Plotting cylinder with revolution plot
Thick annulus (ring) in 3D
So I'm working on this class that's supposed to request help documentation from a vendor through a web service. I try to name it DocumentRetriever, VendorDocRequester, DocGetter, but they just don't sound right. I ended up browsing through  for half an hour trying to come up with an adequate word.   Start programming with bad names is like having a very bad hair day in the morning, the rest of the day goes downhill from there. Feel me? Comments/tips on a (non Latex) pdf including mathematical formulas My goal : I correct copies from students that I scan to pdf. I wish I could make the annotations on the scanned copies rather than on the physical paper. Today, I have to scan the copies again to have my annotations transferable to students by email. Since most of the annotations are similar, I wish to have a stock of annotations I could transfer on the copies.  I went through a lot of technologies, including many "StackExchange Questions" here. I considered pdfcomment, cooltips, fancytooltips, the OCG family (ocgx, ocgp, ocg2, ...), etc.  Two tracks attracted more specifically my attention :    pdfcomments : I like the mouseover to see the comment, the capabillity to move the annotation around so I can have a stock on a pdf and I can copy it onto the scanned copies. This would be my choice if there was not a main drawback : it accepts only plain text when I need to use mathematical notations. (It needs selected pdf readers). Because you can move comments, you can put them on any pdf, even if it is not compiled from Latex or if you don't have the source. fancytooltips : I like the mouseover to see the comment, and the capability to use LaTeX mathematical formulas and images. Drawbacks : I can't move the annotation from a pdf document to the copies. (It works with very few pdf readers.) . I am not sure whether I can put tips on non Latex pdfs.   Is there a way to have pdfcomment have images/Latex mathematical formulas (or references to formulas that can show with a mouseover) ? Or is there a way to transfer fancytooltips to a non Latex pdf ? Or are there other techniques to achieve the goal ? Is $f(x)=10$ a periodic function? Is there a word for someone who has others do all their work for them? In a way like a slave master. More though like say someone who had robots do all their work and they were never themselves productive and had no drive. If you've read R.U.R. you'll understand the question better. I'm looking for a word with more definition than just lazy.  Update 1: It think I may actually go with drone if anything. I think that definition fits what I'm looking for the best. I also liked the definition of the British term layabout that one person mentioned, but I will probably use drone. Thanks for all the help and sorry if I was confusing or unclear.  Update 2: I needed this word for use in an essay I was writing which I have now handed in. Thanks for the help guys. No more suggestions needed. This isn't a particularly major issue, but I've had this thing nagging me for a while. When looking at QGIS 3.4's global variables, user_full_name is assigned my given and surname, which includes a diaeresis (¨) somewhere in there. I can't seem to find any way to get QGIS to switch/adapt encoding and display the name correctly. The accented character gets switched to that ubiquitous black rhombus.  I looked for info on this behavior and found moderately similar issues like  and  but it's not exactly the same problem as it's not a geodata encoding issue but rather how QGIS deals with values pulled from the OS.  I have tried unchecking the Override system locale tickbox in Options|General as I prefer to use American English even though my OS is set to Canadian French. No effect to observe.  There's somewhat of a workaround right now which is to fix the name in the Project variable project_author as it is editable (it's filled with the offending global variable by default).  I'm curious to know, though, if someone has encountered this before and if there's a solution in QGIS. Multiplication operator has no no eigenvalues Statement: Let $M_x$ denote the multiplicative operator acting on $L^2([0,1], \, dx)$ by $M_x(f) = xf$. Show that $M_x$ has no eigenvalues  Attempt: Let $M_x(f) = xf$ then we should have $M_x(f) = \lambda f$  then we get $M_x(f) = \lambda f \Rightarrow xf = \lambda f \Rightarrow xf-\lambda f \Rightarrow (x-\lambda)f = 0$  Now $f \neq 0$ so that implies that $(x-\lambda) = 0$ but this is achieved when $x = \lambda$, so I don't see how it doesn't have eigenvalue, when we achieve the desired result. Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$ As seen in  question, the series $\sum\limits_{n=1}^{\infty} \dfrac{n!e^n}{n^n}$ diverges. (One way to see this is by noting that the terms of the sum are greater than $1$ and, therefore, don't converge to zero.)  However, more is true: not only are the terms greater than $1$, they blow up to $+\infty$! To see this, one can apply Stirling's approximation and get $\dfrac{n!e^n}{n^n} \sim \sqrt{2\pi n}$.  My question is: is there an elementary proof for $\lim_{n \to\infty}\dfrac{n!e^n}{n^n} = +\infty$?  The reason I'm asking this is that I'm taking a Calculus course and I was assigned the exercise of proving the divergence of the series above and I would feel more satisfied if I could prove that its terms go to $+\infty$ (as opposed to merely proving the terms are greater than $1$.) Obviously, things like Stirling's approximation are outside the scope of the course, so I can't really use them.  (To be clear, you can use anything one learns in $4$ semesters of standard Calculus courses. I hope this restriction is not too obscure.) Why do some people use $+\infty$ instead of $\infty$? Why do some people use $+\infty$ instead of $\infty$? Because we usually denote minus infinity as $-\infty$, I think it is sufficient to denote plus infinity as $\infty$. Are there any reasons for this notation? I saw that many people majoring analysis use like $\int_0^{+\infty}$ or $\sum_{j=1}^{+\infty}$ or $\bigcup_{j=1}^{+\infty}$ which is not related to the unsigned infinity. Can't move/snap Nautilus window to occupy left or right half of the 1366x768 screen - is it just me? I'm running Ubuntu 18.04 LTS with GNOME Shell. Nautilus does not want to occupy 50% (left or right) of the screen sized at 1366x768.    Other applications (such as GNOME Terminal, Eye of GNOME, Gedit) are normally snapping to the left/right half of the screen.  But Nautilus can be resized to the width lower than half of screen (I can get 650 px, which is smaller than 1366/2 = 683 px).  The first usable screen resolution seems to be 1400x1050, then goes 1440x900. But large amount of current devices .  Is it just me?     Updates: 1. standard shortcut Super+← or Super+→ do not work too. 2. I reported  which has linked upstream . 3. It does not work on GNOME FlashBack session too. From a link from the question  to the HP Wikia, I started mulling over something I read about Voldemort and the "regeneration" potion (not a canon potion, but I'll use it for lack of a better way of describing it. . .) and would really like to know:  How did Voldemort drink the regeneration potion to turn his body into the grotesque childlike form we see in Goblet of Fire while he was still in a "mangled spectral state"?  Spectres (i.e. spirits or ghosts) are non-corporeal; they obviously can't consume food or drink liquids. So, how did Voldemort overcome this difficulty and manage to drink the regeneration potion? How to blacklist kernel modules? WinterBash site exhibits some strange 404 behavior I was poking around winterba.sh for secret hats and I figured there may be a secret hat linked to a URL so I decided to look at some different URLs and got plenty of 404s but, some pages throw different 404s than others. Why?  Example:  throws the classic "Page Not Found" winterbash style... but  just has the text "404"  ( used to throw just the text "404" but since that has changed)  Still happening at 2016 with . How do I figure out the right size font / text for a given read distance? To avoid printing single letters at varying sizes and measuring how far away I can see it from a distance is there a formula for determining what size font for a particular read distance? Is it better to take the midpoint between the ascender line and x-height or to go purely off of the x-height (since going purely off the ascender line could leave lowercase letters difficult to read)? How does vertical height play into this? Would I need to then figure the hypotenuse distance instead of a straight distance?  For example if I'm shooting for a 20' read distance but the sign is to be placed about 30' up should I use a distance of  35' instead of 20'?  I'm shooting for a 20' read distance for the headline and then possibly a 10' read distance for additional content depending on how it all fits on the active area. Two different solutions to integral Given the very simple integral  \begin{equation} \int -\frac{1}{2x} dx \end{equation}  The obvious solution is  \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2} \int \frac{1}{x} dx = -\frac{1}{2} \ln{|x|} + C \end{equation}  However, by the following integration rule \begin{equation} \int \frac{1}{ax + b} dx = \frac{1}{a} \ln{|ax + b|} + C \end{equation}  the following solution is obtained \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2}\ln{|-2x|} + C \end{equation}  Why are these solutions different? Which is correct?   The second solution can be simplified \begin{equation} -\frac{1}{2}\ln{|-2x|} + C = -\frac{1}{2}\ln{|-2|} -\frac{1}{2}\ln{|x|} + C= -\ln{\frac{1}{\sqrt{2}}} - \frac{1}{2}\ln{|x|} + C \end{equation} but they still differ. Mouse cursor flickering and disappearing I installed Ubuntu today and since the first start up I have a problem with the mouse cursor.  It starts randomly disappearing and flickering a lot.  I have searched for a solution on Google and here but didn't find anything. Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$. Let $a,m,n\in\mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.  Proof:  Let $u,v\in\mathbf{Z}$ such that $\gcd(m,n)=um+vn=1$. Let $b,c\in\mathbf{Z}$ such that $\gcd(m,a)=ab+cm$. Let $d,e\in\mathbf{Z}$ such that $\gcd(a,n)=ad+en$.  So $\gcd(a,m)\cdot\gcd(a,n)=a^2bd+cmen+aben+emad$.  Where do I go from here? Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number Is it possible to have an object ignore a certain light source but still be affected by others? I want to create an effect on a character where their skin and clothing are effected by two different light sources. The clothing should only reflect a bright bounce light, but have the skin should not be affected by this light source.    In the example image I have two objects a cube, a sphere and three emission  lights . I want the two white lights to hit both objects, and I need the purple light to hit and reflect off of the sphere, but ignore the cube entirely (no reflections).  Someone suggested to composite the layers together, it works... but this is very impractical and cumbersome because it forces the background to be transparent and it will be a pain to try and layer together a more complex scene, especially if its animated which is what I want this effect for.  I know you can have objects ignore shadows and all kinds of other things so im hoping someone knows how to get an object to ignore light with a few settings. Why do proof authors use natural language sentences to write proofs? I haven't read very many proofs. The majority of the ones that I've read, I've read in my first-year proofs textbook. Nevertheless, its first chapter expatiates on the proper use of English in mathematical proofs, so I suspect that most proof authors do use both English (or another natural language) and formal proof systems for writing their proofs. However, I can't imagine many circumstances where mathematical notation and a formal proof system wouldn't suffice to convey the author's pertinent thoughts.   I suspect that proof authors have good reasons for making use of both English and formal expressions in their proofs, but I can't think of what those reasons are. Why do proof authors use English and formal expressions to write proofs? Are there stylistic rules (or guidelines) that state how, and in what parts of the proof, an author should, and shouldn't, use English? How to find regression coefficients $\beta$ in ridge regression? In ridge regression, the objective function to be minimized is: $$\text{RSS}+\lambda \sum\beta_j^2.$$   Can this be optimized using the Lagrange multiplier method? Or is it straight differentiation?