What can't a namespace do that a singleton class does?
Singleton: How should it be used
I'm trying to wrap my head around the math/physics of how illuminance on the film/sensor plane remains equal for a given f-number regardless of the focal length of the lens.  Since a longer lens will have a larger entrance pupil at a given f-stop than a shorter lens at the same f-stop, how can the light falling on the film/sensor be equivalent?  Empirically, I know this to be true.  Say I take an incident meter reading (not reflected/TTL) off my subject, and get f/5.6 at 1/100s, I'll get proper exposure at the point at which i took the meter reading with that setting whether I use a 50mm lens or a 200mm lens (obviously composition will be different).    Wikipedia's  reads:     A 100 mm focal length f/4 lens has an entrance pupil diameter of 25   mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of   50 mm. The 200 mm lens's entrance pupil has four times the area of the   100 mm lens's entrance pupil, and thus collects four times as much   light from each object in the lens's field of view. But compared to   the 100 mm lens, the 200 mm lens projects an image of each object   twice as high and twice as wide, covering four times the area, and so   both lenses produce the same illuminance at the focal plane when   imaging a scene of a given luminance.   I'm not sure I agree with the explanation on wikipedia.  The film/sensor doesn't care how big the image is that falls outside the bounds of the sensor; the film/sensor "sees" what it sees, and that's it. Though I never quite understood what those numbers were and they were quite ugly, they were the only reason I ever visited the reviews page.   Can we have similar functionality back on the top bar please? An inequality involving 4 real or complex numbers Let a,b,c,d be real or complex numbers with absolute value less than $1$. Is the following true:  $$|ab-cd| \leq |a-c| +|b-d|?$$ P.d.f of the absolute value of a normally distributed variable I came across this question as an exercise, had a brief idea, but didn't know how to proceed.     Let $X \sim N(0, 1)$. What is the p.d.f of $|X|$ ?   I know the final p.d.f looks just like the right half of the original pdf, but extended vertically for a factor of 2.  Could someone please show mathematically what the p.d.f of variable |X| is going to be, and explain briefly? Thank you. Why I think tension should be twice the force in a tug of war I'm going to provide my argument for why I think the tension in a rope should be twice the force exerted on either side of it.  First, let's consider a different example. Say, there is a person named A and a block in space. A pushes on the block with a force of 100 N. Then, the block will also push A with a force of 100 N by Newton's third law. Now, consider the case where instead of the block, there is a person B who is also pushing on A with a force of 100 N while A is pushing on him. A will experience a force of 100 N because he pushed on B, AND another 100 N because he is being pushed by B. Hence he will experience a force of 200 N. Similarly, B also experiences 200 N of force.  Now, back to the original problem. There are two people A and B in space with a taut rope (no tension currently) in between them. If only A is pulling and B is not, then I agree that the tension is equal to the force A exerts. This situation (in my opinion) becomes analogous to the above if B is also pulling. So, say both of them pull from either side with a force of 100 N. Then the rope at the end of B will pull B with a force of 100 N (this pull is caused by A). By Newton's third law, the rope will experience a pull of 100 N. But B is also pulling his end of the rope with 100 N. Therefore, the tension should be 200 N. Similarly, the end of the rope at A must pull A with 100 N of force (because B is pulling from the other side) and hence experience a force of 100 N itself by Newton's third law plus another 100 N because A is pulling on the rope.  Apparently, the answer is not this (according to my searching on the web). So, could anyone tell me why this reasoning is wrong? Thanks.  EDIT : So apparently people don't agree with my first example, leave alone the second. This is to the downvoters and the upvoters of the highest-rated answer: You all agree that if only A pushes B with a force of 100 N, then A and B both will get pushed by a force of 100 N in opposite directions, right? Then, in the case where B is also pushing with a force of 100 N, it doesn't make sense that the answer would be exactly the same. It doesn't seem right that no matter what B does, B and A will always experience the same force as they would have if B hadn't applied any force.  EDIT 2 : I'm going to provide here a link to a question that I posted:  According to the answer and the comments there, the reason as to why my first example is incorrect is different to the one provided here. So maybe you should all read the answer and the comments provided by the person and reconsider what you think. first post between 12/26 and 1/1   Does that mean your very first post as a user should be made in those days?  Or that you should be the first user to post any post on a site starting 12/26?  Or something else?  The first option seems somewhat more likely but I'm not sure I'm parsing the description right. Wavy stream of liquid How do I convert all files in a folder to a different line ending? (on Windows) Survey database design: associate an answer to a user I'm doing the conceptual model for a survey database.  The goal is store the answers given by users (it's going to be an Android app).  I have three entities: user, question and option.  A question will have one or more options (for example: How many employees do you have? 1-40, 40-1000, +1000).  Options will have a text (1-40) and a value (the value selected by user).  User will select one (or more) of these options.  My conceptual design is:    I don't know how to associate an answer with an user.  How can I represent that relation? Do I have another entity to represent option value?  This model will store questions and pre-made answers (offered answers) and allows them to be re-used in different surveys.  I have to represent question like this one:    This question is related to this one: I have a Student object and have a pick list field  "Student Status" in this object. Status can be Full-Time OR Part Time. Now my requirement is i want this student status list, Part-Time or Full-Time in apex controller. how can i do this?  If i get a student record it will only give me that particular student status Full-Time or Part-Time. But i need all options that are available in student status field.  Please help me How can I disable my internet connection from terminal? How to understand what's taking up disk space? I'm looking for a linux alternative to . I would like to know what is taking up space on my hard drives.  A program that works on console and doesn't require a UI is preferred . How coherent light is created for single slit experiment? Do the Faceless Men take more than just a face? Is a set without limit points necessarily closed? According to the definition on Rudin' Principles of Mathematicial Analysis, closed set is defined as:      $E$ is closed if every limit point of $E$ is a point of $E$.   Then I have a question: if a set has no limit point, is it necessarily closed? I think this idea doesn't contradict the definition of closed sets. Am I right?  And another question is #10 in Chap.2 of Rudin's:      Let $X$ be an infinite set. For $p\in X$ and $q\in X$, define    $d(p,q)=0$ when $p=q$. Otherwises,$d(p,q)=1$.    I have known that every set in the metric space is closed. To prove it, we can show that the complement of any set is open, which is quite trivial. My question is: how can we prove that every set is closed just by checking according to the definition of closed set, i.e. how can we show that every limit point of any arbitrary set $E$ in the metric space is a point of $E$?   Thanks in advanced! Where to securely store API keys and passwords in WordPress? I'm looking to use a few APIs and many come with keys, secret keys and passwords required to work. Where in WordPress can you store that information? Assuming anyone can hack your DB is there anyway for WordPress to make saving that information more secure? Also, consider the ability to change these keys ever so often so I would need to update the keys on an options page.  UPDATE Do I need an airport transit visa through Switzerland if I have no Schengen visa? Am traveling from Cairo to Moscow via Swiss Air Disable autostart on boot and restrict background execution I know that hardly any information is passed to the PDF when a .tex file is compiled.  But is there a tool that can convert a PDF document back to (La)TeX? Why are login forms centered? Why are login forms always centered on the screen? Most horizontally, some vertically also. Sites like Apple/Amazon/Adobe/Microsoft/Google/PayPal/Instagram/Twitter etc. are all centered! Is this an undocumented best practice everyone unanimously decided to use?         &ndash; Wireframes created with   Obviously it's most aesthetically pleasing, but is there any other reasons why?  Edit: Many of these sites do not support mobile either, so it wasn't done specifically for that.