Terminology: Intersection of a Spherical Zone and Lune
What's the name of each pseudo-rectangle in a spherical surface?
Following an online tutorial that uses an object named "icosahedron" from Add > Mesh > Regular Solids > Archimedean > Icosahedron. This object is not available in my version of Blender (2.74). Presenter asks me to include an add-on named "Add Mesh: Regular Solids", which again is not listed in my User Preferences dialog. What can I do about it? How to redirect output to screen as well as a file? My aim is to log all output from a script into a directory that the script is going to create.  For example, I have:  ~/.abc.sh:  #! /bin/bash rails new myapp   When I run...  cd ~/code . ~/.abc.sh   ...that will create a new Rails app in directory ~/code/myapp.  When Rails is creating an app, it outputs a whole lot of text that I want to capture and store in a log file in the same directory the rails command newly created. I also want to display that text in the terminal as well.  How do I go about doing this? Use induction to prove the following: $1! + 2! + .... + n! &lt; (n + 1)!$  Base case:  $n = 1$  $1! &lt; 2!$ true   Inductive step: Assume that $1! + 2! + .... + k! \le  (k + 1)!$ is true   let $n = k + 1$  $1! + 2! + .... + (k + 1)! &lt; (k + 2)!$  $1! + 2! + .... + k! + (k + 1)! &lt; (k + 2)!$  $1! + 2! + .... + k! + (k + 1)! &lt; (k + 2)!$  $(k + 1)! + (k + 1)! &lt; (k + 2)!$  $2(k + 1)! &lt; (k + 2)!$  $2(k + 1)(k)(k - 1).. &lt; (k + 2)(k + 1)(k)(k - 1)....$  $2 &lt; (k + 2)$   the right is always bigger for k are non negative integer. What are the eigenvalues of $\operatorname{ad}x$? Let $x\in \operatorname{gl}(n,F)$ have $n$ distinct eigenvalues $a_1,\ldots,a_n$ in $F$. Prove that the eigenvalues of $\text{ad }x$ are precisely the $n^2$ scalars $a_i-a_j$ ($1\leq i,j\leq n$), which of course need not be distinct.   So we can represent $x$ by an $n\times n$ matrix $X$. We have $Xv_1=a_1v_1,\ldots, Xv_n=a_nv_n$ for eigenvectors $v_1,\ldots,v_n$.   Now, $\operatorname{ad}x$ takes $y\in \operatorname{gl}(n,F)$ to $xy-yx$. I need to show that some $y$ is taken to a scalar multiple of itself, where that scalar is $a_i-a_j$. What could be that $y$? Count occurrences of each element in a List[List[T]] in Scala Finding the limit $\lim_{x\rightarrow \infty} \sqrt[3]{x+1}-\sqrt[3]{x}$ When at home I use my 13" MacBook Pro hooked up to an 27" external monitor. When working on my 27" screen I prefer to have a visible dock at all times. I have enough screen real estate to afford this luxury.  When I'm on the road working on my 13" screen I prefer to automatically hide the dock as it really gets in the way when screen real estate is limited.  I now manually switch between enabling and disabling hiding (using ⌥⌘D) but I would prefer this to happen automatically. Can I enable hiding the dock on my MacBook monitor and disable hiding the dock on my external monitor? How do I remove diacritics (accents) from a string in .NET? I'm trying to convert some strings that are in French Canadian and basically, I'd like to be able to take out the French accent marks in the letters while keeping the letter. (E.g. convert é to e, so crème brûlée would become creme brulee)  What is the best method for achieving this? Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent Let $X$ and $Y$ be independent random variables. Prove that $f(X)$ and $g(Y)$ are independent for any choice of measurable functions $f$ and $g$.   This sounds very obvious, but I have no idea how to approach it.  EDIT: Two random variables are independent if $\Pr\{X = x \text{ and } Y = y\} = \Pr\{X = x\} \cdot \Pr\{Y = y\}$ How to reduce fireflies in Cycles? I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately. Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$? When has Wonder Woman died? I know Wonder Woman has died in canon before, but in which issue did this happen? The command history between sessions is not getting saved. I'm using guake and the history for the session is working fine. I noticed that .bash_history had some commands I executed in sudo -s mode and tried the same again and all the commands while in the session got saved so I tried: chmod 777 .bash_history  Now the old commands appear at the start of a session but no new commands are getting saved. Looking for a (short?) story about a cryo ship looking for habitable planets I'd like to create a LaTeX document that when rendered into PDF, has forms that can be filled out using Adobe Reader or other such programs. Then I'd like to be able to extract the data. I deliberately would like to avoid using Acrobat for all the usual reasons (non-free, need different versions for different platforms etc).   Can this be done ? Group cohomology is one thing I don't seem to get my head around.  I understand $H^0$ as being the "fixed points" but when it comes to anything higher I have no idea what the notions are meant to be capturing...if anything.  For example I can see that 1-cocycles are homomorphisms with a specific property but that property doesn't seem to mean anything to me...and I think it should!  Is there an intuition or example that explains the meaning or is it just something that "stuck" and seems to work in lots of places? Embedding images explodes generated PDF size What's the grammar behind "A'warring", from the lyrics of Symphony of Destruction? What's the grammar behind A'warring, from the lyrics of Symphony of Destruction by Megadeth? It's the first time I'm seeing the use of such apostrophe. If I have Optimize iPhone Storage enabled on my iPhone and my phone storage is completely full, I understand that iOS will only store a low-res thumbnail of many of my photos on the device. (The full high-res version of the image will only exist in iCloud and on devices with Download and Keep Originals enabled.)  But when only thumbnails exist on the device, how does that work in relation to other photo apps on iOS? For example, do third-party cloud-based photo apps (like Google Photos, Dropbox's Carousel, or Amazon Prime Photos) have access to the full high-res images from the iCloud Photo Library? Or will they only see the low-res thumbnails in some cases? How can I iterate over an enum?