Ok, please ignore my silliness.  So, why do we use radians in calculus and why is it considered more scientific than degrees. And how did mathematicians know or prove that radians would work for all integration, differentiation in other fields or is there a method to prove it?
I think this is just something I've grown used to but can't remember any proof.  When differentiating and integrating with trigonometric functions, we require angles to be taken in radians. Why does it work then and only then?
How can I get more of this macro photo in focus? I want to make a full focus on the body, for example: I need to have a clear focus on the each balls in the photo. I used just single point focus.    In this picture I used:   shutter speed: 8 aperture: F/4 ISO: 200 2 flashes, one in the right and one on the top of project camera: nikon d300s lens : 105mm micro 2.8   Thanks Change the title size in scrartcl I'd like to use a smaller title. I'm using the scrartcl documentclass from the . I can change it's color font but not it's size.  \setkomafont{title}{\normalfont\bfseries\small}   Everything works exept the size. Layover at Tokyo Narita airport: can I travel outside, and what kind of visa would I need? I am travelling from Singapore to San Francisco and the airline has a layover of 7.5 hours at Tokyo Airport (NRT). I am wondering if I would be allowed to go out to experience the city for a while in some form a visitor visa.  I know Singapore has such facilities, but does anyone know if I can do it in Tokyo? Any suggestions or pointers are welcome. Note - I do not have a visa for Japan yet, but I am hoping that 1 day visitor visa could be possible at airport. How do I install the latest version of EMACS and pick the appropriate UI? I'm running the latest Kubuntu (12.04 beta 2) and I would like to run the latest emacs (currently v24). The repos are one version behind. What's the best way to install v24 or later (and avoid future version conflicts)?  Also, is there any reason not to aways use the GUI version of emacs if X is running? For example, could I set the GUI emacs version as the default text editor and use it to edit cron jobs (crontab -e)? I'm assuming the answer is yes, but since I haven't done that yet (my default editor is nano), I want to check if there are reasons I should leave nano as the default editor.  Usually when I'm working on the command line I end up using nano. Now that I think about it, I have no idea why I keep doing that. Is there any downside to calling a GUI editor when working in an X terminal?  EDIT: I briefly tested these two versions   GNU Emacs 24.0.94.1 (x86_64-pc-linux-gnu, GTK+ Version 3.3.20) from  GNU Emacs 23.3.1 (x86_64-pc-linux-gnu) installed by default in Kubuntu.   .  Unfortunately (for me) the defaults installed version (23.3.1, 23.3+1-1ubuntu9) is the nox version.   Package: emacs23-nox Status: install ok installed Version: 23.3+1-1ubuntu9 Replaces: emacs23, emacs23-gtk, emacs23-lucid   The package with version 24 opens in GUI mode by default. That's what I prefer. Some of the version 24 changes that interest me are listed in the references below.   But there appear to be a multitude of different packages and versions I could install.  References:   What’s New In Emacs 24 (part 1) | Mastering Emacs  "    shell-mode uses pcomplete rules, with the standard completion UI.  Yowzah! There’s a lot of cool, new functionality hidden away in this gem of a change." EmacsWiki: Recent Changes You can't see the question owner's special color CHECK constraint in MySQL is not working Is it possible to write one CSS rule for several prefixed selectors? Negative y value in polar plot I'm having some trouble with polar plots. I have to plot negative values, but without changing direction. I tried to set the ymin value to be negative, but it doesn't work.  \documentclass[10pt,border=10pt]{standalone} \usepackage{pgfplots} \usepgfplotslibrary{polar}  \begin{document} \begin{tikzpicture} \begin{polaraxis}[    xticklabel=$\pgfmathprintnumber{\tick}^\circ$,    ymin=-10,    xtick={0,30,...,330}] \addplot table{    0  -1     30 -2    45 -3    60 -4    75 -5    }; \end{polaraxis} \end{tikzpicture} \end{document}   Any suggestion?  For clarity, this is what I expected. number of ways to make $2.00 How many different ways can you make $2.00 using only 1 cent, 5 cent, 10 cent, and 25 cent pieces, and 1 and 2 dollar bills (there are 100 cents in a dollar)? I have worked out an equation:  $$p + 5n + 10d + 25q + 100l + 200t = 200$$  Where all variables are non-negative integers. But I don't know what to do from here to figure out how many different sets of non-negative integers there are that satisfy this equation. What do I do next? Javascript - alert("zoo">"house") returns true 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. Is there any way to know when I will receive my UK visa? Google Spreadsheets: IF not working I have problems with my IF command in Google Sheets. If gives #ERROR! all the time. See this simple test:    Not even if I put in the number directly and avoid references:    Am I using the IF wrong? Or what could such a problem be? This example is from a new document. What is a serialVersionUID and why should I use it? Eclipse issues warnings when a serialVersionUID is missing.       The serializable class Foo does not declare a static final   serialVersionUID field of type long   What is serialVersionUID and why is it important?  Please show an example where missing serialVersionUID will cause a problem. How to down-weight older data in time series regression In a regression fit of vectors varying with time $t$ $\qquad y \sim [x_t\ x_{t-1}\ x_{t-2}\ ...] \cdot [c_t\ c_{t-1}\ c_{t-2} \ ...] $ , how can one down-weight the older $x_t$ to model "older is less relevant" (than the regression gives) ? Say that rows in data matrix $X$ are observables (stocks, market segments ...) and columns are times. Correct me,   weights rows; how does one weight columns, times ?  Added: Down-weighting older data in time series looks complex, much more so than linear least squares with i.i.d. errors in rows (observations) -- just divide through by $\sigma_i$; or classification  with i.i.d. errors in columns (e.g. features) -- just centre each column. Can anyone say either   yes, I downweight time series; here are some examples on the web no: down-weighting time series is complex, not for novices.   (  discussed this question 10 years ago, mentioning Kalman filters and hierarchical Bayes, but with no examples.) When A and B are positively related variables, can they have opposite effect on their outcome variable C? A is positively related to B.  C is the outcome of A and B, but the effect of A on C is negative and the effect of B on C is positive.  Can this happen? Can I change my itinerary and hotel reservation after getting a Schengen visa? If i try to update node revision like this:  $node = node_revision_load(59); $node-&gt;set('publish_on', null); $node-&gt;save();   or simple save:  $node = node_revision_load(59); $node-&gt;save();   I have a PHP memory error, (i have 1gb allocated) How can I get better results when doing camera motion tracking? Whenever I do camera tracking in Blender the reconstruction is always zooming out or not on the axis. I have a great quality camera, but the end results of the camera tracking always has the model sliding. If you have a solution please tell me. Can the effects of a person's mass upon the local gravitational field be detected and measured remotely?