@DylanMoreland I don't know, I never bothered, but those who did, manage to do a lot of good stuff with it. On the other hand, I think with a bit of practice XY can draw pretty nice diagrams, too.
@tb for large enough index, Fibonacci numbers are nearly indistinguishable from $\phi^n/\sqrt 5$, so I'd think a plot of these with increasing index wouldn't stay below some line.
@Srivatsan "I don't know if it was intended that way, but the tone of the response to Srivatsan is very hostile. –" I'm very tempted to say youtube.com/watch?v=AKtwlHV1-O8
@Ilya It looks as if it is already opened. Sorry, I was gone today, so I didn't get to it earlier. I tried to forestall the closure, but I was unsuccessful, it seems.
@robjohn well, yesterday I had negative score and today one upvote (and a non-answer that I deleted because I was too lazy to fix it and now someone else wrote it up).
@tb, About the convex function question, wikipedia seems to think that composition of convex functions need not be convex. The outer function should be monotone increasing...
It will suffice to show this, no? If $\stackrel{\frown}{AC}$ is an arc and $B$ is a point in between, then the area of the triangle $ABC$ is maximised when $B$ is the midpoint of the arc.
I'm wondering if using this inductively finitely many times will show that the given optimal n-gon is regular.
Lemma: Suppose $\stackrel{\frown}{AC}$ is an arc, and $B$ is a point in the interior of the arc. Then the area of the triangle $ABC$ is maximised when $B$ is the midpoint of the $\stackrel{\frown}{AC}$.
Suppose that there is an $n$-gon of largest area. Assume it has two adjacent sides $AB$ and $BC$ (say) unequal. Focus on the arc $ABC$ and apply the lemma: you can "correct" the $B$ to $B'$ such that $AB'C$ is of strictly larger area than $ABC$.
The rest of the polygon is the same. So we got an even larger $n$-gon, contradiction.
I have no idea what the suggested edit is doing. I think the answer is fine, but I want to understand the suggestion. That seems very hard in this case...
I'm not quite sure what you're trying to say: is that image a mathematical object or is it an actual image? (in any case write $x \in \Omega \subseteq R^2$.
I think you're trying to squeeze a bit too much information in one sentence. You should say that you work with planar coordinates in $\mathbb{R}^2$. Then say what $\Omega$ is. Then you can simply say that "where $x \in \Omega$ is the location of the given image"
or "where $x \in \Omega$ describes [or: determines] the location of the given image"
I have too books by him. One is "Analytic Quotients" another one is about forcing (joint with Todorcevic). I hope I will get to reading the books some day.
@AsafKaragila I only wrote that accepting can be useful, so that the question does not pop out on the main site repeatedly. He admitted this might be a reasonable point, but that this seemed different to him from what preceding comments were saying.
He didn't want to follow the norms, when you gave a very good reason for accepting he agreed with that - but since it is not what the other users said he will not accept answers... that's just standing on the principle of things without a good reason.
Well, there are plenty users with low acceptance rate. I am just saying I am not too happy that he went away from the site (that the user was deleted).
I know there are many, often they do not know about accepting answers and rectify that when being told. However he was a bad case of "Never do what you're told." and preferred to leave rather than trying to understand.
@JM : D @Srivatsan You guys are thinking way too much : D They were not being silly. I also wear their trousers sometimes because they're baggy and that's comfy : ) And yes, they were offering new clothes.
@Matt I started reading back on the replies of the replies of this message, and I got to the strange question "Do you think you can fall in love with someone that you met online?"
From that to this is quite a digression, and to think I wasn't even involved in the conversation!
In [this](http://math.stackexchange.com/questions/82240/proof-of-the-lebesgue-number-lemma) one I think you can delete the 3 first sentences in the second paragraph. For the inclusion argument I think I'd choose $\delta := \frac{\min r_x}{2}$ and then because $d(x,y) < 2 \delta$ you get $B(y, \delta) \subset B(x, r_x) \in \mathcal{A}$. What do you think?
The leg bone connected to the hip bone, the hip bone connected to the pelvic bone, the pelvic bone connected to the spine bone, the spine bone connected to the backbone, the backbone connected to the neck bone, the neck bone connected to the wish bone, the wish bone connected to the fairy bone, the fairy bone connected to the gay mafia, the gay mafia connected to the film industry, the film industry connected to the Oscar, the Oscar is the first name of Zariski...
@Gigili Oh, I thought you meant here in chat. On SE I wouldn't know which tag. Try with heap, the worst that can happen is that you get migrated to SO.
@Matt "Suppose a max heap with N different elements which is implemented by array (the biggest element is the first one in array), what's the index of the fourth biggest element?" If you have time to think about it , please ping me so I'll read your answer later. Thanks a lot.
@Gigili There is more than one valid index for the 4th largest element. Take for example N=4, then you get 3 valid max-heaps and if you look at the index where the 4th largest element is stored you'll find that it could be array position 2 or 3. For bigger N you get more possibilities. Are there any further constraints on that heap?
I don't get it, even for N=4 *=* .. But your answer is correct according to my book, it says there are possibilities from 2 to 15 index) where the 4th biggest element is stored.
Does anyone know how to get all solutions of the equation $a^3=b^3+c^3$ when $b,c$ quadratic irrationals or $b$ rational and $c$ quadratic irrational?
