Look at these two photos of my shadow from sunlight.  Case 1: My shadow is separated from the shadow of the ceiling and my head is round.  Case 2: But when I walk a little more and the shadow of my head and the shadow of the ceiling are almost together, the shadow of my head tends to deform. Why?  Edit: Ok. The deformation is because the sun is not a point source and there are fuzzy shadows. But when I look the second picture only my head is deformed and not the ceiling, why?   Here is another picture.
I was laying on my bed, reading a book when the sun shone through the windows on my left. I happened to look at the wall on my right and noticed this very strange effect. The shadow of my elbow, when near the pages of the book, joined up with the shadow of the book even though I wasn't physically touching it.   I have posted :The video seems to be the wrong way up, but you still get the idea of what is happening.  What is causing this? Some sort of optical illusion where the light gets bent?  Coincidentally, I have been wondering about a similar effect recently where if you focus your eye on a nearby object, say, your finger, objects behind it in the distance seem to get curved/distorted around the edge of your finger. It seems awfully related...  EDIT: I could see the bulge with my bare eyes to the same extent as in the video! The room was well light and the wall was indeed quite bright.
"Closed" (square) root symbol I found a cool trick in the  which allows the square root sign to be altered such that it &quot;closes&quot; over its contents. Here's an example:  (&quot;closed&quot; root on the left, normal one on the right) The way they do this is as follows: % New definition of square root: % it renames \sqrt as \oldsqrt \let\oldsqrt\sqrt % it defines the new \sqrt in terms of the old one \def\sqrt{\mathpalette\DHLhksqrt} \def\DHLhksqrt#1#2{% \setbox0=\hbox{$#1\oldsqrt{#2\,}$}\dimen0=\ht0 \advance\dimen0-0.2\ht0 \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}% {\box0\lower0.4pt\box2}} The cool thing is that (as far as I've tested it) this works regardless of the math font and with pdftex as well as xetex. However what is not possible is mulitple roots, such as \sqrt[3]{a}. Those produce incorrect output when this &quot;trick&quot; is being used. So my question is, is somebody able to tweak this code so that it works for multiple roots as well? Adding a reference between Eclipse Java projects I constantly stay up to date with each new release of Blender, but this means my preferences are wiped clean each time. How do I export/import these preferences to avoid loosing my carefully crafted set up each time? I deleted an answer which had no upvotes or downvotes, but after some time I saw that my reputation was -2 and the reason is linked to my search engine.    I want to know why this happened and what "linked to my serach engine" means? Looking for a basic PostGIS viewer to use as basis for own application I'm looking for a rather basic PostGIS viewer. It should be possible to pan, zoom and retrieve coordinate information on mouse click. No need to support coordinate transformations. It should introduce as little further dependencies as possible. Preferably written in C++. Basically, I'm trying to override some files of the Uncode theme. But this is not a theme-specific question: it can be applied to any theme. The Uncode theme has a custom dir 'partials' (/uncode/partials/) that contains some layout elements. On my child theme I created a 'partials' folder as well (my-child-theme/partials), but the inner files seem not to be overridden. Is it normal? WP docs say that any file of the same name should be overridable, but is seems that's not true. Am I doing something wrong? Intuitive explanation for dividing by $n-1$ when calculating standard deviation? How to install World of Warcraft? Constraint the camera to look at an object In my scene I have a camera sitting at the origin. I would like to contraint it so that it always looks at the center of a given object. But the camera should not change its position.  I found some answers using a "TrackTo" or "LockedTrack" constraint but could not manage to make it work.  Could I probably use a Driver for this and if yes, how can I adjust it?  Thanks in advance! How to create subfloat figures (two in first row and one below)? I want to place three figures like this on the page:  (a) (b)   (c)   How do I achieve this using subfloat or any other method in LaTeX? The three figures need to have a common caption and label.  I have tried this:  \begin{figure}[h] \centering \begin{tabular}{c c} \subfloat[] { \includegraphics[scale=0.4]{1.pdf} } &amp; \subfloat[] { \includegraphics[scale=0.4]{2.pdf} } \\ \multicolumn{2}{c} \subfloat[] { \includegraphics[scale=0.6]{3.pdf} } \end{tabular} \caption{Some caption} \label{some-label} \end{figure}   But, this is displaying [] for the third figure instead of (c). Also it displays [] to one side of the page instead of center. How do I fix a "Problem with MergeList" or "status file could not be parsed" error when trying to do an update? The computer gave me this output in a window:  E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_natty_main_binary-i386_Packages E: The package lists or status file could not be parsed or opened.   How can I fix this? Why does "touch -a" also set the ctime? Is it touch(1) from coreutils-8.4-37.el6.x86_64 or my brain which is broken?  $ touch abc $ LANG=C stat abc   File: `abc'   Size: 0               Blocks: 0          IO Block: 4096   regular empty file Device: fd04h/64772d    Inode: 10485773    Links: 1 Access: (0664/-rw-rw-r--)  Uid: (3060399/ nodakai)   Gid: (  418/   quant) Access: 2016-10-14 18:42:06.189751847 +0800 Modify: 2016-10-14 18:42:06.189751847 +0800 Change: 2016-10-14 18:42:06.189751847 +0800 $ touch -a abc $ LANG=C stat abc   File: `abc'   Size: 0               Blocks: 0          IO Block: 4096   regular empty file Device: fd04h/64772d    Inode: 10485773    Links: 1 Access: (0664/-rw-rw-r--)  Uid: (3060399/ nodakai)   Gid: (  418/   quant) Access: 2016-10-14 18:42:17.374235446 +0800 Modify: 2016-10-14 18:42:06.189751847 +0800 Change: 2016-10-14 18:42:17.374235446 +0800 $ touch --help | grep 'access time'   -a                     change only the access time   As you see, it was not only atime but also ctime which was updated by touch -a !?!?  The filesystem is ext4 over LVM if that makes any differences. If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$ Let $A\in M_n(\mathbb{R})$be a matrix. Then, if we have $A^{2n}=I$, can we say that $A^n=\pm I$?  I think yes, because the annihilating polynomial is $x^{2n}-1$. Therefore the characteristic polynomial should be one of $x^n-1$ or $x^n+1$. Thus, since the matrix consists of real numbers, therefore, the matrix $A^n=\pm I$. Am I wrong?Thanks beforehand. How to "add existing frameworks" in Xcode 4? Subtracting even and odd binomial coefficients? Is there some sort of classification of all minimal non-cyclic groups? Does there exist some sort of classification of all minimal non-cyclic groups (non-cyclic groups, such that all their proper subgroups are cyclic)  I know the following classes of such groups:  1) $C_p × C_p$, where $p$ is a prime  2) $Q_8$  3) $\langle a,b | a^p = b^{q^m} = 1, b^{−1}ab = a^{r}\rangle$, where $p$ and $q$ are distinct primes and $r ≡ 1 \pmod q$, $r^q ≡1 \pmod p$.  (These three classes completely cover the case, when our group is finite: )  4)$C_{p^{\infty}}$, where $p$ is a prime  5)$(\{ \frac{n}{p^m}| m, n \in \mathbb{Z} \}, +)$, where $p$ is a prime  (These two classes completely cover the case, when our group is infinite abelian: )  6)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{p}$ for a fixed prime $p$ (Tarski monster groups)  7)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{\infty}$ ().  However, I do not know, whether there exists anything, that does not fall into these classes. I only know, that if such groups exist, they have to be infinite non-abelian. Ok, I must be missing something obvious, but I'm having trouble adding a link to user/%/edit to the main menu.  In the Menu UI, I clicked "add link," set the title to "Account settings," and then was at a loss about what to put for the path.  I know how to generate a link to the account edit page using views, which is what I've always done before, but this time I actually need to add the link to the "Main Menu." Read from location on console C# Word 2010 Number of pages without first page I show the number of pages as 1 / 4, with 4 being the total number of pages. But I do not want to count the first page.  Important: I know how to do it for the current page number (Starting at ..), I mean the total number of pages.  So if the document has one cover page + 3 pages, I want to show it as 1/3, 2/3 ..., not as 1/4. App crashes, dock icon remains, can't reboot, yet no process in ps aux to kill