Is focal length measured relative to the sensor or the lens?
What is "angle of view" in photography?
Extended Euclidean Algorithm: backward vs. forward I'm confused about how to do the extended algorithm. For example, here's the gcd part gcd(8000,7001)  $$\begin{align}8000 &amp;= 7001\cdot1 + 999\\ 7001&amp;=999\cdot 7+8\\ 999&amp;=8\cdot 124+7\\ 8&amp;=7\cdot 1+1\\ 7&amp;=1\cdot 7+0\\ \gcd(8000,7001)&amp;=1\end{align}$$    Now, the extended algorithm  $$\begin{align}1 &amp;= 8 - 1\cdot7\\ &amp;= 8 - 1\cdot(999 - 8\cdot124)\\ &amp;= -1\cdot999 + 8\cdot125\end{align}$$  How do you get this 8*125 from the previous line? Isomorphism involving Eilenberg-Maclane space, Tors. Let $\pi$ be a group and let $K(\pi, 1)$ be a connected CW complex such that $\pi_1(K(\pi, 1)) = \pi$ and $\pi_q(K(\pi, 1)) = 0$ for $q \neq 1$. Does there exist an isomorphism between $H_*(K(\pi, 1); A)$ and $\text{Tor}_*^{\mathbb{Z}[\pi]}(A, \mathbb{Z})$? There have been several discussions regarding code-only answers (answers that contain only code blocks with no textual explanation whatsoever):         Personally, I can't see why the quality filter should let such answers through at all. The main problem I have with code-only answers, especially once they're flagged as not an answer or very low quality, is that we can't determine at a glance whether these answers are:   Genuinely attempting to answer the question  answers Trying to correct an error in the question without actually answering it Random code dumps that may or may not relate to the question even by programming language or keyword(s) in the question   In particular, what exactly is an "informative code-only answer"? Does it mean the code is self-documenting? Does it mean the code substitutes code comments for a proper write-up? This is all very fuzzy. From  to the last question above:     I have never seen a code-only answer that couldn't be made better with the addition of appropriate text. They are of lower-quality than the same answer with some text.   This text makes all the difference, IMO, between an answer and a non-answer. Without it, it's often needlessly difficult to tell.  Existing code-only answers that are good-faith attempts to answer the question should be edited or downvoted, yes. But if the quality filter already tries to block code-only questions, why not block code-only answers too? These answers are often low quality, and (almost) always have ample room for improvement, just like questions. How to install the previous version of a .deb package and pin it? I am trying to install the latest version of subversion on Sid, and because it has a bug I receive a warning and I abort the installation. How do I get to locate the previous version version, install it and pin until the bug is resolved?  root@server01:~# apt-get install subversion   Reading package lists... Done                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                              Suggested packages:                                                                                                                                                                                              db5.3-util subversion-tools                                                                                                                                                                                  The following NEW packages will be installed:                                                                                                                                                                    subversion                                                                                                                                                                                                   0 upgraded, 1 newly installed, 0 to remove and 205 not upgraded.                                                                                                                                               Need to get 0 B/981 kB of archives.                                                                                                                                                                            After this operation, 4,844 kB of additional disk space will be used.                                                                                                                                          Retrieving bug reports... Done                                                                                                                                                                                 Parsing Found/Fixed information... Done                                                                                                                                                                        critical bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;                                                                                                                                                          b1 - #803725 - subversion: dump-load of a repository modifies verbose log output: M line lost serious bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;  b2 - #803589 - FTBFS with ruby2.2 (only) Summary:  subversion(2 bugs) Are you sure you want to install/upgrade the above packages? [Y/n/?/...] n ********************************************************************** ****** Exiting with an error in order to stop the installation. ****** ********************************************************************** E: Sub-process /usr/sbin/apt-listbugs apt returned an error code (10) E: Failure running script /usr/sbin/apt-listbugs apt I've heard it is possible to add tags to a file's meta data in OS X, and have Spotlight search through such tags.   In a nutshell, how would one access this feature in Finder &ndash; not Spotlight (Command+Space) &ndash; but the adding of tags themselves? Where are these tags stored?  Do they go in .DS_Store (I tend to delete those!) or elsewhere in the filesystem? Does this tagging mechanism work on removable drives?  What are the requirements? Does this tagging mechanism work over a network share?  I have some Windows SMB network shares at home that I frequently store files on.  Would it work on those or is another configuration required? Aside from Spotlight, are there any command-line tools for searching through or accessing the tag data for files?   Thank you! Removing unnecessary vertices? I have over sampled polygons that I need to simplify, without changing the shape. basically, I want to reduce the number of vertices, by eliminating the ones that are useless and have the polygons represented with the significant vertices only. I used to do that with ET GeoWizards Plug-in, but I don't have a license anymore. My table has 500.000 features, water polygons.   Any ideas? Can hard drives fully utilize SATA III? My motherboard currently supports both SATA II and III (3 Gb/s and 6Gb/s respectively), but after reading some online, it seems as though connecting a HDD to the 6 Gb/s is pretty much pointless. If this is the case I'm going to leave my two SATA III ports open for something that can actually use it (which at this point I'm not really sure what can).  This is part of an article I read:     In terms of everything else, we saw basically no difference from the same single drive being plugged into a SATA 6Gb/s or SATA 3Gb/s port. All of this is obviously due to the hard drive not being able to actually take advantage of the 6Gb/s bus.   from . Trying to make aliases that open the last modified file One thing that I frequently do is edit the most recently modified files, so instead of typing "ls -lr" and then "vim lastfile", I thought I would make some shortcuts in my ~/.bash_profile file:  alias via="vim `ls -rt | tail -1`" alias vib="vim `ls -rt | tail -2 | head -1`" alias vic="vim `ls -rt | tail -3 | head -1`" alias vid="vim `ls -rt | tail -4 | head -1`" alias vie="vim `ls -rt | tail -5 | head -1`"   The problem is that, weirdly enough, these commands don't work.  They open some file that isn't one of the last, or even a file was deleted from the current directory (I wonder if there's some kind of file cache updating issue in the directory.  This occurs on both my local machine and the cluster I work on).  However, if I type vim `ls -rt | tail -1` directly, without using the alias, it works every time. JDK 1.4.2 - where can I download the source? I want to install Java JRE 1.4.2 or JDK 1.4.2 on a recent Amazon Linux server. The best option so far seems to install from source. However - where can I download this? I believe 1.4 is still from the Sun era, but I can't find it on the  site, and the sun site is gone.  has no 1.4 download afaik.   Where can I download Java 1.4.2 source code?   As the goal is to get the installation working, other options are welcome. I tried to install the bin file, but got an error: cannot execute binary file. What is the difference between a synchronized method and synchronized block in Java? What is the difference between apt and apt-get? How do I create a Java string from the contents of a file? What is a good general document size for web page mockups and prototypes? I do mockups and prototypes of sites and designs all the time, but I've always wondered if there is a standard size or width I should be using. Generally I'll make my document either 1024, 1200, or 2560px wide, depending on what I'm doing.  So what do you think? What is a good or standard size for this? Can hypercomputation compute the impossible? There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be inconsistent and illogical/logically impossible.   There are other types of logic systems apart from classical logic, like paraconsistent logics or even trivialism, that allow these contradictions to occur, prove them as right and work with them.   We can make a paraconsistent or trivialist system and work with it. For example, with trivialism, in theory, we would be able to derive and state everything we would want (since literally everything, even including illogical/logically impossible inconsistencies and contradictions), but we as humans (or as brains), are limited and can't conceive everything we want (at least to what I know). Therefore, no matter how many trivialist models we create and how much time we would work with them, we would never find or conceive many illogical/logically things because they are just that: impossible. There are impossible things to describe and conceive. For example, Russel's set is the set of all sets that do not contain themselves. If Russel's set contains itself, then it cannot contain itself, since it only contains sets that don't contain themselves. But if Russel's set does not contain itself, then it must contain itself, since it contains all sets that don't contain themselves.  There are quite a few logic bombs like this. You cannot ever compute the contents of Russel's set, and there are more formal, mathematical ways to present it. All of them have in common that you can't actually compute what the set is, whether you do it by hand, in your head, or on a computer. It's just a statement that cannot be fully logically processed.  If you take every possible state the human brain can be in, none of them include the computation of Russel's Set's contents. That is, not only can the contents not be computed, they cannot even be represented. No stimulus can cause us to comprehend Russel's Set, since such comprehension is not possible to begin with. It does not have a solution. Even if we try to solve it using trivialism, we would just be able to write a solution that does not make sense and prove it has sense and it is the real solution, but we could not be able to have a solution that would make sense "outside" the realm of trivialism (for example in classical logic), even though, using trivialism, we could prove that such solution would have sense in whatever context and logic system.   But what about hypercomputational machines (for example oracle-like machines)? I've read about some models of hypercomputation which are compatible with paraconsistent or trivialism logics. I've also read there are some models of hypercomputation (particularly those oracle-like models which use a black box) where, essentially, the hypercomputer is an algorithm that cannot exist. It might be because such an algorithm is fundamentally forbidden by logic itself (which is hided in a black box). Would any of these be capable of computing/"conceiving" these impossible things I wrote before? Do you know of anything that would help? How do I round a number in JavaScript? While working on a project, I came across a JS-script created by a former employee that basically creates a report in the form of  Name : Value Name2 : Value2   etc.  The peoblem is that the values can sometimes be floats (with different precision), integers, or even in the form 2.20011E+17. What I want to output are pure integers. I don't know a lot of JavaScript, though.  How would I go about writing a method that takes these sometimes-floats and makes them integers? How to connect two Dell P2415Q 4k displays to MacBook Pro 2016 What's the best way of connecting two Dell P2415Q 4k displays to the MacBook Pro 2016 with TouchBar and TouchID?  I have the monitors connected to an older MacBook Pro currently with two mini-DisplayPort cables. Can I somehow reuse those cables or do I need new ones?  Apple's support page  lets me know that:  "Note that although it uses a Mini DisplayPort connector, the Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter doesn't support connections to Mini DisplayPort displays."  So I guess reusing the cables is not the way to go? Loop "Forgets" to Remove Some Items Why is AES resistant to known-plaintext attacks? At least it's my understanding that AES isn't affected by known-plaintext. Is it immune to such an attack, or just resistant? Does this vary for chosen-plaintext? Is vocative comma rule vanishing? I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space of state functions, from where this arises? and why 2-order space that assumes the following inner product:  $\langle\phi|\psi\rangle =\int\phi^{*}\psi\,dx$  While there is many ways to define the inner product.  In Physics books, this always assumed as given, never explains it, also I tried to read some abstract math books on this things, and found some concepts like "Metric weight" that will be minimized in such spaces, even so I don't really understand what is behind that, so why $L_2$? what special about them? Who and how physicists understood that those are the one we need to use?