Pgfplots surface looks "wiry"
addplot3[surf] creates lines instead of a surface
Storing output of command in shell variable Can an irrational number raised to an irrational power be rational? Is there a good Valgrind substitute for Windows? What would be the effects of warp collisions? Triggered by a  I was wondering what actually would happen to a ship (e.g. the Enterprise-D NCC-1701) that collides with a stationary object such as a) another ship of a similar configuration or b) a gigantic structure like a moon or even a planet.  We know the deflector is supposed to keep interstellar dust (not to be confused with ordinary dust, which is a different thing) from ripping large holes in the ship.  At first, one thinks "Obvious. ." But does it really? Would the deflector manage to actually deflect both masses? If not, where is the threshold of what a deflector can handle? Would the ship maybe tunnel right through the object, because of wibbly-wobbly space wobblification by the warp field? It does do some weird things to the space right in front and behind the vessel.  Important remark: We cannot approach this with what we know about physics at all. For all intents and purposes, both ships must measure the other ship travelling faster than light, resulting in it having infinite (or rather undefined) mass and by extension momentum. If we start with that reasoning any ship jumping to warp would suck in the entire universe (it takes a moment, but think about it). So, obviously we cannot apply our intuition (even our relativistic intuition) here. How do that charge gets transferred while rubbing? How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ I have a graph. This is my code.    \documentclass[10pt]{article}     \usepackage{pgf,tikz}     \usetikzlibrary{arrows,patterns}     \pagestyle{empty}      \definecolor{ttqqcc}{rgb}{0.2,0,0.8}     \definecolor{ffqqtt}{rgb}{1,0,0.2}     \definecolor{ttqqff}{rgb}{0.2,0,1}     \definecolor{uququq}{rgb}{0.25,0.25,0.25}      \begin{document}      \begin{tikzpicture}[line cap=round,line join=round,&gt;=triangle 45,x=1.0cm,y=1.0cm]      \draw[-&gt;] (-3.63,0) -- (3.67,0);     \foreach \x in {-3,-2,-1,1,2,3}       \draw[shift={(\x,0)}] (0pt,2pt) -- (0pt,-2pt)          node[below] {\footnotesize $\x$};     \draw[color=black] (3.48,0.07) node [anchor=south west] { $x$};      \draw[-&gt;] (0,-1.93) -- (0,5.57);     \foreach \y in {-1,1,2,3,4,5}       \draw[shift={(0,\y)}] (2pt,0pt) -- (-2pt,0pt)          node[left] {\footnotesize $\y$};     \draw[color=black] (0.06,5.19) node [anchor=west] { $y$};      \draw (0pt,-10pt) node[right] {\footnotesize $0$};      \clip(-3.63,-1.93) rectangle (3.67,5.57);     \draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0]      plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;     \draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772]      plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;      \begin{scope}[xscale=-1]     \draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0]        plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;     \draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772]        plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;     \end{scope}      \draw[smooth,samples=100,domain=-3.6342419080068153:3.665758091993186] plot(\x,{(\x)^4-4*(\x)^2+3});      \fill [color=uququq] (-1.73,0) circle (1.5pt);      \fill [color=uququq] (-1,0) circle (1.5pt);      \fill [color=uququq] (1,0) circle (1.5pt);      \fill [color=uququq] (1.73,0) circle (1.5pt);      \end{tikzpicture}     \end{document}   When I see the DVI output DVI, I have    And if I look at the PDF file, I have How to compile .c file with OpenSSL includes? 80s/90s book where boy stumbles on game where aliens gamble their planets I don't remember much about it other than the setting. It's about a boy who one night stumbles upon some different alien races playing a game in which their civilizations will end if they lose. He gets involved in the game somehow and is hunted. According to the well ordering theorem "". Whenever we have a well ordering on a set, it is not difficult to construct a new well ordering with a largest element. My question is:     For a given infinite set, can we find a well ordering on it such that there is no largest element? Blender Internal glossy BSDF equivalent? Answer appears automatically converted as a comment Prove holomorphism of expression I have to prove that given $\gamma$ contour of $G \subset \mathbb{C}$  and $f$ continuous function on $G$. Then the function $g(z) = \int_{\gamma} \frac{f(w)}{w-z}dw$ is holomorphic on $\mathbb{C} - \bar{G}$ My attempt: I started by using that given any parametrization $\alpha :[a,b] \rightarrow \gamma$ we can rewrite $g(z)$ as: $g(z) = \int_a^b \frac{f(\alpha(t))}{\alpha(t)-z}\alpha'(t)dt$ Now using the fundamental theorem I derivate to see where $g'(z)$ is defined and I get: $g'(z) = \frac{f(\alpha(b))}{\alpha(b)-z}\alpha'(b) - \frac{f(\alpha(a))}{\alpha(a)-z}\alpha'(a) $ Here I get stuck, I fail so see how this links back to $g$ being holomorphic at $\mathbb{C} - \bar{G}$. Any hints on how to proceed? Thanks! What is the difference between: Rooting, Jailbreak, ROM, Mod, etc.? What is the difference between:   Unlocking the bootloader (prerequisite for doing many, though not all, other things below) Rooting Jailbreaking ROM NAND and Nandroid Operating System Mod (e.g. CyanogenMod) Recovery (ClockworkMod, Amon Ra) Custom Kernel (e.g. LeshaK's kernel) Firmware Driver Over The Air (OTA) update Fastboot SIM unlocking Flashing SPL (Second Program Loader)   (any other often-confused terms that I've missed?) How do I automate a key press in AppleScript? How to use Mathematica functions in Python programs? Is space expanding equally in every direction? Does space expand equally in every direction, so that it draws a perfect sphere or is expansion asymmetric, so it creates "bubbles" (when seen from the outside)? Can you use an external 301 redirect for a blog post hosted on wordpress.com? Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$ I want to prove the assertion:      The unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ when $p \equiv 1 \pmod{4}$, respectively $\mathbb{Q}(\sqrt{-p})$ when $p \equiv 3 \pmod{4}$.   My first attempt is this. In $\mathbb{Z}[\zeta_p]$, $1-\zeta_p$ is prime and $$ p = \epsilon^{-1} (1-\zeta_p)^{p-1} $$ where $\epsilon$ is a unit.  Since $p$ is an odd prime, $(p-1)/2$ is an integer and  $$ \sqrt{\epsilon p } = (1-\zeta_p)^{(p-1)/2} $$ makes sense and belongs to $\mathbb{Z}[\zeta_p]$.    How do I deal with the $\epsilon$ under the square root?  I guess the condition on the congruence class of $p$ comes from that.  Is this even the right way to proceed?  Uniqueness is not clear to me either.  I thought about looking at the valuation $v_p$ on $\mathbb{Q}$, extending it to two possible quadratic extensions beneath $\mathbb{Q}(\zeta_p)$, then seeing how those have to extend to common valuations on $\mathbb{Q}(\zeta_p)$, but I didn't see how to make it work.  I would appreciate some help. Translating cooking terms between US / UK / AU / CA / NZ