A spherical planet of radius $R$ is inhabited by $n\ge 2$ aliens. Due to the emergence of a novel deadly virus, the aliens must  practice social distancing, staying away as far as possible of each other. What is the maximum distance that can be achieved in terms of $R$ and $n$? If Euclidean distance is used (not Geodesic), the answer for $n=2,3,4$ the answer should be $2R$, $\frac{R}{\sqrt{3}}$, and $\frac{R\sqrt{6}}{4}$ respectively. Note: this problem is about maximum distance to the nearest neighbor, not about total distance, as wrongly marked as a duplicate.
What is the configuration (set of locations) of $n$ points on the surface of a sphere such that the sum of distances is maximum for $n=1,2,3,...$?  The sum of distances is measured by summing the lengths of every straight line (through the sphere) connecting every possible combination of $2$ points.  All the points are on a single sphere of radius $R$.  Here's a visualization:   Acknowledgements: Based on  Physics S.E. question. Image from .
How can I improve my color selection skill? I'm a web developer, started to become a web designer. However, I think my understanding of colors is not practical yet. There are tools out there that can give you color harmonies, and more stuff, like , but they don't give you the start point. I mean, how should I know that for this web site, I'd better use green and for that website, choose red. How should I know that?  I think color selection is more like an art, instead of being a science, and I'm like "you should become an color artist, in order to become a web designer".  How can I improve my color selection skill? I have this, in D1:  =sum(D3:D)   I want D1 to always be the sum of the rest of column D (D2 is a header)  I sometimes move a row, from eg 8 to 3, and that causes D1 to change to sum(d4:d).    I want D1 to stay as my sum of the column. Vitali-type set with given outer measure I am testing against the following test document:  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"                        "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"&gt; &lt;html xmlns="http://www.w3.org/1999/xhtml"&gt;    &lt;head&gt;         &lt;title&gt;hi there&lt;/title&gt;     &lt;/head&gt;     &lt;body&gt;         &lt;img class="foo" src="bar.png"/&gt;     &lt;/body&gt; &lt;/html&gt;   If I parse the document using lxml.html, I can get the IMG with an xpath just fine:  &gt;&gt;&gt; root = lxml.html.fromstring(doc) &gt;&gt;&gt; root.xpath("//img") [&lt;Element img at 1879e30&gt;]   However, if I parse the document as XML and try to get the IMG tag, I get an empty result:  &gt;&gt;&gt; tree = etree.parse(StringIO(doc)) &gt;&gt;&gt; tree.getroot().xpath("//img") []   I can navigate to the element directly:  &gt;&gt;&gt; tree.getroot().getchildren()[1].getchildren()[0] &lt;Element {http://www.w3.org/1999/xhtml}img at f56810&gt;   But of course that doesn't help me process arbitrary documents.  I would also expect to be able to query etree to get an xpath expression that will directly identify this element, which, technically I can do:  &gt;&gt;&gt; tree.getpath(tree.getroot().getchildren()[1].getchildren()[0]) '/*/*[2]/*' &gt;&gt;&gt; tree.getroot().xpath('/*/*[2]/*') [&lt;Element {http://www.w3.org/1999/xhtml}img at fa1750&gt;]   But that xpath is, again, obviously not useful for parsing arbitrary documents.  Obviously I am missing some key issue here, but I don't know what it is.  My best guess is that it has something to do with namespaces but the only namespace defined is the default and I don't know what else I might need to consider in regards to namespaces.  So, what am I missing? Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$ Let $m$ be the largest real root of the equation $$\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4.$$ Find $m$.   do we literally add all the fractions or do we do something else  I have no clue how to solve this I saw this in the end of an awesome shell script but I can't understand the login here because I think it's being short-handed for a longer command.  spark ${@:-`cat`}   This apears at the end of . Any ideas?  + Marks for some one who extends it into a full segment of code, even if its slower (Better for explanation) What to look for in the datasheet when choosing a MOSFET? Let $L$ denote the set of all lines in the Euclidean plane $\Bbb R^2$. We say that two lines $L$ and $M$ are parallel if either $L = M$ or $L$ and $M$ have no points in common.  Using Euclid’s Parallel Postulate prove that parallelism is an equivalence relation on the set $L$.  I need some help determining if I have the right idea about this.  $L=L$ which means that $L$ is parallel to itself. So this is reflexive.  Suppose we have $L || M$. Then Either $L=M$ or $L$ and $M$ share no points. So Then $M=L$ or $M$ and $L$ share no points. Then $M||L$. So this is symmetric.  Suppose we have $L || M$ and $M || N$. So then either $L=M$ or $L$ and $M$ share no points and either $M=N$ or $M$ and $N$ share no points. So we have that either $L=N$ or $L$ and $N$ share no points. So $L || N$. So then this is transitive.  So from all of this, parallelism is an equivalence relation. I'm not sure if this is correct or not. Any help would be appreciated. Can you explain the "Axiom of choice" in simple terms? As I'm sure many of you do, I read the  webcomic regularly. The  involves a joke about the Axiom of Choice, which I didn't get.     I went to Wikipedia to see what the Axiom of Choice is, but as often happens with things like this, the Wikipedia entry is not in plain, simple, understandable language. Can someone give me a nice simple explanation of what this axiom is, and perhaps explain the XKCD joke as well? Can I put 700c tires on rims made for 27 x 1.25"? The disk that contains Ubuntu on my computer is 115GB in size.  When the disk was 114.7GBfull.  I started deleting some files here and there to free up around 5GB.  But I noticed the disk was 114GB filled again. I thought it was some cache or swap thingy so didn't give it much thought and went ahead and freed around 40GBby shifting some media files out of the disk.  I have a notification in an hour or so that the disk is full yet again!! 40GB!!! All gone!  So I debugged the problem down to the /var/log/syslog file which was initially definitely less than 20GB. I know this because /var folder was 17GB before I cleared the memory.  /var/log/syslog file is currently 55.9GB!  Could someone be so gracious to explain this anomaly? Is this a bug? Or am I affected with some malware or virus? Recommendations for good Newtonian mechanics and kinematics books How to toggle Scroll Lock in Excel 2010 without a Scroll Lock key in the keyboard I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? How to add startup applications in lubuntu? Cannot authenticate without a password Laptop water damage repair procedure I'd love some advice in repairing a water-damaged laptop.  My girlfriend spilled a glass of water on her Sony Vaio and now it doesn't turn on...at all...dead! What steps should I go through to work out where the problem is and which part(s) I'll need to replace?  I can't seem to find out what has happened by just looking at the circuit boards. I'm new to electronics but could buy relevant volt-meters etc. I'm just looking for a decent trouble-shooting guide. Typically, to box in some text, I use the following:  \fbox {     \parbox{\linewidth}{     This is some text! Blah blah blah...     } }   However, say I have a verbatim block within that. It will never compile. Anyone know how I could draw a box around text which contains a verbatim block? I should note that I want to be able to draw a box around not just a verbatim block. For example, I would want to draw a box around something like:  This is text. \begin{verbatim} This is some more text. \end{verbatim} And this is even more text. I have 2-3 different column names that I want to look up in the entire DB and list out all tables which have those columns. Any easy script? The Download CSV link seems broken in SEDE query result window I've created   which works nice. I would really like to download those results as an CSV file. Therefor I click on the provided link on the right hand side of the screen called Download CSV. The result is:  The webpage cannot be found  https://data.stackexchange.com/stackoverflow/csv/202355?UserId=187606 I expected: A file in CSV format. It looks like a regression of  Queries without a parameter work as advertised. Can this be fixed? How can I dual boot Windows and Ubuntu?