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How can I tell whether a circle and a rectangle intersect in 2D Euclidean space? (i.e. classic 2D geometry) Is it ok to say 'sorry' where you otherwise would use 'excuse me'?  Example: "Sorry, but could you show me the way to the next train station?" Matlab arrays operation Rack Mount Servers - Build them or Buy them? This is the  for "Should I build coomputing hardware myself?" questions.   I have put together countless PCs, but never a large server. The geek in me says build it, but the realist in me says let the manufacturer handle it when there is a problem. Ignoring the time penalty involved with the initial assembly time of a built one, which is a better solution? Have you ever run into a problem with a home build server that would have been solved easier/quicker/cheaper by going with a manufacturer? Are there any features that manufacturers give that aren't easily attainable with a home built server? A question about using the "v-ing" verbs To native speakers, normally do you use adverbs to modify these v-ing worlds especially when they are the objects of the verbs?  Like:      I regret swimming hurriedly     Not      I regret hurried swimming.      Right? And what about these two sentences:     I regret stamp-collecting     or     I regret collecting stamps   Besides, when using these words, it still retains the verbal characteristics right? Like:       The house needs a careful cleaning.     has the same meaning with       The house needs carefully cleaning.     or       The house needs to be cleaned carefully.   (SOMETHING like passive voice) How to create a Sierpinski triangle in LaTeX? I have been trying to recreate the following image in LaTeX    and for me personally it has to be done with pdflatex. Although answers using pst-fractals From Jake I got a good start which led to the following code  \documentclass{standalone} \usepackage{tikz} \def\level{5} \usetikzlibrary{lindenmayersystems}  \begin{document} \begin{tikzpicture}[l-system={step=5pt, order=\level, angle=120},rotate=180]     \pgfdeclarelindenmayersystem{Sierpinski triangle}{     \symbol{X}{\pgflsystemdrawforward}     \symbol{Y}{\pgflsystemdrawforward}     \rule{X -&gt; X-Y+X+Y-X}     \rule{Y -&gt; YY}     }     \draw [black] (3,2) l-system     [l-system={Sierpinski triangle, axiom=X, anchor=north east},fill=white]; \end{tikzpicture}  \end{document}   There are however two problems with the code.   I layer a black triangle behind the lindenmayersystem? How do I keep the size of the triangle consistent with different number of recursion levels. I know enough amount of set theory and logic to study grad-level math. However, I don't know more advanced set theory and logic, such as the ones on Kunen's or Shoenfield's texts. Although it's good to learn such advanced topics, I may not have enough time to do so, since I will probably put my emphasis on algebra, analysis or geometry as well as mathematical physics.   Although how much set theory and logic I should learn is totally up to what sort of analysis, algebra or geometry I will study, I want to know how much of them typical competitive algebraists/analysts/geometers know. If you are one of them, how much do you know? Render result is completely blank A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [ What's the difference between the five masses: inertial mass, gravitational mass, rest mass, invariant mass and relativistic mass? Dual-system Windows and Ubuntu I did dual boot with Windows 7 &amp; Ubuntu 14.04. I get both in boot menu but can't boot into Windows 7. The primary drive where Windows 7 was configured now shows to be logical drive with all files in it. How to resolve it ?  This is what it shows:  irshad@irshad-desktop:~$ lsblk NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 465.8G  0 disk      ├─sda1   8:1    0  58.6G  0 part /media/irshad/B2E08E69E08E339F     ├─sda2   8:2    0     1K  0 part      ├─sda5   8:5    0 195.3G  0 part /media/irshad/8E90A6A690A6946D     ├─sda6   8:6    0 182.8G  0 part /media/irshad/7650B08250B04B1F    ├─sda7   8:7    0    25G  0 part /    └─sda8   8:8    0     4G  0 part      sr0     11:0    1  1024M  0 rom     I tried to run update-grub but I get the following result.  $ sudo update-grub  Generating grub configuration file ...  /etc/grub.d/06_custom: 31: /etc/grub.d/06_custom: function: not found  /etc/grub.d/06_custom: 34: /etc/grub.d/06_custom: save_env: not found  /etc/grub.d/06_custom: 36: /etc/grub.d/06_custom: Syntax error: "}" unexpected How can I concatenate two arrays in Java? Indefinite Integral of $\sqrt{\sin x}$ $$\int \sqrt{\sin x} ~dx.$$  Does there exist a simple antiderivative of $\sqrt{\sin x}$? How do I integrate it? According to "Moving Around Other Creatures" (PH p. 191 / SRD p. 92):     You can move through a nonhostile creature’s space. [...] another creature’s space is difficult terrain for you.    Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.   So it's possible for Alice to , the only penalty being that the ally's space counts as difficult terrain to enter.  If an enemy adjacent to the ally's space has readied a grapple against Alice and is successful, then Alice (unwillingly) ends her move in her ally's space.  Do allied characters in the same space suffer any negative effect?  Now the rest of Alice's allies do the same thing.   Is there a limit to the number of characters that can be stacked on a space?   What if Alice's ally was the one with the readied grapple?  Can you stack an ally on your space by readying a grapple to prevent them from leaving? Horned Mohawk looking insect. What is it? Any ideas? I didn't know any other way to explain it.  I live in Indiana, USA if that helps.   Someone said it might be a "stink bug" but I'm not sure and not willing to find out! Are there any other methods to apply to solving simultaneous equations? We are asked to solve for $x$ and $y$ in the following pair of simultaneous equations:  $$\begin{align}3x+2y&amp;=36 \tag1\\ 5x+4y&amp;=64\tag2\end{align}$$  I can multiply $(1)$ by $2$, yielding $6x + 4y = 72$, and subtracting $(2)$ from this new equation eliminates $4y$ to solve strictly for $x$; i.e. $6x - 5x = 72 - 64 \Rightarrow x = 8$. Substituting $x=8$ into $(2)$ reveals that $y=6$. I could also subtract $(1)$ from $(2)$ and divide by $2$, yielding $x+y=14$. Let $$\begin{align}3x+3y - y &amp;= 36 \tag{1a}\\ 5x + 5y - y &amp;= 64\tag{1b}\end{align}$$ then expand brackets, and it follows that $42 - y = 36$ and $70 - y = 64$, thus revealing $y=6$ and so $x = 14 - 6 = 8$. I can even use matrices! $(1)$ and $(2)$ could be written in matrix form: $$\begin{align}\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}&amp;=\begin{bmatrix}36 \\ 64\end{bmatrix}\tag3 \\ \begin{bmatrix} x \\ y\end{bmatrix} &amp;= {\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}}^{-1}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;= \frac{1}{2}\begin{bmatrix}4 &amp;-2 \\ -5 &amp;3\end{bmatrix}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;=\frac12\begin{bmatrix} 16 \\ 12\end{bmatrix} \\ &amp;= \begin{bmatrix} 8 \\ 6\end{bmatrix} \\ \\ \therefore x&amp;=8 \\ \therefore y&amp;= 6\end{align}$$  Question Are there any other methods to solve for both $x$ and $y$? Set origin to vertex in edit mode? I want to make the origin in edit mode at a vertex, but it keeps setting it to the last clicked-on face :( So now in edit mode the pivot is on the last clicked-on face ;( Should we have a tag for significant points in time? Why don't shell builtins have proper man pages? All shell builtins share the same manual page:  BUILTIN(1)                BSD General Commands Manual               BUILTIN(1)  NAME      builtin, !   etc.   Then there is a little text describing what shell builtins are, and then a list that  looks something like this:    Command       External    csh(1)    sh(1)        !             No          No        Yes        %             No          Yes       No   But if we do man grep we get sections such as   Bugs History See also Standards Description   etc.  Don't shell builtins have their own history, description and arguments like -A or -r? Why isn't that provided in the manual pages and how would I learn to use them correctly and efficiently? How to Detect workstation/System Screen Lock/unlock in windows OS using java? Landscape topography from grayscale image