Can anyone do this with the latest OS and XQuartz? On my machine, XQuartz opens but displays nothing. E.g., after loading a file with  drawdot (35,70); showit; drawdot (65,70); showit; draw (20,40) .. (50,25) .. (80,40); showit;   I see a blank XQuartz screen.
I tried the first experiment in chapter 5 in the Metafontbook: ran mf, typed \relax and drawdot (35,70); showit;.  This opened a window entitled Metafont, but containing nothing.  What's missing?  Using TeXlive 2020 on Linux. PS. After adding drawdot (65,70); showit; I see both dots. PS II. Which have now disappeared, after I changed window-manager workspace and back. PS III.  Typing showit; before the first drawdot opens a window and allows the first dot to be seen, but after having switched workspaces and back, I haven't found any way of bringing the picture back, short of drawing something more and showing it.
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$ How would you go about proving that $$\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$$  for any two integers $a$ and $b$?  Intuitively it is true because when you divide $a$ and $b$ by $\gcd(a,b)$ you cancel out any common factors between them resulting in them becoming coprime. However, how would you prove this rigorously and mathematically? Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even I have a question:     Suppose $f$ is continuous and even on $[-a,a]$, $a&gt;0$ then prove that   $$\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$$   How can I do this? Don't know how to start. How to add "Refresh" option to right click menu in Lubuntu? I have many users at the place I work, expressing the notion of switching to Ubuntu.  Most of them, for whatever weird reason wanting to know if its possible to have refresh added when you right click on the desktop.   Is that possible? How does a magnet work? I'm having trouble understanding how a  (not the  that is generated as a result but the material itself) work. The particles are aligned in a specific direction to give rise to force but I don't see how this alignment gives rise to "attraction" or force. Let $E_n$ be $$E_n:=\{f\in C[0,1]\mid \text{exist } x_f\in[0,1] \text{ such that } |f(x)-f(x_f)|\leq n|x-x_f|,\, \forall x\in[0,1]\}.$$  How show that $E_n$ is nowhere dense, that is, $\mathrm{int}\  \overline{E_n} = \emptyset$?  Can someone help me? An easy bash completion tutorial? Let $X$ be a space that satisfies the hypotheses used to construct a universal cover $\overline{X}$. Let $\pi = \pi_1(X)$ and consider the action of the group $\pi$ on the space $\overline{X}$ given by the isomorphism of $\pi$ with $\text{Aut}(\overline{X})$. Let $A$ be an abelian group and let $\mathbb{Z}[\pi]$ act trivially on $A$, $a \cdot \sigma = a$ for $\sigma \in \pi$ and $a \in A$.  Now, assume that $X$ is a CW complex. How do I see that $\overline{X}$ is a CW complex such that the action of $\pi$ on $\overline{X}$ induces an action of the group ring $\mathbb{Z}[\pi]$ on the cellular chain complex $C_*(\overline{X})$ such that each $C_q(\overline{X})$ is a free $\mathbb{Z}[\pi]$-module and$$C_*(X; A) \cong A \otimes_{\mathbb{Z}[\pi]} C_*(\overline{X})?$$ QGIS installation error How do I calculate rotation caused by bounce friction? Apostrophes for possession: nouns My best friend of the moment - 'Essential Grammar in Use' for elementary students by Raymond Murphy - says that 'we normally use -'s for people.'     I stayed at my sister's house. (not the house of my sister).   Then, bellow in the same unit (64) says that 'we use of... for things, places, etc.'     Look at the roof of that building. (not that building's roof)   After that I thought:  Finally!!! I understand the rules for apostrophes!!!  But soon I lost all that naif excitement when I saw other written examples on the internet that were not following those 'rules'.     I've learnt that we can apply apostrophes to ...     one year's pay   and, finally, amazingly enough ... to , which means ANY kind of nouns (I deduce uncountable nouns are also part of the possibilities). This demolishes what is said in the grammar. So, it seems that eventually:     That building's roof -> is valid   So, now I need your help.    1) Can you tell me the rules concerning the apostrophe to show possession in respect to its usage with nouns? Can we really apply to all kind of nouns? e.g. teeth's, vehicle's, Paula's, forest's, manager's, Ireland's, etc     Scotland's worst drivers   Metadata improves information's accessibility       2) Is there a sense that justifies what is written in the grammar: 'we normally use -'s for people'? or it does not make sense at all? Change pivot or local origin of an object How can I change the local origin of an object, without changing the object location in the world space.  This is the object located at position (0,0,0) in the world space    This is the same object located at position (0,1,0) in the world space, but with its local origin offset so that the object is in the same place    Is there a way to do this in a single step? Animations about a young man pulled into a fantasy setting with dragons? I'm looking for an animation (more likely a film not a series) that I watched as a kid, watched early 90's I'm sure it contained a book loving male main character (wears glasses might have even had an amulet) who gets pulled into a fantasy via a magic book  Setting with dragons and an evil wizard, I remember it being on TV as I never had it on VHS.  Same sort of animation technique as visionaries or thundercats.  Thanks. What is the difference between a 'closure' and a 'lambda'? Windows 10: Keyboard type rate extremely slow after boot I have upgraded my computer using a core i5 2500K from Windows 7 x64 to WIndows 10 x64, and the whole system runs fast and reliable, with one exception: after booting from SSD, which takes only about 10 seconds, my keyboard is really slow for the first 1 or 2 minutes right after booting. "Slow" means that when I start notepad, and type some characters, it takes a second for each character to appear on screen. Everything else is fast, including mouse movement, starting programs, only keyboard input is that slow. After 1 to 2 minutes, the keyboard suddenly behaves normally again.  This happens with every kind of keyboard I connect, no matter if I use the legacy PS/2 adapter, or USB.  Does anybody have any idea what might be the cause of this strange behaviour? Abount linear functional: If $T(B)$ is bounded, is $T$ bounded? Let $H$ be a infinite dimensional Hilbert space and let $B$ be a basis of $H$ that $H=\overline{span(B)}$  moreover, let $T : H \rightarrow K$ be a linear functional   If $T(B)$ is bounded, is $T$ bounded? Zariski Tangent Space and $k[\varepsilon]/\varepsilon^2$ Let $X$ be a scheme over a field $k$, and let $x\in X$ be a rational point, that is, we have $k(x):=\mathcal{O}_x/\mathfrak{m}_x\cong k$.  Let $\alpha:\mathfrak{m}_x/\mathfrak{m}_x^2\rightarrow k$ be an element of $T_x=(\mathfrak{m}_x/\mathfrak{m}_x^2)^*$, the Zariski tangent space to $X$ at $x$.  Using $x$ and $\alpha$, I'd like to define a $k$-morphism of schemes Spec $k[\varepsilon]/\varepsilon^2\rightarrow X$.  In the course of the construction, I need to define a local map of local rings $\mathcal{O}_x\rightarrow k[\varepsilon]/\varepsilon^2$.  Using $\alpha$, what is a natural way to define such a map?  It might be helpful to note that I have an injection $k\hookrightarrow\mathcal{O}_x$ arising from the $k$-scheme structure on $X$.  I think this leads to a decomposition $\mathcal{O}_x/\mathfrak{m}_x^2=k\oplus(\mathfrak{m}_x/\mathfrak{m}_x^2)$ as $k$ vector spaces, from which the desired map would follow, but I can't seem to explicitly see what this decomposition is inside of $\mathcal{O}_x/\mathfrak{m}_x^2$.  This is part of exercise II.2.8 in Hartshorne. How can I get my graphics card to be recognized in System Info? I am new to Linux/Ubuntu. I installed Ubuntu 11.10 on my Lenovo IdeaPad y510.   System info says    Graphics: unknown.   Driver: unknown,   Experience: Standard.   What should I do to use all my laptop hardware components to work properly with Ubuntu? Screenshot: What is the angle at which water is splashed when a vehicle tyre rides in water on the road? I would like to know the following:   What is the angle at which water gets splashed when I ride my vehicle through a water on the road? How does angle of water varies with speed? What is the relation between the distance the water goes with the speed of the vehicle?   Thanks! How to search for only folders in Windows 7 instead of folders AND files At what point is the ~/.bashrc file created?