Function relations to determine
Functional equations leading to sine and cosine
Following my question , I am wondering if there are strong views for or against the use of standard deviation to detect outliers (e.g. any datapoint that is more than 2 standard deviation is an outlier).  I know this is dependent on the context of the study, for instance a data point, 48kg, will certainly be an outlier in a study of babies' weight but not in a study of adults' weight.  Outliers are the result of a number of factors such as data entry mistakes. In my case, these processes are robust.   I guess the question I am asking is: Is using standard deviation a sound method for detecting outliers? Is it true that a dihedral group is nonabelian?  I'm not sure if the result is true. I checked it for some lower order and I think the result may correct.   But I failed to prove/disprove the result. The new notice for protected questions looks like this:     Earn 10 reputation in order to answer this question. The reputation requirement helps protect this question from spam and non-answer activity.  The phrasing of this notice leaves out a lot of info, and is incorrect in many cases:  In the case where the user has just created their account on the site (whether or not they have the association bonus of +100), the default 1 for signing up does count toward the required 10. The message implies that the user has to earn 10 more reputation for a total of 11 (or 111), while the actual requirement is 10 (or 110).  If the user just registered and started off with the association bonus, then later lost part of it (e.g. through bounties or making a downvoted post), earning 10 reputation is not enough to answer protected questions. According to the literal wording of the notice, earning 10 reputation is enough regardless of previous rep loss, but this is not the case.   The easiest fix that can be made, to at least fix part of the problem, would be to explicitly indicate that the association bonus does not count. This was implemented in the prior protected question notice in response to , but was omitted from the new notice. This omission  , and adding this back would remove that. Can we please fix this notice? Which way is up? (electric outlet) My house has electric outlets in both orientations.  Which one is correct?  Should the ground hole be at the bottom or the top?    OR Trigger to check for duplicate contacts on lead conversion I'd like to write a Lead trigger, to check for duplicate Contacts before inserting the lead, or converting it.   Contacts fields I'd like to check:   Firstname - should not be the same as the leads name Lastname - should not be the same as the leads name Email - should not be the same as the leads phone   After checking these fields &amp; failing to find a duplicate, only then should the lead be converted. Induced metric on a null hypersurface After reading  It seems that there is no perfect solution for getting rid of the stretch at the poles of UV spheres.  According to , icospheres can be used for stretch-less UV mapping:     All faces have the same area, which may be useful for certain types of UV mapping containing non-organic textures. An example that comes to mind is an isocahedral die or billiard balls where stretch must be minimized near the point where the number is printed onto the ball.   Incidentally, a lowish-poly billiard ball is exactly what I'm attempting to create.  However, my attempts at neatly unwrapping an icosphere have mostly failed (smart UV unwrap works perfectly for using baked textures, however I was hoping for something more like the example in the 6th post of , with a nice clean rectangular map).  How can an icosphere (I assumed the term "geosphere" in the thread was referring to a (geodesic) sphere made of triangles, like an icosphere) be cleanly unwrapped? Or if it's not possible, is there another way to do this which I'm missing?    I'm planning on using the resulting sphere in the BGE. How can I install Sun/Oracle's proprietary Java JDK 6/7/8 or JRE? I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7? Get text from pressed button What's interesting in latus rectum? I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical applications of the curves (in engineering, physics, finance, etc.), on their geometric properties, or both.  I know there's this really easy formula to find the latus rectum of a conic from its key parameters. It's quite nice and straightforward to derive it, but...  ... What's its use? Why should anyone be interested in knowing the latus rectum of a curve? Is there any physical phenomenon, any architectural trick, or anything else where its position and/or length plays a key role?   I know just the relation between angular momentum, standard gravitational parameter and latus rectum in an astronomical orbit ($l=\frac{h^2}{GM}$, where $l$ is half the latus rectum, and $h$ is the ratio between the angular momentum associated to the orbiting body and its mass). It's cool, but a bit tricky, and probably too far-fetched for secondary school students... Is there anything simpler? Or just anything else, at any difficulty level?  Many thanks! Line of Bones to Travel and Conform to Curve (Train or snake following path) I've searched google extensively on this. Can't seem to find an answer.   I know about spline IK, which is wonderful for conforming a row of bones to a path. But combining the armature object with a follow path modifier causes the point of origin to move, but the bones themselves stick to the beginning of curve.   Ultimately my goal is to make a creature like a snake or centipede follow a curve path, thus animating it fairly realistically ... About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$ Allow bounty to be set with reputation from another site? Here's one to get shot down: How about letting bounties to be set using the reputation gained through the use of another site? So, for instance, I'm a programmer with a high Stack Overflow rep who hates using computers. Wouldn't it be useful for me to be able to exchange some of my excess Stack Overflow credit to incentivise a question on Super User?   Or perhaps I'd like to highlight a question on Meta Stack Overflow, but I don't spend my time there. The computer gave me this output in a window:  E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_natty_main_binary-i386_Packages E: The package lists or status file could not be parsed or opened.   How can I fix this? Within 300 km of Tokyo: Where for flora, landscape, nature? I plan to visit Japan for 10 days and apportion 5 days to Tokyo. For the remainder, I want to escape the megalopolis and enjoy picturesque backwoods or countryside. Please recommend? Criteria:   No dangerous animals or untamed boondocks. No  or snakes. I won't drive, and must rely on public transport and walking less than 5 km in total.  No shrines, temples or any religious edifice. OPTIONAL: I fancy  , the more  the better.   This instantiates, doesn't duplicate, . I need to find the cardinality of the set $S$ of all infinite subsets of $\mathbb{Q}$.   It's easy to prove $\operatorname{card} S=\mathfrak c$ if you first prove that the cardinality of the set of all finite subsets of $\mathbb{Q}$ is $\aleph_0$.   But is there some other proof for the statement without using the second one (about finite subsets)? Probably there is =) Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$ I need to show that $ \forall x,y \in \mathbb R, |\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$  I tried using concavity of log function: $\log(1 + x^2) - \log(1 + y^2)=\log(\frac{1 + x^2}{1 + y^2})=\log(\frac{x^2y^2}{(1 + y^2)y^2}+\frac{1}{1 + y^2}) \ge \frac{2(\log(x)-\log(y))}{1+y^2}$  Also the middle value theorem: $0&lt;\frac{\log(1 + x^2) - \log(1 + y^2)}{x^2-y^2} &lt;1$  But both attempts has not led too far. How to set scale across all blender objects and keyframes? How can I bind the meta key (a.k.a.  / Windows key) to a left click? Hitting the meta key should trigger a left click, and pressing down on it should allow me to drag and drop (just like it would do when holding down left click).  I tried using System Preferences -> Shortcuts and Gestures:    but I cannot set "meta" alone as being a shortcut.  I use Kubuntu 14.10 Plasma 4 and Kubuntu 14.04 LTS x64.   (On Windows 7 SP1 x64 Ultimate I can achieve that using the program .) What is the argument selector tracking a defined score (not [score_min=])? What if I want to make a command like this:  execute @e[score_A=10] ~ ~ ~ summon Creeper   So that the entity must have a score of 10 (not less, not more)?  Does it even exist that or a [score_A_max=] argument?  I know about scoreboard players test, but i guess it is not the case to use it.