Is $\pi = 4$ really?
The staircase paradox, or why $\pi\ne4$
How to create a table with long text and which packages use I want to make a persistent live Ubuntu USB drive with more than 4GB of storage.   I know there is an option of installing directly on the drive but I don't want to do this as it will restrict the drive from working on different computers.   One option is to make an additional partition with extra space but if I do this how can I get newly installed software to be stored on this partition? Clerical mistake in UK visa application: should I make a pen-and-ink correction or electronically edit the PDF? I've gone through all similar questions but I believe my specific question doesn't have an answer yet.  I've applied for a Standard Visitor visa. After I completed the application, made an appointment and paid the fee, I noticed that the way I spelled my name on the application differs from how it is spelled in the passport by 1 letter (this is partially because of myself being an idiot, but mainly because my new passport has an incorrect transliteration of my name, whereas my old passport and any other document in my life has the correct one).  So here are the options I see:   Print the application and make a pen-and-ink correction with a black ballpoint pen by crossing the printed name/letter and writing the correct one - as answers to other similar questions suggests. Edit the PDF electronically and print it so that there are no visible corrections. However, as the form is saved at their end, there will be a discrepance between the printed form and saved form with no visible signs of correction.   Which way has better chance for me to have my application accepted?  Also (probably doesn't matter much but still): if it's the pen-and-ink correction, is it better to cross-out the whole name or only the wrong letter? How to model effectively using exact measurements? I always struggle when trying to create a floor plan or furniture. How do I model using exact measurements. how to replace multiple strings together in Oracle I have a string coming from a table like "can no pay{1},as your payment{2}due on {3}". I want to replace {1} with some value , {2} with some value and {3} with some value .  Is it Possible to replace all 3 in one replace function ? or is there any way I can directly write query and get replaced value ?   I want to replace these strings in Oracle stored procedure the original string is coming from one of my table I am just doing select on that table   and then I want to replace {1},{2},{3} values from that string to the other value that I have from another table I masked an image in the UV/Image editor masking section. I then used that mask in the compositor for background replacement. However, the mask size seems to be different. Why is that? Here's a screenshot: Why won't vertical-align: middle work?  And yet, vertical-align: top does work.   span{   vertical-align: middle; } &lt;div&gt;   &lt;img src="https://via.placeholder.com/30" alt="small img" /&gt;   &lt;span&gt;Doesn't work.&lt;/span&gt; &lt;/div&gt; Can I ever play Undertale again normally? The ending I got is :      the genocide   When I reset my file, my past choices still take effect. I want to start a clean run.  I don't want to buy the game again, what do I do? This is a pretty simple question, at least it seems like it should be, about sudo permissions in Linux.  There are a lot of times when I just want to append something to /etc/hosts or a similar file but end up not being able to because both &gt; and &gt;&gt; are not allowed, even with root.  Is there someway to make this work without having to su or sudo su into root? How to customize title page in beamer so that it looks like How can I modify title page so that it looks like it is in  video. Please seek to 16 seconds and watch title page. I do not have permission to post images. I liked this theme and I want to make a beamer theme that looks similar. I tried with beamercolorbox but I failed to position the box to the bottom.      Edit: Here is my minimum working example  \documentclass[xcolor=dvipsnames]{beamer} \defbeamertemplate*{title page}{customized}[1][] { \usebeamerfont{subtitle} \usebeamercolor[fg]{subtitle}  {\flushright \setbeamercolor{author}{bg=white,fg=Red} \usebeamerfont{author} \insertauthor\par \usebeamerfont{institute}\insertinstitute\par }  \vspace{0.2in}  \setbeamercolor{postit}{fg=white,bg=YellowOrange}  \begin{beamercolorbox}[sep=1em,wd=1.062\textwidth,ht=3cm,dp=3cm,right]{postit} \usebeamerfont{title} {\huge \inserttitle}\par \usebeamerfont{subtitle} {\insertsubtitle} \end{beamercolorbox} } \usecolortheme[named=YellowOrange]{structure} \useoutertheme{infolines} \setbeamertemplate{navigation symbols}{}  \institute{Harvard College Professor and\\ Johnstone Family Professor in Psychology, Harvard University}  \title{SAY WHAT?} \subtitle{Linguistics as a Window to\\ Understanding the Brain} \author{Steven Pinker}  \begin{document} { \setbeamertemplate{footline}{} \begin{frame} \titlepage \end{frame} } \end{document} Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction I was looking at: $$\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$$  It's pretty easy proving the above using induction, but I was wondering what is the actual way of getting this equation? Can you concentrate on a special ability while also concentrating on a spell? There exist several abilities that have the text similar to, this effect lasts while you maintain concentration (as if you were concentrating on a spell). One such example is the Bard College of Glamour: Mantle of Majesty ability.     At 6th level, you gain the ability to cloak yourself in a fey magic   that makes others want to serve you. As a bonus action, you cast   command, without expending a spell slot, and you take on an appearance   of unearthly beauty for 1 minute or until your concentration ends (as   if you were concentrating on a spell). During this time, you can cast   command as a bonus action on each of your turns, without expending a   spell slot.   Another example is the Cleric Trickery Domain: Channel Divinity: Invoke Duplicity ability.     Starting at 2nd level, you can use your Channel Divinity to create an   illusory duplicate of yourself.      As an action, you create a perfect illusion of yourself that lasts for   1 minute, or until you lose your concentration (as if you were   concentrating on a spell).   While you are concentrating on maintaining such an ability would you also be able to maintain concentration on a spell that requires concentration?  There does not seem to be any RAW that limits this however the limitation around concentrating on a second spell exists which may suggest that the intent is that a character cannot concentrate on 2 effects at the same time unless explicitly stated. Call blocking for iPhone? How do I block unwanted callers without jailbreaking? Equivalence between least squares and MLE in Gaussian model I am new to Machine Learning, and am trying to learn it on my own. Recently I was reading through  and had a basic question.   Slide 13 says that "Least Square Estimate is same as Maximum Likelihood Estimate under a Gaussian model". It seems like it is something simple, but I am unable to see this. Can someone please explain what is going on here? I am interested in seeing the Math.   I will later try to see the probabilistic viewpoint of Ridge and Lasso regression also, so if there are any suggestions that will help me, that will be much appreciated also. Origin/reason for the expression "on the bus" instead of "in the bus" This is sort of a follow up to my question .  I was told a while ago that the reason why we use "on the bus" instead of "in the bus" is because back in the day buses were open, that is, they didn't have a roof.   Is this story correct or is there another reason why the correct expression is "on the bus", in spite of the fact that when one gets on the bus, he is actually inside the bus? How does the human eye knows how far the object from which the photon was reflected? A photon is emitted from a source and reflected off an object (or objects) until it hits the human eye. The color of the object we see depends on the photon wavelength. If photon travels with constant speed how does the human eye know how far the object from which the photon was reflected? I  have had no luck getting the buffer tool to accept anything but degrees as units of measure.  I have found lots of stuff saying the layer needs to be reprojected and saved but it hasn't worked at all for me.   Is there a way I could create a buffer without using ftools or at least force the units to meters somehow?  As a workaround I converted meters to degrees (lat) and used that but the final product needs to be as close to reality as possible.  Things I've tried:   setting every unit option I could find to meters (where possible). setting everything to NAD83/Maryland (data is for Washington, DC) and saving it as such (as layers in ESRI shape files). reimporting the reprojected layers setting relevant layers to Google Mercator   The was tried followed by creating a buffer. Many were tried in combination. QGIS 1.7.3 Slackware64 current (qgis from SBo-13.37 repo, tried on multilib and plain 64it with same results) A little look through an etymology dictionary shows that the root is Latin gigas with adjective form gigant.  So in its derivation to English, why did the second "g" get retained in gigantic but was dropped from giant?  I have an inkling that the word giant may have travelled through French on its way to English, where it may have been pronounced "gee-yant" or "jee-yant" with a change to the second "g" that was then dropped when taken into English.  However, the "g" is retained as a hard "g" in gigantic. Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$ Show a connected metric space (X,d) is $\epsilon$-chainable for $\epsilon &gt;0$       $\epsilon$-chainable Definition      (X,d) is $\epsilon$-chainable if given any two points $a,b \in X$, $\exists$ a finite set $\{ x_0,x_1,...,x_n\}$ of points in X with $x_0 = a$, $x_n=b$ and $d(x_{n-1},x_n)&lt;\epsilon$, $\forall$ n      Clopen Definition      A set is clopen $iff$ its boundary is empty      Connected Metric Definition      Let $(X,d)$ be a metric space. It is connected $iff$ it has no proper subsets which are clopen      The following are equivalent:         $X$ is connected   The only subsets of $X$ that are clopen are $\emptyset$ and $X$   $\nexists$ non-empty, disjoint, open sets $A$ and $B$ such that $X=A\bigcup B$   $\nexists$ non-empty, disjoint, closed sets $A$ and $B$ such that $X=A\bigcup B$         Theorem      Let $(X,d)$ be a metric space, and let $S$ be any subset of $X$. Then $S$ is closed $iff$ $S^c$ is open.     So how would someone show this exactly?  Let the set $A$ be the set of all elements in $(X,d)$ that can be reached from $a\in X$ in a finite number of steps with length less than $\epsilon$.  Does this mean that there should be no isolated points? (an isolated point would be at distance infinity from any other point, or distance zero from itself, since $\epsilon &gt;0$ we don't want this?)  Knowing that $X$ is connected $\implies$the only subsets of X that are clopen are $\emptyset$ and $X$  Also, by construction of A;   A is the set of all $\epsilon$-chains between any element and $a$  And, so $A^c = \emptyset$ if $A$ was $\epsilon$-chainable (because A has to have a path from all elements to a, for this to be true, the complement wouldn't have anything in it)  Leaving only $A$ as the remaining clopen set  Does this make any sense? Or should an alternative be used, and how to formalize it.  Thanks. Quitting a job in the US on a work visa, going to Canada and re-entering on a tourist visa (ESTA waiver) I have been working in the USA on an E-3 visa and intend to return home to Australia, but I want to travel around the US before I do so. I am under the impression that after leaving my current company, I will have 10 days to leave the country.   Will I be able to go into Mexico or Canada and re-enter with an ESTA waiver as a tourist?