I'm planning to play a Sun Soul Aarakocra monk. With the flight of the Aarakocra I can essentially hit someone, fly up and repeat. Let's say I fly up 50 feet and decide to drop to the ground. Does the 50 feet drop count against my movement or no? Is there any rules that specify that so I can justify it to my DM.
If you willingly fall on your turn does it cost movement?  As a DM I'm thinking about how to handle things such as creatures who are immune to being prone, diving into the water from a height, or a flying creature diving off a cliff and taking a fall before taking flight. There are many circumstances where you can fall without taking damage or being knocked prone afterward, and I'm not sure how to determine movement following the dive.  For example, my character walks up to a ledge above a 10 foot drop to the ground below. After taking 5 feet of movement to step off the ledge, I allow myself to fall. When I hit the ground have I used 15 feet of movement or just 5?
Helpful flags not getting updated after getting 'close question' privilege Possible Duplicate:          I recently got the ability to cast close votes. So, even if I flag a question as 'not constructive' or 'not a real question', it is still considered as a close vote. What is strange is that my 'helpful flag' count has stopped increasing after this change. Or at least it doesn't increase in cases where my flagging was automatically changed to a close vote and the post actually was closed. Is this how it is supposed to be?   I am guessing that once the post gets closed, the moderators are probably not bothered about marking flags as helpful. The only problem is that the Deputy badge will be much more difficult to get now. Earlier all the flags were getting converted to helpful, but now they just go in as close votes and don't show up on my profile page. Problem numbering environment What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?  Some subjects off the top of my head that probably need covering:   Differential geometry, Manifolds, etc. Lie groups, Lie algebras and their representation theory. Algebraic topology. How do I save terminal output to a file? How do I save the output of a command to a file?  Is there a way without using any software? I would like to know how. Is it correct to sometimes capitalize words mid-sentence in computer user interfaces? What is a good book to learn number theory? What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks. existence of sequence of polynomial Is there a sequence of polynomials $P_n$ such that   $\displaystyle\lim_{n \to \infty} P_n(z) = \begin{cases} 1, &amp; \text{Im } z &gt; 0\\ 0, &amp; z \text{ is real,} \\ -1, &amp; \text{Im } z &lt; 0 \end{cases}$  I have no clue where to start from. Please provide some hints. Thanks in advance. Dealing with multiple private DNS servers How to obtain and use the .bbl file in my tex document for ArXiv submission? I am trying to solve a problem from Stanley's book, it says:  Fix $k,n \in \mathbb{P}$. Show that: \begin{align} \sum a_1 a_2 \cdots a_k = \binom{n+k-1}{2k-1} \end{align} where the sum ranges over all compositions $(a_1 , a_2 , \ldots , a_k)$ of $n$ into $k$ parts.  I am trying to reason like this:  we need to find the coefficient $c_n = \sum a_1 a_2 \cdots a_k$ from this generating function --  \begin{align} \sum_n c_n x^n &amp;= \sum_n \sum a_1 a_2 \cdots a_k x^n \\  &amp;= \sum_n \sum a_1 a_2 \cdots a_k x^{a_1 + a_2 + \cdots + a_k}\\ &amp;= \sum_n \sum a_1x^{a_1} a_2x^{a_2} \cdots a_kx^{a_k} \end{align}  after that, I have no clue, how do I solve this ?   moreover, what is the range in the inner sum ?    If we consider Mark Riedel's answer, and assume $n=4$, $k=2$; then the sum will be  \begin{align} \sum (z + 2z^2)^2 = z^2 + 4z^3 + 4z^4 \end{align}  On the other hand the compositions will be $(1,3), (2,2), (3,1)$, therefore the above sum will be counted as:  \begin{align} (1.3)z^{1+3} + (2.2)z^{2+2} + (3.1)z^{3+1} &amp;= 1z^1.3z^3 + 2z^2.2z^2 + 3z^3.1z^1\\  &amp;= 3z^4 + 4z^4 + 3z^4 = 10z^4 \end{align}   what's going on? what am I missing? Print only the Nth line before each line that matches a pattern I'm trying to print only the &lt;N&gt;th line before a search pattern. grep -B&lt;N&gt; prints all the &lt;N&gt; lines before the search pattern. I saw the awk code  that can print only the &lt;N&gt;th line after the search pattern.  awk 'c&amp;&amp;!--c;/pattern/{c=N}' file   How to modify this to print only the &lt;N&gt;th line before each line that matches pattern ? For example, here is my input file  ... ...    0.50007496  0.42473932  0.01527831    0.99997456  0.97033575  0.44364198 Direct configuration=     1    0.16929051  0.16544726  0.16608723    0.16984300  0.16855274  0.50171112 ... ...    0.50089841  0.42608090  0.01499159    0.99982054  0.97154975  0.44403547 Direct configuration=     2    0.16931296  0.16553376  0.16600890    0.16999941  0.16847055  0.50170694   ...   I need a command that can give me back the 2nd line before the search string Direct configuration. I'm trying to run this in SUSE-Linux Undefined Symbol ___gxx_personality_v0 on link I've been getting this undefined symbol building with this command line:  $ gcc test.cpp Undefined symbols:   "___gxx_personality_v0", referenced from:   etc...   test.cpp is simple and should build fine.  What is the deal? Are the LIGO observations proof of a black hole merger, and what happened to the black holes? Here's a pickle: reference style links in markdown are fantastic. Numbered footnotes, however, can be a pain. Named references are a beautiful solution, but the editor seems to choke on them in certain contexts, throwing an error:  your post appears to contain code that is not properly formatted as code...  I've looked at a  and tested it out quite a bit and I'm pretty sure line breaking isn't the problem, named references are valid , and I can get multi-word named references to work basically every time (in this post, even). Is there a reason for named references to be seen as improperly formatted code in certain contexts? At the risk of being verbose (but for the sake of completeness), here's the source of the specific question I was trying to post when I encountered the problem: I'm trying to build a [Google Apps Script] that integrates with [Trello], the idea being to use it to push information from spreadsheets and forms into the [Trello API] and create cards on a `pending` list on a certain board.  I found this [question] on here that pointed me in the right direction, and added in OAuth based on the [GAS OAuth Documentation]. The problem is I can't post the the board. I run the script, the OAuth prompt fires, and the script completes with no errors. I can also `GET` data from the private board, so I assume the authorization is working properly.  So, what am I doing wrong that prevents my script from `POST`ing to Trello?  Here's the code I'm working with:      var trelloKey = [Trello API key];     var trelloSecret = [Trello API key secret];     var trelloList = [the id of the list we're posting to];      var oauthConfig = UrlFetchApp.addOAuthService('trello');         oauthConfig.setAccessTokenUrl('https://trello.com/1/OAuthGetAccessToken');         oauthConfig.setRequestTokenUrl('https://trello.com/1/OAuthGetRequestToken');         oauthConfig.setAuthorizationUrl('https://trello.com/1/OAuthAuthorizeToken');         oauthConfig.setConsumerKey(trelloKey);         oauthConfig.setConsumerSecret(trelloSecret);      function createTrelloCard() {        //POST [/1/cards], Required permissions: write       var payload = {'name': 'apiUploadedCard',                       'desc': 'description',                       'pos': 'top',                       'due': '',                       'idList': trelloList};        var url = 'https://api.trello.com/1/cards'       var options = {'method' : 'post',                      'payload' : payload,                      'oAuthServiceName' : 'trello',                      'oAuthUseToken' : 'always'};        UrlFetchApp.fetch(url, options);     }  [Trello]: http://trello.com [Google Apps Script]: https://developers.google.com/apps-script/ [Trello API]: https://trello.com/docs/ [other question]: http://stackoverflow.com/questions/18710641/trello-api-how-to-post-a-card-from-google-apps-script-gas [GAS OAuth Documentation]: https://developers.google.com/apps-script/guides/services/external#making_requests_to_services_with_oauth  If I'm being a complete dunce, please let me know. It seems like one of those errors where it's either a hardcore backend bug or a really stupid user mistake and I'm ready to admit to the latter. Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $? I've worked out a few summation formulas, and I am hoping to find a pattern. Unless I have made a mistake somewhere, we have the following identities:  $$\sum_{1 \le i \le n} i = \frac{(n+1)n}{2} $$  $$\sum_{1 \le i &lt; j \le n} ij = \frac{(3n+2)(n+1) \, n \, ( n-1)}{24}$$   $$\sum_{1 \le i &lt; j &lt; k \le n} ijk = \frac{(n+1)^2 \, n^2 \, (n-1)(n-2) }{48}$$   It seems clear that $$p_k(n)= \sum_{1 \le i_1 &lt; i_2 &lt; \dots &lt; i_k \le n} i_1 i_2 \cdots i_k $$ is a polynomial in $n$ of degree $2k$. But is there a nice closed-form formula for it? Maybe in terms of its factorization?  Comment: I realize that what I am looking for is the coefficient of $t^k$ in the expansion $$(1+t)(1+2t) \dots (1+nt),$$ so maybe generating function techniques could be helpful. But the main way I know to extract the coefficient of $t^k$ is to take derivatives $k-1$ times and on the surface of things that looks like a huge mess. We know that wizards in the Harry Potter universe are subject to regular physical harm (e.g. witness injuries from being hit by Bludgers or just colliding with things when playing Quidditch).  Therefore, it's almost a certainty that an average wizard would be vulnerable to, say, a bunch of bullets.   There may likely be spell(s) to protect from projectiles - witness Dumbledore's  deployed when Voldemort sent a bunch of glass at him during the  at the end of Harry Potter and the Order of the Phoenix (according to , possibly an unusually powerful Protego or the Silver shield).   But:   those spells obviously take effort/energy/time to cast (not everyone's Dumbledore) AND more likely than not most Death Eaters wouldn't recognize a Muggle gun for a threat (or realize what kind of threat) till too late.   So, the guns should at best allow an over-matched OotP member (e.g. Harry or Hermione) to greatly equalize the power between any regular Death Eaters and themselves, and even perhaps help against Voldemort (who can't be killed with a bullet, but, at best, would need to expend magical energy and time into conjuring a shield, and, at worst, be stopped/interrupted/driven off).  So I'm looking for an explanation - ideally in-universe, but possibly just some statement by JKR - of why the Muggle-born OotP - who are likely very much at ease AND familiar with Muggle technology and live in the late 20th century - do not use guns. Or, for that matter, ANY Muggle technology of the late 20th century? Cue Arthur C. Clarke's "indistinguishable from magic" meme.  Even if they are on some kind of idiotic moral crusade to never kill their opponents (even the Jedi aren't this dumb), given the time-frame, non-lethal weapons would have already existed, such as rubber bullets and tasers.  NOTE: Please don't offer the "if they do it, Death Eaters would start using guns as well" theory. First, Death Eaters would have used the guns if they knew how to, anyway. Second, the guns, like any "secret weapon", could be reserved for strategic battles, say the defense of Hogwarts in Deathly Hallows.    The origin of the question stems from two things.  First, Harry's fascination with all things that are different in the magical world (e.g. moving photographs), based on his knowledge of the Muggle material world, as well as the somewhat amusing cluelessness of the "Muggle artifacts" expert, Mr. Weasley, regarding Muggle items and how they work.   Basically, from the books, it's clear that the Wizarding world wouldn't know details about guns or what they are for or how they work.  The second thing is it's clear, at least initially, that wizards are afraid of Muggles finding out about them. Hence all the efforts to cloak their society (basically, do you REALLY want every Muggle gunning for you, even with Magic)? The idea of how control over the Muggle world seems to be more indirect, by Death Eaters asserting mind-control over the government. This means there's an implicit understanding by Death Eaters that they don't stand a chance against armed Muggles even given the magical disparity.  Considering Harry and Hermione's overall adaptability and inventiveness (and brains in the latter case), it's mind-boggling that the idea of fighting Death Eaters with modern technology completely slipped their mind. I mean, it's a basic part of human myth (see Steel vs. Magic themes in Conan books, or Beowulf, or heck, A Yankee in King Arthur's Court). So it's not like the idea of using technology against magic would be impossible to come up with. The question begs itself - why not? Considering the fact that Rowling generally tried to be logical and consistent in building the HP universe, I feel like there must be some in-universe explanation for this that I just didn't notice.   (in-universe answers only unless there are some authoritative out-of-universe statements that are part of canon). I installed or upgraded to Ubuntu 16.04, but I'm having some problems with my graphics card.   The display is blank The display flickers Items on the screen do not display correctly Certain programs complain of graphics issues The computer boots to low-graphics mode Your specific issue may not be here, but try the solutions described in the answers anyway.   This question is very broad, but each one of these issues likely has one solution.    If you are experiencing a login loop, check the last part of my answer.    If you experience one of the listed issues and have your own solution (mine didn't work, or there's a faster way), feel free to post another POLITE answer, describing your problem and how you fixed it.    Those attempting to install Ubuntu, please refer to the section titled: If you are unable to enter a TTY or are trying to install Ubuntu. Exercise from Atiyah-Macdonald, Chapter 1, 2.iv) Let $A$ be a ring and let $A[x]$ be the ring of polynomials in an indeterminate $x,$ with coefficients in $A.$ Let $f=a_0 + a_1x+\cdots+a_nx^n \in A[x].$ $f$ is said to be primitive if $(a_0,a_1,\ldots,a_n)=(1).$     Prove that if $f,g\in A[x],$ then $f$ and $g$ are primitive $\Rightarrow$ $fg$ is primitive.   I know Gauss lemma holds true for UFDs, but in this case it isn't required $A$ to be UFD: is it possible to drop the assumption, or is some hypothesis missing here? Fish vs Fishes for plural use Now, I encountered a sentence in a text book, saying     Many fish are specially adapted to live only in certain places.   I know that plural of the word fish can be fish as Merriam says    But wouldn't it someway or somewhat sound unusual or "too unique"?  Is it only to me? Problems with wifi range on laptop. Wifi card: realtek rtl8723be So I just started using linux/ubuntu today and I've been getting problems with my wifi, ive tried the solutions on this page:  When im really close to my router, its fine, i can see wifi signals, but when i go just a few steps back it disappears right away. Im using the latest version of ubuntu 17.10  Any suggestions would be nice! :)