I have this photo before and after being blurred (From Macphun software ad):    I dont know about you but for some reason the blurred version almost makes the island look like it is an intricately created miniature. I am not sure why.  I have seen this effect used in the Game of Thrones intro as well as some games but I cant explain how it works. Why does our brain perceive size differently in these scenarios?
This question isn't so much about how to achieve the effect of making a scene look like it's modelled in miniature, but why tilting the focal plane creates the effect. What is it about photographing miniatures that makes them look like miniatures, and how is this replicated by tilting the focal plane?  I can understand how when photographing a model of a scene, you have a much higher magnification, which leads to a shallower depth of field compared to when capturing the real-sized scene, but how does tilting the focal plane help? Is it just that you have the focal plane tilted relative to the plane that most of your subject is on, so that you can achieve a narrower depth of field for the focal length and aperture, or is there more to it than that?
Area of an ellipse. (Calculus) Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$ $$\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}\ dx$$   My approach :   Dividing the denominator by $\cos^2x$ we get $\dfrac{x^2\sec^2x }{(x -\tan x)(x\tan x +1)}$ then  $$\int \frac{x^2\sec^2x}{x^2\tan x -x\tan^2x+x-\tan x}\ dx=\int \frac{x^2(1+\tan^2x)}{x^2\tan x -x\tan^2x+x-\tan x}dx$$  But I am not getting any relation between numerator and denominator so that I will take any substitution and solve further please suggest whether it is correct and how to proceed in this. Thanks. Sometimes, when I upgrade a system via do-release-upgrade, the update process fails and the script tells me to finish the process manually via dpkg --configure -a. This is a not serious problem - after manually solving the dependencies problem and the finishing upgrade process all works well.  But the do-release-upgrade script has a cleanup process after finishing the upgrade:  Remove obsolete packages?   XXX packages are going to be removed.   Continue [yN]  Details [d]y   which removes some obsolete packages from old version of system.  Seems that this process doesn't execute when the automatic upgrade fails and I finish upgrade manually, so obsolete packages from old version remain installed in the system.  How I can run the "Remove obsolete packages" process manually after finishing the upgrade by hand? Is there an option to create and Opt-in a user in the same API call? Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$ Prove $\sin(x)\tan(x) &gt; x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$  So I did the following: Let $f(x) = \sin(x)\tan(x) - x^2$.  Then of course $f(0) = 0$ and I want to show that for $x \in ( \,0, \frac{\pi}{2}) \,$ $f'(x) &gt; 0$ but I don't really know where to go from here as I can't get anything reasonable done with the derivative.  I was thinking of approximating it using the following inequality $\sin(x) &lt; x &lt; \tan(x)$.   Is that a good direction? Trouble with Vakil's FOAG exercise 11.3.C I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty hypersurface, then $X$ and $H$ meet.   Following the hint, I've done the following: By assumption, $X$ is given by $V(I)$ for some homogenous prime ideal $I\subset k[x_0,\dots x_n]=:A$ and $H$ by $V(f)$ for some homogenous polynomial $f\in A$. We wish to prove that there is a homogenous prime ideal $\mathfrak{p}$ (that's not the irrelevant one) containing both $I$ and $f$.  Consider the affine cone $\mathrm{Spec}\ A/I$ of $X$ in $\mathrm{Spec}\ A$. Being homogenous, both $I$ and $f$ are contained in the ideal $(x_0,\dots x_n)$. By Krull's principal ideal theorem, every minimal prime ideal containing $f\mod I$ has codimension one. $X$ having dimension at least one implies that there are homogenous prime prime ideals $\mathfrak{q}\supsetneq \mathfrak{r}\supset I$. This implies that $(x_o,\dots x_n)$ has codimension at least two. Thus there are prime ideals containing $f\mod I$ that are contained in $(x_o,\dots x_n)$. However, I'd need to show that there are homogenous such prime ideals, right? I'd rather get hints than full solutions. How to give permissions to specific command? I would like to run fastboot command without sudo. it's working if I put sudo in front of it, otherwise it wont.  like this:  $ sudo fastboot devices 2738006a    fastboot  $ fastboot devices no permissions  fastboot   How do I solve this? Any way to tell apart a CPU defect from a mainboard defect? I have a fairly modern desktop computer, an AMD Athlon II X2 based silent PC, that does not work.  When turned on, it will start physically (all fans are rotating, disks start up...) but not give a signal on any of the graphics ports (DVI, VGA, and HDMI, I tried all three). Also, the reset button does not seem to have any effect.  I have stripped the mainboard bare of all SATA connections, extension cards, and the one 2GB RAM chip to eliminate them as the problem source, but to no avail, so I think it's fair to assume it's either the mainboard or the processor that are at fault.  However, I have neither a replacement mainboard, nor a replacement processor handy to identify which one is broken. The cause of the defect is unknown, so for all I know, it could be both. Therefore, I'm reluctant to buy replacement hardware blindly before knowing more.   Is there any way to further diagnose (or at least get some indication) which component is broken without buying replacement hardware? Every element of a group has order $2$. Why, intuitively, is it abelian? I have a Schengen visa valid from 19/07/2016 to 10/08/2016. But the duration of stay is 7 days only.  I want to stay for 6 days more, for a total of 14 days. And my flight includes travel from a Schengen state to another. System.LimitException: Too many query rows: 50001 What I am trying to do is to set a date in my date field and also update the object. I am using the class below to do so which works just fine in my sanbox but in production I am getting this error:      System.LimitException: Too many query rows: 50001   public with sharing class updateObject{     public  List&lt;NRProducts__c&gt;  values;     public PageReference updateObject() {         values=[SELECT Refreshed_Date__c FROM NRProducts__c ];         for (NRProducts__c s :values){            s.Refreshed_Date__c =Date.today();          }          update values;         return null;                       }     }   VF Page:  &lt;apex:page showheader="false" controller="updateObject" sidebar="false"&gt; &lt;apex:form&gt;  &lt;apex:commandButton action="{!updateObject}" value="Update"/&gt; &lt;/apex:form&gt; &lt;/apex:page&gt; I am compiling LaTeX files with Texmaker on Ubuntu 12.04 system.   When I run pdflatex and then view the pdf file (internal), it does not show me the exact place where I am editing on Texmaker i.e. the generated pdf file does not show me the position of the cursor.   But some days before it was working fine. I don't know what causes this problem.  I already tried uninstalling and then reinstalling, I did update and upgrade too. But the problem still persists. According to Wikipedia      extra disks should not be mounted in /mnt/ according to the first link, but doesn't seams so according to the second link.  Both say thought that they shouldn't be in /media.  Question  So where should extra permanent disks be mounted? If $X,Y$ are equivalence relations, so is $X \times Y$ Someone has pointed their domain (www.bomberball.net) to the same IP as my domain (www.kapparate.com) , and Google is now showing the former when searching for Kapparate, rather than the latter. What's the best way to block requests coming from www.bomberball.net ? How does the coin limit work? How do I perform a Perl substitution on a string while keeping the original? List of chat rooms with host stackoverflow.com is not the same as the actual list of rooms on stackoverflow.com chat itself Generally chat.&lt;site&gt;.com redirects to chat.stackexchange.com/?tab=site&amp;host=&lt;site&gt;.com and go for same thing but here you can check your self:       Both are Different!  If one visits  and select site: StackOverflow, then it outputs  and they miss rooms that are only listed by .  So, why does this happen? Is this a bug?  Note: I found this while  for general chat-room at StackOverflow; see chat-discussion Sometimes after I fry something, I wash it immediately in water because it's a bit easier to wash (before the remains stick to the pan).  Does this damage the pan in any way? Do you say IN one of the computers or ON one of the computers? Which is right?