Hawk they were gone for a week or so. I can expect a downvote or two a day for a while probably.

@WillHunting I agree.

@robjohn something must be done about this!! I just hate people, who hide themselves and unnecessarily(without playing around) attack others or try to harm others

I think given enough time I could produce a long list of punctuation and typeface offenders.

@Hawk A little bit more .... and I know MVT.

@MattN. Since that comment was originally on the (now deleted) pretty senseless answer, I would cut Asaf some slack for expressing extreme incredulity by a double question mark.

@Sawarnik which bit more?

@Hawk Bit of the solution.

@Hawk Your head is very uninteresting to eat :P, anyways I m good at that ... means you didn't like my solution?

@DanielFischer Alright. I will cut slack for him. And what's your take on the other one?

@Hawk there is nothing we can do. Voting is anonymous and completely up to the voter's whim.

@Sawarnik No, I get messed up...when more than one person talks to me...

@MattN. I think he could use less formatting, lol.

@MattN. No comment.

@WillHunting Is so agree.

@DanielFischer I will interpret this according to my liking.

@Hawk Ok sir :)

Or perhaps... my liking.

Or my liking.

@Hawk most people are responsible enough to vote to the benefit of the site, but there are a few that don't.

@robjohn hehe :P

@robjohn why can't we? you can inform SE mods who can see all the votes...

So I guess I am not the only one who gets annoyed.

@r9m did I say that? ;-)

@robjohn Not sociopaths. Even r9m could be inculded in them :P

@MattN. Something like this math.stackexchange.com/questions/728173/… irritates me. Fine answer, but did the colors and the different font really enchance the answer?

@Sawarnik and yes, I liked your solution too...

@N3buchadnezzar sounds like Bill Dubuque...he uses a lot of colouring...

@Sawarnik I only downvoted once .. that too was an accidental click when I was accessing MSE from cell phone :P

@N3buchadnezzar but his solutions are good...

@N3buchadnezzar I'm not sure.

@Hawk I don't like Bill Dubuque.

@Hawk Not to say anything negative, but he has 10k rep, and 900 answers. You can calculate the avreage number of upvotes..

@Sawarnik did I say I don't like him?

@N3buchadnezzar I don't like formatting like that either.

@Hawk Well, at least his answers are good, not like userXXX.

At least Bill provides correct answers of a good standard.

@WillHunting yes, that is what I feel too...

@Hawk I use minimal coloring, and when I do, I try to make it help the clarity of the answer.

@DanielFischer I'm away from my library. Can I use you as a reference?

@Mike Maybe. What for?

Haha.^

@robjohn Yes, I know that...and I always liked your answers...others who are my favourite answerers are DanielFischer, Andre Nicolas, Gerry Myerson, Don Antonio...and some other people...whom I cannot recollect now...

@robjohn Like I said, I really like your coloring.

@WillHunting I like Bills answers=)

@Hawk Studying from Bartle is hard, you get terribly bored after reading 2-3 pages because its soo condense.

@N3buchadnezzar Yes, you should like my lhf as well, lol.

Sometimes a tad cryptic, but in contrast to all those who blurt out full answers to every hw question on the site. That is a good thing, imho.

@DanielFischer I don't remember what class of functions on the boundary of a domain has a unique solution to the Dirichlet problem

@Sawarnik yes...so you get...I used to get that too...

@N3buchadnezzar Bill's answers are quite dense. When you understand them, they are quite good. It is sometimes hard to understand them though.

@WillHunting Just ordered PMA

What is PMA?

Ah.

@N3buchadnezzar I have the hardbacks of PMA, RCA and FA.

Rudin.

I know it's true for continuous functions.

@robjohn Plus his very aggressive style.

And certainly quite a few discontinuous ones.

@MattN. PMA = Pickup Mathematical Art.

@Mike If the domain is bounded.

@Mike But I don't know the exact conditions for uniqueness either.

@DanielFischer Thanks. I'm only thinking about bounded domains, so that's fine today.

I will be back...

Hasta la vista, baby.

Ok :)

(had to look it up, didn't remember the exact line)

@Hawk Besides r8m is telling that he has found the solution of the bounty inequality q with a general form, but will not post on main.

@DanielFischer Can one not just apply Hahn-Banach extension theorem?

@DanielFischer By Riemann mapping, shouldn't we only need to find what class of functions has a unique solution to the Dirichlet problem for the unit died?

disc

@Mike Died? LOL!

Ah, I guess not.

@MattN. That would only give you a linear extension, a multiplicative extension is not as easy.

The extension will only be linear but not necessarily multiplicative.

Yeah, sorry, just figured it out myself : )

Maybe use the "multiplicative Hahn-Banach extension theorem"? : )

@WillHunting that's not good :(

@Mike That would only deal with simply connected domains where the conformal mapping behaves nicely on the boundary.

@meer2kat Hi.

@DanielFischer Yes, it was a silly error. Especially given the obvious test case fails: the upper half plane and the unit disk.

@Chris'ssis I answered a question on the main with your method $x_i \mapsto 1-x_i$ ..

@r9m OK

@WillHunting He also uses colours.

I need to make a plan for this year. What to study and such.

The homework tag is also annoying. It's completely pointless.

@MattN. Yup, I think so too. Great minds think alike, lol.

: )

Hello everyone

Hm... if I learned some complex analysis I might get lots of Daniel's answers.

Could please somebody explain question? What are the similarities and differences between a function existing at a point and a limit of a function approaching a point? Really can't get it.

For example:

@Sawarnik yo

@DanielFischer What I'm actually interested in is harmonic measure. I've gotten this far: if a domain is bounded by smooth arcs, then we can solve the Dirichlet problem for the indicator function of the union of some of those arcs.

This is annoyingly specific, though.

@KirillZhukov Define $f(x) = 1$ on $\mathbb R \setminus \{0\}$. Then this function is not defined at $0$ (it does not exist there) but yet the limit of $f$ for $x \to 0$ is $1$.

I tried to come up with a more interesting example.

@MattN. so I have to provide any example? There is no general answer?

@ParthKohli Hi.

@KirillZhukov Ah, no. I just thought an example might help you.

@MattN. yep, I know how to answer with example, just wondering should I give general answer or with example...

@Mike Do you remember the matrix form of the generators of $\text{PSL}(2, \Bbb F_5)$?

@KirillZhukov A general answer complemented with examples is probably optimal.

Alright, thanks!

Uh-oh, got to run! Byes.

Bye

@meer2kat ah The Hobbit...

@robjohn is it bad i haven't seen the second one? i just know the song

@meer2kat I am a great Tolkien fan, but I never saw the second Hobbit movie until last week on DVD.

@robjohn i might find it somewhere and watch

..

@robjohn was it good?

@Sawarnik sup kid?

@meer2kat What do you call a teacher in US, ma'am?

@Sawarnik at what level? grade school or university?

@meer2kat high school?

@Sawarnik Mr. or Mrs.

@meer2kat Oh. Very formal.

@Sawarnik and then in university it is Professor or Dr. (depending on their level of education)

@meer2kat There was a lot of story added. Some of the story was essentially changed, but despite that, I enjoyed it.

@robjohn i see :)

@robjohn Your favourite scene from the movie ?

@r9m I don't know... Peter Jackson eating a carrot... Gandalf battling Sauron... I really don't know.

@r9m Hav you seen Kung Fu Panda (2) ?

@robjohn haha .. I like the dwarves floating in barrel scene :) Hilarious

@Sawarnik I and II, though no one asked me...

@Sawarnik both :) .. awesome movies :)

@robjohn Nice!

@r9m I actually have a poster drawn by Tolkien of that scene from the book.

@r9m Your favourite scene from the movie KFP 2?

@robjohn Totally Awesome !!!!!

@r9m funny how the orcs don't appear in the poster...

@robjohn cool ! ..

@Hawk Hav you seen Legends of Awesomeness - Kung Fu Panda?

@Sawarnik that movie .. I like all the scenes :D

@r9m yup :D in particular i remember the conversation between shen and po!

@Sawarnik What is Legend of Awesomeness .. is that a new part ??

@r9m A tv spinoff they made ... some episodes are just as awesome! I can give you Youtube links of my fav episodes if you want!

it's the director's cut - shen & po go gay togeth

@r9m this poster. Need to find a better image. (came from this search)

@Sawarnik later :) ..

@robjohn nice ..

Does $\zeta(s), s \in mathbb{R}$ have a Fourier series?

@Alyosha is it periodic?

@robjohn No. I was wondering whether there exists a Fourier-like series for it, perhaps naive.

@Alyosha $$\sum_{n=1}^\infty e^{-s\log(n)}$$

that's as close as you'll probably get ;-)

A shame. Thanks.

@robjohn have you seen this ?

@r9m haha!

@r9m Just 20 mins .. 1 episode.

@r9m I've only seen the "Find $x$" one before.

@robjohn I heard a ping. Was it you?

@Chris'ssis Ah, I edited the answer that is in the star bar... it was taking up a lot of room because of an extra $$

@robjohn I'll show you soon the other way ... (I'm working on it - I mean put it in latex)

@robjohn did Tolkien sign your poster ?

@r9m no, he died 14 years before the poster was made.

@robjohn I had four downvotes yesterday in the span of 3 minutes, but they weren't reversed overnight. Are they there to stay?

@Mike probably...

alas.

Ooh :P

I find it hard to believe that someone legitimately disliked four things I posted in such a short span of time

@Mike Impossible to believe.

@Mike I agree. People should love everything you say.

Without knowing $\zeta(s)$'s Laurent series, is there a way of directly working out $$\int_{|z-1|=R}\frac{\zeta(z)}{(z-1)^n}dz$$ for $n \in \mathbb{Z}$?

@meer2kat While I do agree in my own infallibility, there's a bit of a difference between "people should love everything I say" and "someone went through various things I posted and decided to downvote a few without having taken the time to look through them".

@Mike Clearly they meant to upvote

people shouldn't upvote without taking the time to read through what they're upvoting, either.

i don't think this is a particularly contentious opinion

@Mike it sounds like a revenge thing, but the script did not see it as such. I think the downvotes I have gotten recently are similar, but they are spaced much further apart. The script cannot tell if the answers are good or not.

If someone here is upvoting my various questions to counteract the downvotes, I would prefer you didn't

unless you found the questions legitimately interesting

:)

@robjohn the second approach that came to mind (it might seem longer, but it's so only because I provided with more details there)

@robjohn do you have a private chat room for moderation or private messages between moderators?

Dang it.

Octahedral invariants.

@Chris'ssis Why do you remove your answers?

@Sawarnik why do you do this as well?

@GabrielR. Instincts.

@Chris'ssis That was my first approach (except using $\{\dots\}$ without changing to $\lfloor\dots\rfloor$). When I saw that the sum simplified back to the symmetric integral, I just used that.

@robjohn Both ways are nice and love them much.

@Chris'ssis deleted b4 I could see it ! .. why delete the proofs ?

@r9m take it.

@Chris'ssis Arigato gozaimasu :)

@r9m Wat!

Hey, while you are at it, evaluate $$\int_0^\pi \log(\sin(x)) dx$$

Bonus : Evaluate complex analytically.

@BalarkaSen this one is for kids.

@Chris'ssis I know, but not the bonus. (complex analytically)

=p

That part is for @robjohn.

@BalarkaSen I think @robjohn has such a solution somewhere.

@BalarkaSen I think I answered that somewhere... if not I can write one up pretty quickly... let me look...

I wonder why don't you guys look at Integrals & Series. It's a better place, really.

At least for you people.

WAAAT

V. Moll joined there!

Holy snakes!

integralsandseries.prophpbb.com/topic258.html#p2327

If $F \subset X$ is an irreducible subset, then so is $\bar{F}$ how to prove?

@BalarkaSen sos440 !!

He is there, all right, but V. Moll!

Really, they are running great there.

That guy, Victor Moll, is one of the leading analyst working on closed-form expressions of infinite series and integrals.

He probably did works on this particular branch of special functions than anyone in history.

@Sawarnik the infamous @BalarkaSen has returned!

Seems I have to got to go and let the octahedral invariants eat my brain. Ta ta!

@BalarkaSen I can't find the answer, but using $$\log(\sin(x))=-\log(2)-\sum_{k=1}^\infty\frac{\cos(2kx)}{k}$$ I get the integral is $-\pi\log(2)$

@robjohn Good shot!

@BalarkaSen Ah, here is a different way, and yet another

@robjohn Heya

@N3buchadnezzar what's up?

@robjohn I just read this. Very nice!

@N3buchadnezzar wow... I'd forgotten answering that.

Haha

Quick question - If I have a probability, say throwing a regular dice until I have tossed two values that are the same, e.g. I can throw 1, 2, 3, 1 then I'm done, what is the lower bounds for this (in term of dice tosses)? It must be two right?

@JohanS So...it would seem

@meer2kat Are you sure? It seems only logical with that, but we have a homework with hash collisions, and one of the questions are what is the lower bounds for a hash collision i.e. x1 != x2 but h(x1) = h(x2)

and the hash function is a "random oracle model", that is like it's with the birthday problem

@JohanS Never taken stats. Of course I'm not sure.

Okay, thanks for the response though! Anybody else who knows?

@Pedro: ping

HAI

@FernandoMartin

@PedroTamaroff Or should we call you Number 8?

@robjohn :confus:

@Pedro: I'm stupid

@FernandoMartin Yes.

Why?

AM proved that localization commutes with finite sums, products and RADICALS

@PedroTamaroff your avatar is Jackson Pollock's "Number 8"

Yes.

@robjohn I thought it was "Convergence."

@FernandoMartin That's what we pointed out when looking at the page.

well, that proves the theorem

Yes.

N = $\sqrt 0$

Alicia was a bit absent minded today, I think.

done

@PedroTamaroff Here is Convergence. I don't think that is it.

@robjohn True, I edited.

=)

I like Number 8 much more.

@robjohn Quite nice. My answer to the question is the way Naslund did it.

Anyone with an expertise in Galois theory here? I have a question.

Is there a condition for transformation of polynomials with variable coefficients over $\Bbb Q$, i.e., any particular restriction for the Galois group?

Of course, the variable coefficients must be independent in a sense to avoid the decomposition of galois groups which would make the solubility function field much much smaller.

@Fernando Hi

Hi @mike

having a great time here in sociology

@Mike Defend the Unabomber?

For example, the Unabomber is labelled a "serial murderer" but killed only 3 people.

He was a good mathematician.

Euler blew up airports too.

I hear that algebraic geometers like blowing up stuff on planes

@Mike ORLY.

Good afternoon guys.