How to take a photograph as it is?
How to capture the scene exactly as my eyes can see?
How are first digits of $\pi$ found? Since Pi or $\pi$ is an irrational number, its digits do not repeat. And there is no way to actually find out the digits of $\pi$ ($\frac{22}{7}$ is just a rough estimate but it's not accurate). I am talking about accurate digits by either multiplication or division or any other operation on numbers.  Then how are the first digits of $\pi$ found -     3.1415926535897932384626433832795028841971693993...   In fact, more than 100,000 digits of $\pi$ are found (sources - )  How is that possible? If these digits of $\pi$ are found, then it must be possible to compute $\pi$ with some operations. (I am aware of breaking of circle into infinite pieces method but that doesn't give accurate results.)  How are these digits of $\pi$ found accurately? Can it be possible for a square root of some number to be equal to $\pi$? I have spent a whole day trying to solve the following problem. Please help if you know how to do this.  I am using natbib (\usepackage[sort&amp;compress,square,comma]{natbib}), and my current citation style looks like [1-4], [5, 8-9].  What is the easiest way to change the citation style to [1]-[4] and [5],[8]-[9]? How can I get a reference to a method? Is it possible in Ruby to get a reference to methods of an object ( I would like to know if this can be done without procs/lambdas ) , for example , consider the following code :   class X   def initialize     @map = {}     setup_map   end    private   def setup_map     # @map["a"] = get reference to a method     # @map["b"] = get reference to b method     # @map["c"] = get referebce to c method   end    public   def call(a)     @map["a"](a) if a > 10     @map["b"](a) if a > 20     @map["c"](a) if a > 30   end    def a(arg)      puts "a was called with #{arg}"   end    def b(arg)      puts "b was called with #{arg}"   end    def c(arg)     puts "c was called with #{arg}"   end end   Is it possible to do such thing ? I would like to avoid procs/lambdas because I want to be able to change the behaviour of A,B,C by subclassing . "The following" vs. "Following" I wrote      "Following examples show ..."   and my colleague revised it as      "The following examples show ..."   Why do we need "the" here even though the examples have not been mentioned before? Repeat each line multiple times Would like to have each line in a file repeated a fixed number of times.  e.g. have each line repeated four times:  a b c   becomes:  a a a a b b b b c c c c   I've done some searching, and there are a lot of questions and answers along the lines of doing the reverse, e.g. merging duplicate lines into single lines, and maybe a few about doubling lines by printing them again.  It would be easy to do this in C, but I wish I knew more about the native commands so I wouldn't have to resort to these kinds of one-off throw-aways all the time. In  thread, the question was to find a $f: \mathbb{R} \to \mathbb{R}$ such that  $$f(f(x)) = f(x) + x$$  (which was revealed in the comments to be solved by $f(x) = \varphi x$ where $\varphi$ is the  $\frac{1+\sqrt{5}}{2}$).    Having read about  shortly before though, I came up with this train of thought:  $$f(f(x)) = f(x) + x$$ $$\Leftrightarrow f^2 = f^1 + f^0$$ $$f^2 - f - f^0 = 0$$  where $f^n$ denotes the $n$'th iterate of $f$.  Now I solved the resulting quadratic equation much as I did with plain numbers  $$f = \frac{1}{2} \pm \sqrt{\frac{1}{4} + 1}$$ $$f = \frac{1 \pm \sqrt{1+4}}{2} = \frac{1 \pm \sqrt{5}}{2}\cdot f^0$$  And finally the solution $$f(x) = \frac{1 \pm \sqrt{5}}{2} x .$$  Now my question is: *Is it somehow allowed to work with functions in that way?** I know that in the above, there are denotational ambiguities as $1$ is actually treated as $f^0 = id$ ... But since the result is correct, there seems to be some correct thing in this approach.  So can I actually solve certain functional equations like this? And if true, how would the correct notation of the above be? How do I properly compare strings in C? Can a virtualized machine have the CPU and RAM resources of multiple underlying physical machines? Additive group contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$ Persistent do not disturb toggle in Yosemite possible? Differences among "It feels...", "It looks...", and "It seems..." How do I remove "permission denied" printout statements from the find program? Code   find / -name netcdf   Output  find: `/root/.dbus': Permission denied find: `/root/.gconf': Permission denied find: `/root/.gconfd': Permission denied find: `/root/.gnome': Permission denied find: `/root/.gnome2': Permission denied find: `/root/.gnome2_private': Permission denied Can I use Class.newInstance() with constructor arguments? Enumerate paragraphs and subparagraphs like sections but with letters Location of /etc/fstab in El Capitan I want to activate the . But I can't find the /etc/fstab on my mac. osx 10.11.5 El Capitan Which answer do I accept if I have multiple correct answers? I asked  that turned out to have multiple correct answers. How do I pick between them to determine which to accept?  All of the answers were different. They were not the same answer given multiple times. When should I implement IDisposable? Also show "Add a comment for the author" selection when deleting/voting to delete an answer I'm aware that this only affects high rep users and mods, but nevertheless it would be nice if the following selection would appear when a user casts a delete vote on an answer.    If I am not mistaken, this only appears when casting delete votes from the review queues. I don't see a reason why this shouldn't also appear when casting a vote directly to the answer, instead of the (java script) alert with "Delete this post?".  Or in other words, the selection should always appear when a user does some kind of 'delete answer' action. How can I add a PPA from a previous release? Segmentation fault error occurs for a simple function I have coded