For a given fixed volume, can we find the minimum surface area of any shape? We kind of know the minimum surface area is a sphere(restrict our problem in 3 dim space). (correct me if the sphere is NOT a minimum surface area) How do we prove that the sphere is the minimum surface for a given volume?
Has the below question been answered here before?  Prove: For a given enclosed volume, a sphere has minimum surface area.  Please provide link or ways to solve it. I know it is a problem of Minima and involves finding derivative and second derivatives. However, how to to frame the leading equations which has to be differentiated?  I am looking for a way to solve only using High School level Calculus. I think there must be an answer.
Can we exempt downvoted accepted answers from getting the top spot? What is a good way of parsing command line arguments in Java? Do immigration checks exist between Northern Ireland and England/Scotland? (not just for flights but also ferry/bus/train) Do immigration checks exist between the Republic of Ireland and England/Scotland? The basic 6T structure used for storing data is same as one used in "Positive Feedback Differential Voltage Sense Amplifier", then how come while the data is stored in SRAM memory cell it doesn't get amplified? How can I set up Samba shares to only be accessed by certain users? I have a RAID10 array mounted on Ubuntu Server 12.04. I have created a few folders within the mount point and want the following functionality.  There will be 4 users, 3 of them are windows users: 'one' 'two' &amp; 'three'. 'four' is a media streamer that only needs to access the MEDIA share. One Two and Three need to have full access to the media share and their own personal shares (for documents) which no other users but them can access.  Currently, User Four works perfectly (Has full access to the MEDIA folder and can't access folders owned by other users). The problem is, when logged in as the other user, I can't access either share; (tried using valid users =  and using chmod to add permissions to no avail).  TL;DR: I need to know how to configure Samba properly to restrict access to certain shares for certain users and allow all of them to access one communal folder (all files on a RAID10 mount). Is there a way to disable access to certain Settings components? What is numeric promotion? In Java, why do people prepend fields with `this`? When referencing class variables, why do people prepend it with this? I'm not talking about the case when this is used to disambiguate from method parameters, but rather when it seems unnecessary.  Example:  public class Person {             private String name;      public String toString() {         return this.name;     } }   In toString, why not just reference name as name?  return name;   What does this.name buy?   a stackoverflow question whose code has this pre-pending. Modern Linux commands that parallel uuencode/uudecode functionality I need to get binary files into text format.  Years ago, I used uuencode/uudecode, and it was easy:  uuencode file.xls &gt; file.txt # Delete file.xls # Do whatever with file.txt # Now I need file.xls back uudecode file.txt &gt; file.xls   But uuencode/uudecode is not on my system, and as I look around, the yum/rpm process is ugly--this gives me the clue that maybe no one uses it any more and instead there is something more modern to do this.  I looked at xxd and hexdump but couldn't get them to do it.  Could just be dumb user issues.  What can I use on Linux to do this?  Would like it to be something that tends to be in the native install so I don't need to yum/rpm it if possible.  Just for your own understanding, what I'm specifically trying to do now is source control an *.xls file but the corporate tool doesn't allow *.xls in.  I respect that constraint normally, but in my context, an *.xls is a configuration table for my code so It is logically like source code, but the corporate SVN trigger is physical--if it's *.xls, it gets rejected, so I'll encode it and source control the *.txt file.  Thanks! I don't understand, because if 'don't' is 'do not' then wouldn't the sentence without conjunctions be 'do not you dare' which I'm pretty sure isn't grammatically correct. Like, when we say the term it means something else, certainly not 'do not you dare' anyway. Any ideas on why? I am so glad English is my first language. When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? How are pronouns resolved? Are pronouns in English resolved syntactically or semantically? Do they always refer to the closest matching noun?  A  has these examples:        We gave the bananas to the monkeys because they were hungry.   We gave the bananas to the monkeys because they were ripe.   We gave the bananas to the monkeys because they were here.       My understanding was that pronouns are resolved syntactically, and so sentence 2 is semantically incorrect (unless the author really meant that the monkeys were ripe) and sentence 3 is not ambiguous. Is this wrong?  Citations and references are most welcome. I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe? Find $\lim_{n\to\infty}\frac{a^n}{n!}$ if there are 4 different tables and 18 people, how many ways can the people be seated to have at least 4 in each table? For example with 15 people at 3 different tables each seating 5 people, is the number of combinations of seating equal to: $$\binom{15}5\binom{10}5(4!)^3$$ Word that describes being "patriotic" for something that is not a country? I'm looking for a word that is similar to patriotic but does not relate to one's country (or state).  For what it's worth, I'm specifically referring to "overly patriotic" in a negative sense, to describe someone who has a overly sentimental/cultural or otherwise less-than-rational attachment or devotion to something and makes it part of their very identity. A common example might be an extremely zealous football fan. What is the maximum number of people that will join a settlement? I've got two settlements on the go that I'm paying attention to - Sanctuary and the Starlight Drive In. Both of these settlements have radio towers and beds and all resources in the green however they appear to have stopped growing at 10 people in each settlement even though happiness is above 80 and I've got 15+ beds at each location.  What is the maximum number of people that will join a settlement? "inputenc Error: Unicode char \u8" error while trying to write a degree symbol (invisible character) No matter how I try to do it I always get the following error :      ! Package inputenc Error: Unicode char \u8:­ not set up for use with LaTeX.    I have tried using ­­­$^{\circ}$, \deg, \textdegree, pasting the ° symbol directly, to no avail.  Here is the header of my document, in case one of those could be causing the errors :  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[francais]{babel} %\FrenchItemizeSpacingfalse \frenchbsetup{CompactItemize=false} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm} I failed to open a lock. Now what? Which profile details does an account merge preserve? When one has to merge two accounts, they're prompted by something like this with input fields for each account link:     Account 1:  Account 1 link.       Account 2:  Account 2 link.    When the merge completes, which account details are preserved, like the display name, or the profile description? Account 1, or account 2?