Number of ways to connect sets of k vertices in a perfect n-gon
Number of ways to connect sets of $k$ dots in a perfect $n$-gon
How can I get back to Blender's default theme? Can anyone help me out with how to make Bing Picture to my Desktop Wallpaper?    So it works by downloading the highest quality of todays picture. Then storing it ex in the Picture folder of your account. After that automatically changing the picture itself.  It should continue the same everyday without hassle in the background.  Probably something I have to add in the Startup Applications. Any differences between Ubuntu versions?    -Do I have to write a script?  This would be appreciated by many others too! Thank You in Advance :) I have created a fishnet grid (3km x 3km) over a vector polygon.   I now want to clip the fishnet over the vector polygon retaining all grid squares within the boundary of the polygon.   Therefore I want all squares that would typically be clipped into partial squares to remain as whole squares.   Does anybody know how to do this? I was looking at coreutils and found this as one of the files included as part of coreutils:  /usr/bin/[. What is [ and what does it do? It is an executable. I just don't know what it does or how to use it. $ file /usr/bin/[   /usr/bin/[: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared  libs), for GNU/Linux 2.6.15, stripped    When I try to run it, I think it is defaulting to the bash built in line expansion. Instead of actually running the file. $ &quot;/usr/bin/[&quot; /usr/bin/[: missing ‘]’ $ /usr/bin/\[ /usr/bin/[: missing ‘]’ Clamp velocity along local axis In the attached , I have a representation of a airplane/jet fighter (cube scaled at one end to indicate direction of flight). I am using torque to steer, and adding Linear Velocity along a local axis for thrust/brakes. What I want to know is how to clamp the velocity along the plane's local axis so when the plane steers, it does not simply keep flying in the direction that is was before it turned. I would prefer a solution with logic bricks, but if that is not possible, python would be acceptable. (it just needs to keep a speed relative to how long the thrust/breaks have been held no mater which direction it is pointing.) What is the earliest work considered to be Science Fiction? Unable to load DLL (Module could not be found HRESULT: 0x8007007E) 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? This question is essentially the same as one of my , except the only difference is that I am using "only" to change the text at the same location (i.e., ). In other words, I am destroying my earlier text as I go, and not adding new ones underneath the previous ones.   Since the text for the first "only" is shorter than the second "only", therefore the image will shift location. I would like for the image to remain at its location.   Here is an example     it may not be obvious but the second image is higher up than the first.  The code is here, can someone find a solution?  \documentclass{beamer}  \usepackage{graphicx}  \title[Title]{Presentation} \author{Sandro Botticelli} \institute{Italy} \date{1484}  \begin{document}   \begin{frame} \begin{figure} \includegraphics[scale = 0.8]{Venus}     \caption{Nascita di Venere} \end{figure}  \only&lt;1&gt;{In the centre the newly-born goddess Venus stands nude in a giant scallop shell. Its size is purely imaginary, and is also found in classical depictions of the subject. }    \only&lt;2&gt;{Alternative identifications for the two secondary female figures involve those also found in the Primavera; the nymph held by Zephyr may be Chloris, a flower nymph he married in some versions of her story, and the figure on land may be Flora. Flora is generally the Roman equivalent of the Greek Chloris; in the Primavera Chloris is transformed into the figure of Flora next to her, following Ovid's Fasti, but it is hard to see that such a transformation is envisaged here.} \end{frame}   \end{document} How to increase camera frames view area? The Camera view area is so small (see picture). How can I increase it? What will result in better page ranking in search results: Page views or time spent on page? Do I use ext4 for all partitions (such as / and /boot)? What are the other formats used for? I'm installing ubuntu onto a new laptop with 24gb SSD and a 500gb HDD. I wanted to put / and swap onto the SSD and /home onto the HDD. Is there anything I shouldn't use ext4 for?  I do not ever intend to dual boot. Ubuntu only. Undefined Symbol ___gxx_personality_v0 on link I've been getting this undefined symbol building with this command line:  $ gcc test.cpp Undefined symbols:   "___gxx_personality_v0", referenced from:   etc...   test.cpp is simple and should build fine.  What is the deal? I have heard several times that some mathematician has given another and more rigorous for an established theorem, but I don't know what does it really mean and what differences makes it to be more 'rigorous'. My understanding of a proof is that a proof is some explanation to convincing others that a statement is true. If some proof is not rigorous, does it mean that while the proof is acceptable for many but it is not for everybody? If so, the proof is not correct since it going to be rejected by some people and it is not a proof at all. Or, does rigorous mean it uses more advanced tools? If so, why not any alternative (but simpler) proof is also acceptable as rigorous (which is more 'valuable' as well since it's simpler!)?   Saying those limited insight of mine, my questions are:   $1-$ What does rigorous proof mean, in general definition?  $2-$ In order to understand your answers, as an example I am re-writing three of the proofs for the compactness of the torus. Which of the following proofs are most rigorous, 'normal' and least rigorous; and why so?    Theorem: The torus $T^2$ is compact.  First proof: The torus is homeomorphic to the product space $S^1 \times S^1$. The circle $S^1$ is compact. Therefore the torus is the product of two compact spaces, and thus it is compact.   Second proof: The torus $T$ is the subspace of $\mathbb{R}^3$ obtained by rotating a circle about the $z$-axis. The torus is closed since given any point in its complement, there is an open ball of sufficiently small radius centered at that point and disjoint from the torus. Also, the torus is bounded since it is contained in the ball of radius $4$ centered at the origin. Since the torus is closed and bounded in $\mathbb{R}^3$, it is compact.   Third proof: The torus is homeomorphic to a space obtained as a quotient  space of the square by identifying opposite edges. The square is a closed and  bounded subset of $\mathbb{R}^3$ and therefore is compact. Furthermore, a quotient map on the square is a continuous function, and the image of a compact space under a continuous function is compact. Therefore the torus is compact.   Thanks a lot for your guidance. On Windows 10 Professional, with the November update (Build 10586, Version 1511) , is there any possibility to completely remove Windows Defender ?  I don't want to just disable Windows Defender.  I want to completely uninstall from my system. Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$. Prove that $ℚ^*_{&gt;0}$ is not isomorphic with $ℚ$. What is the best way to convert an array to a hash in Ruby In Ruby, given an array in one of the following forms...  [apple, 1, banana, 2] [[apple, 1], [banana, 2]]   ...what is the best way to convert this into a hash in the form of...  {apple =&gt; 1, banana =&gt; 2} Recently I saw a widget on the Stack Overflow website which says Stack&nbsp;Overflow now has its own currency called "unicoins". According to this widget, a user can earn reputation, customize Stack Overflow by changing its colors and the user can also remove the vote down button from their questions and answers by spending "unicoins".  This widget does not look real, because this is out of standard of the Stack Overflow website.  Also today is 1st April. Is Stack Overflow fooling us?  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; "the police conspiracy" vs. "the police's conspiracy" Solving Hardy Weinberg problems I really fail to understand Hardy-Weinberg equilibrium and can't find an easy enough source of information.  Can you help me to understand Hardy-Weinberg equilibrium?  My goal is to be able to solve the following kind of problem     In a population with two alleles for a certain locus, B and b, the allele frequency of B is 0.7. What is the frequency of heterozygotes if the population is in Hardy-Weinberg equilibrium?