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Arithmetic and geometric sequences: where does their name come from? Where does the name of these two famous types of sequences come from?  The article  of Wikipedia says that the geometric sequence is called like this because every term is the geometric mean of its two adjacent terms. Though it is true, it only reduces the question to: why is the geometric mean geometric (in opposition to the arithmetic mean).   Continuing my investigation on , I was told that a square with the same area than a rectangle with sides $a$ and $b$ has their geometric mean $\sqrt{ab}$ for side. That's again totally true, but a square with same perimeter than this rectangle of sides $a$ and $b$ has their arithmetic mean $\frac{a+b}{2}$ for side!  Thus, my question: Who coined these names? And why? Why is the geometric mean more geometric than the arithmetic mean? Functions that are their Own nth Derivatives for Real $n$ Has user testing found that the "three horizontal bars" for main menu on mobile is commonly understood? "Three horizontal lines" aka "hamburger icon" seems to be becoming a convention for the "main menu" button, especially on mobile sites:    Has anyone done any user testing of this convention, or got any A/B testing results? (i.e. is there an increase in bounce rate compared to using the word "Menu"?)  I did some quick user testing with wireframes featuring this icon for the main menu. 3 out of 6 people got it and used it. The others did not.  One person in particular had a lot of trouble "getting back to the top" (i.e. restarting their navigation from the top level of the site) as they didn't know about the convention, or that the logo would link to the home page.  I guess it will be different for different demographics - users of Facebook on mobile probably know it.  Anyone got any findings they can share? I need to get a nice picture about how electron moves around nucleus? I find concept of probability and orbitals quite difficult to understand? How to check whether a JavaScript variable defined in cross-browser way?  I ran into this problem when writing some JavaScript utilizing FireBug logging. I wrote some code like below:  function profileRun(f) {     // f: functions to be profiled     console.profile(f.constructor);     f();     console.profileEnd(f.constructor); }   It works fine in FireFox/FireBug, but it reports error in IE8 RC1. So, I'd like to do some checking whether console variable exists in the execution environment.  Below code works fine in FireFox, but not in IE8 RC1.   function profileRun(f) {     if (console != undefined) {         console.profile(f.constructor);     }      f();      if (console != undefined) {         console.profileEnd(f.constructor);     } }   However, if I do it this way. It works in IE8 RC1. Why?   function profileRun(f) {     if (window.console != undefined) {         console.profile(f.constructor);     }      f();      if (window.console != undefined) {         console.profileEnd(f.constructor);     } }   Is there any cross-browser way to check it? Is it possible and if so how can you pass flags to the ShareLaTeX compiler which one would have passed as parameters to the LaTeX compiler?  I am using the minted package and need to pass the -shell-escape flag. I just need to check the reasoning in my proof is correct, I think it is valid although I'm not totally convinced because I can't follow the logic; does proving that $x$ is an integer prove that $ac|bd$?  Theorem: Let $a$, $b$, $c$, $d$ be integers. If $a|b$ and $c|d$, then $ac|bd$.  Proof: $aj=b$ and $ck=d$ for integers $j$, $k$. Then, $ac|bd$ implies $acx=ajck$ and thus $x=jk$ for some $x$. Since the product $jk$ is an integer, $x$ is an integer and thus $acx=ajck$ and thus $ac|bd$. My question is from Apostol's Vol. 1 One-variable calculus with introduction to linear algebra textbook.  Page 57. Exercise 12. Show that the following are polynomials by converting them to the form $\sum_{k=0}^{m}a_kx^k$ for a suitable $m$. In each case $n$ is a positive integer. $a)$ $(1+x)^{2n}.$ $b)$ $\frac{1-x^{n+1}}{1-x}, x\not=1.$ $c)$ $\prod_{k=0}^{n}(1+x^{2^k}).$  The attempt at a solution: a) part of the problem is pretty easy I guess, it is example of binomial theorem, so the answer would be $(1+x)^{2n}=\sum_{k=0}^{2n}(^{2n}_{k})x^k.$ Answer to part b) would be the following: $$\frac{1-x^{n+1}}{1-x}=\frac{(1-x)(1+x+x^2+\cdots+x^n)}{1-x}=1+x+x^2+\cdots+x^n=‌​\sum_{k=0}^{n}x^k.$$thanks to @DiegoMath's hint. As for part c), we have $$\prod_{k=0}^{n}(1+x^{2^k})=(1+x)(1+x^2)(1+x^4)(1+x^8)\cdots(1+x^{2^n})$$ and I have trouble &quot;converting&quot; this to sum which would be of a form of polynomial. What is a Vanilla JS or jQuery solution that will select all of the contents of a textbox when the textbox receives focus? I want to reinstall Ubuntu from scratch.   I have read ( and ) that it is recommended to have 3 partitions for the desktop installation: root, home and swap as having a separate home and root can simplify the process if you want to upgrade or reinstall Ubuntu (if you break something by mistake).  But there is no type of formula (that I can find) on how big each partition should be. I know this is somewhat dependant on what you plan to install. I want to have flexibility down the line to install new software without having to worry about shifting the partition sizes around.  Does anyone know of a formula or percentage breakdown that they have used to successfully calculate partition sizes?  i.e. x% of space will be allocated to the swap, y% of space to the root partition and z% of space to the home partition Prove by induction $\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{n}\ge\frac{2}{3}n\sqrt{n}$ for all positive integers Assumption: $\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}\ge\frac{2}{3}k\sqrt{k}$   Prove true for $n=k+1$ $$\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}+\sqrt{k+1}\ge\frac{2}{3}(k+1)\sqrt{k+1}$$  I'm upto :$$\sqrt{1}+\sqrt{2}+\sqrt{3}+...+\sqrt{k}+\sqrt{k+1}\ge\frac{2}{3}k\sqrt{k}+\sqrt{k+1}$$after which I'm stuck. In a script I'm trying to find the Terminal.app window containing a specific tty device and raise that window to the top. Here's what I have in Applescript so far:  tell application "System Events"   set foundWin to false   if (name of processes) contains "Terminal" then     tell application "Terminal"       set theTabs to first tab of every window where tty is "$(tty)"       repeat with theTab in theTabs         if class of theTab is tab then           set theWin to (first window whose tabs contains theTab)           set selected tab of theWin to theTab           set foundWin to true         end if       end repeat     end tell   end if   if foundWin then     --RAISE THE WINDOW?!   end if end tell   Where I'm getting stuck is the "raising the window" part.  Here are some things that are not quite what I want:  set frontmost of theWin to true -- this brings the window to the front of the group of Terminal.app windows but doesn't raise it above any other windows.  tell application "Terminal" to activate -- this brings every Terminal window to the front in a big stack. I just want the one window.  tell application "System Events"     set theSysWin to first window of process "Terminal" whose name is (name of theWin)     perform action "AXRaise" of theSysWin end tell   This almost does it, but what it does is to raise the terminal window to the #2 position, still underneath the active window (if the active app is something other than Terminal.app.)  click theSysWin at {10,50} -- doesn't seem to do anything.  click first static text of theSysWin -- doesn't seem to do anything.  Is there a way to do this? It doesn't have to be in Applescript.  EDIT I did find this web page (  ) quoting an Obj-C/Cocoa call:  SetFrontProcessWithOptions(&amp;psn, kSetFrontProcessFrontWindowOnly);  I'm not familiar with either ObjC or Cocoa, and this is (ultimately) getting invoked from a shell script, so not sure where to go from there. Getting the class name of an instance? How do I find out a name of class that created an instance of an object in Python if the function I am doing this from is the base class of which the class of the instance has been derived?  Was thinking maybe  might have helped me out here, but it doesn't seem to give me what I want. And short of parsing the __class__ member, I'm not sure how to get at this information. What is the difference between #include  and #include "filename"? In the C and C++ programming languages, what is the difference between using angle brackets and using quotes in an include statement, as follows?   #include &lt;filename&gt;  #include "filename" Where are the Unity desktop wallpapers located? I've not seen/read any female Orcs mentioned in the movies or in the books. In one of the movies, an Uruk-hai is momentarily shown emerging from a giant, grown-Orc sized flesh packet. So are they created with spells, or do they follow the Standard Reproductive Model. When on the road as a tourist, I often do not carry a reflector of flash. Now I am at a location with very strong sunlight and I want to take a photo of a companion in front of a nice scenery or building, the classic "we have been here" photo.  With very strong sunlight however, specially at a slight angle, I either get it into the person's eyes and they squint like crazy, or they are in the shade and their whole face is black.  Please note that I do not have aspirations to take a professional photo in such circumstances, but at least something acceptable.  Is there an easy trick to deal with that? "become a President" or "become President" If he had not been a film star, he would not have become President.     In my opinion, "a President" is correct. Examples:     "My dream is to be a teacher"   "My dream is to be a President"   Which is correct usage? President or a President? Can't restart nginx, bind() failed (98: Address already in use) I'd like to create a PDF report with knitr with LaTeX-code in RStudio with biblatex for citations. However, the in-text-citations are always undefined and no bibliography is printed. The same bibliography works perfectly with a pure .tex-document stored in the same folder and containing the same citations, same path to the .bib-file etc. However, as for all references (also with hyperref) I have to compile twice. I thought this might be the problem with knitr (that the compilation is run only once), but the hyperref-references to figures work well. Any idea what might go wrong with the bibliography when using knitr and how I can solve the problem?  MWE:  \documentclass{article}  \usepackage[style=authoryear-comp, maxnames=1, bibencoding=utf8, backend=biber]{biblatex} \bibliography{ZoteroOutput.bib}  \begin{document}  According to the literature \parencite{gonzalez2003} we can assume...  \printbibliography  \end{document}   From the log-file:  Package biblatex Warning: Please (re)run Biber on the file: (biblatex)                mwe (biblatex)                and rerun LaTeX afterwards.