My question is different from that question. I'd like to randomly draw a number of dots with different colors and sizes, for example, 50 dots, 60 dots... It will be better if these dots can distribute in a circle.      \documentclass{article}     \usepackage{tikz,pgfmath}     \begin{document}     \thispagestyle{empty}     \begin{pgfpicture}     \pgfmathdeclarerandomlist{color}{{red}{blue}{green}{yellow}{white}}     \foreach \a in {1,...,50}{     \pgfmathrandominteger{\x}{1}{200}     \pgfmathrandominteger{\y}{1}{200}     \pgfmathrandominteger{\r}{5}{10}     \pgfmathrandomitem{\c}{color}     \pgfpathcircle{\pgfpoint{+\x pt}{+\y pt}}{+\r pt}     \color{\c!40!white}     \pgfsetstrokecolor{\c!80!black}     \pgfusepath{stroke, fill}     }     \end{pgfpicture}     \end{document}    Example output:
I want to fill a part of a picture with more or less evenly and randomly distributed circles which should not overlap. It would be okay if circles are only partly inside the shape.  The density should be like what you see on this page  with values 80-100. (But I do not need so many circles, 30 should be enough, I could repeat the pattern).   I cannot use a grid and "wobble" the circles a bit: The circles are too large and it simply does not look randomly.   Currently I am thinking about a random attempt: Get some random point, measure its distance to existing circles, either paint or throw the point away. Try 100 times and hope that you get the right number of circles (and that it does not take too long). But perhaps someone has a better idea.   The example draws the circles simply manually:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{backgrounds} \begin{document}   \begin{tikzpicture}[framed,gridded,radius=0.5cm]  \draw[red](0,0) rectangle (5,5);   \draw (1,1) circle;   \draw (2.3,1.1) circle ;   \draw (4.5,0.8) circle ;   \draw (5.1,1.8) circle ;   \draw (0.4,3.3) circle ;   \draw (2.1,2.8) circle ;   \draw (3.8,3.5) circle ;   \draw (4.8,4.2) circle ;   \draw (0.8,4.9) circle ;   \draw (2.1,4.1) circle ;   \draw (3.8,2.0) circle ;   \draw (3.5,0.6) circle ;   \draw (3.0,5.0) circle ;      \draw (4.1,5.1) circle ;             \draw (0.9,2.1) circle ;  \end{tikzpicture}  \end{document}
I am on Ubuntu and I did this command:  $ uname -a Linux slabrams-desktop 2.6.32-29-generic #58-Ubuntu SMP Fri Feb 11 19:00:09 UTC 2011 i686 GNU/Linux   Does it mean I am on 32bit or 64 bit processor?  The reason I am trying to figure this out is that I was getting errors which looked like this:  cannot execute binary file   and from Googling, I thought it was a processor issue.  Any ideas? I've tried every combination of "CLEANUP AND OUTPUT" settings that might conceivably prevent munging my HTML, but nothing works.  No matter, what, my HTML gets flattened or in some way rewritten, mainly with whitespace being trimmed off that I want to leave in.  I would suspect CKEditor (version 3.6.4.7575) except that when I tell WYSIWYG to "Apply source formatting", CKEditor doesn't prevent that, so it seems that logically this problem is in the WYSIWYG module.  "Apply source formatting" simply causes the HTML to be screwed up differently.  Some linebreaks are left in place, but spaces at the beginning of the line are left in place.  How can I prevent this, and still use a WYSIWYG editor? Auto-incrementing field in feature class using ArcGIS Desktop? So I'm relatively new to ArcGIS and ArcCatalog.  I have created a field name of PROJECTID in a feature class in a Personal Geodatabase.  The data type is TEXT.  This will be a ten digit ID.  The first five characters will be a acronym.  The sixth character will be a digit that represents the type of feature.  It will be a number.  The last four characters will be numbers that should be incremented starting at 0001.    Example:     WATER-1-0001  Screen shot of the field:   So my question is how can I do this in ArcCatalog.  I've seen some Python code that will autoincrement like the following:  rec=[OBJECTID] def autoIncrement(a):   global rec   return "water" + str(a) + "-" +  format(rec, '04d')   Again I'm a newbie when it comes to ArcGIS . Now I am getting an error NameError name 'OBJECTID' is not defined. What documents to show if I'm a US citizen with no US passport to re-enter the US? Suppose I am a naturalized citizen of the US, but also a citizen of another country, "XYZ". I then boarded a plane and left the US to another country (maybe not necessarily to XYZ), without first getting a US passport, but using my old, but valid XYZ passport.   In this case what would be the best documents to have for me to gain entry back into the US as a US Citizen without a passport?  Would I need to contact the US Embassy for help in order to be able return?  If the airline does let me aboard to return to the US, even without the US passport, what are the best documents could I show at the border to prove I am a US citizen but that I just don't have a passport, for whatever reason? Recommendations for good Newtonian mechanics and kinematics books What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.? Command Shift Period (show hidden files) stop working On my MacBook with OS Mojave, Command Shift Period (show hidden files) stop working. How to restore it?? Thanks in advance! To prove Cayley-Hamilton theorem, why can't we substitute $A$ for $\lambda$ in $p(\lambda) = \det(\lambda I - A)$? Cayley Hamilton Theorem states that if $A$ is an $n \times n$ matrix over the field $F$ then $p(A) = 0$.  We note that $p(\lambda) = \det(\lambda I - A)$. Hence, why can't we just substitute $\lambda$ with $A$ and directly prove Cayley-Hamilton Theorem by saying that $p(A) = p(\lambda) = \det(\lambda I - A) = \det(AI - A) = 0$? This is the first part of the first half of the a proof in the Axiom of Choice. The proof that the Axiom of Choice is equivalent to the choice function. REsources: Keith Devlin's Joy of Sets: pg. 58. F.R. Drake and Singh Intermediate Set Theory: pg. 110).   I am confused on proving disjointness and will ask further questions of proof once I get this first part v. clear for myself.   AC1: Let $\mathcal F$ be a family of pairwise disjoint, non-empty sets. Then there is a set $\mathcal M$ that consists of precised one element from each member of $\mathcal F$  AC2: For every family $\mathcal F$ of non-empty sets, there is a choice function $\mathcal f$. (I.e. $\mathcal f(X)$ is a member of X, for each X in $\mathcal F$.   Disjointness: Two sets are disjoin if Q $\cap$ R = $\emptyset$. Meaning that they have zero elements in common. These sets do not overlap.   Show: AC1 $\leftrightarrow$ AC2   (1) ($\rightarrow$) Let $\mathcal F$ be a set of nonempty sets.   (2)For each X $\in$ $\mathcal F$, let $X^*$ = (X $\times$ {X}) = {(x, X) | x $\in$ X})  (3) Show Disjointness.  An outline of how book proves  disjointness:  (a) if u = {(X $\times$ {X}) | x $\in$ X} then u is of the form $\lt  z, t \gt$ where z = X and t=x, i.e. x $\in$ X.   (b) then if u $\in$ ({X} $\times$ x) $\cap$ ({Y} $\times$ Y) $\rightarrow$ u = $\lt z, t \gt$ with z = X and z=Y, i.e. X=Y. Which means ({X} $\times$ x) = ({Y} $\times$ y).  Questions: (1) Apparently we cannot prove disjointness in $\mathcal F$ but must prove in a different set. If so, why is that?  (2) why is the case that if u $\in$ ({X} $\times$ X) $\cap$ ({Y} $\times$ Y) then z =X and z=Y? I am not following that step at all.   (3) why does the axiom of choice have to do with ordered pairs? Why are we setting X $\in$ $\mathcal F$, let $X^*$ = (X $\times$ {X})?    Thank you! Working with a huge file. Illustrator is super slow. What can I do to ease the load? jQuery doesn't submit a form It would be nice if backticked code in question titles were rendered the same way they are in question bodies. Since there are so many questions with code in them I feel it would be a big plus. .  This would look a lot nicer in listings and on the page itself if the code strings were rendered as such.  Similar ideas discussed . I always thought water sources were called taps in kitchens, bathrooms etc, but a Google search only returned outdoor taps.  So my question is, what are indoor taps really called? Like this one: Python does not find packages installed without Anaconda I have a  beautiful  inequality, but I can only prove part of cases. Given any positive real numbers $a,b,c$, we have   $$(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$$  How can we prove this statement? Cross-validation for timeseries data with regression I just installed a new Ubuntu Server 18.04. I set my hostname hostnamectl set-hostname ****.openbayou.biz and I set /etc/hosts:  127.0.0.1 localhost [ip address] ****.openbayou.biz hostname # The following lines are desirable for IPv6 capable hosts [ip6 address] *****.openbayou.biz hostname ::1     localhost ip6-localhost ip6-loopback ff02::1 ip6-allnodes ff02::2 ip6-allrouters   I also installed OSSEC to monitor for new files, errors and changes to my server and I'm now getting these alerts:  Server returned error NXDOMAIN, mitigating potential DNS violation DVE-2018-  0001, retrying transaction with reduced feature level UDP.`   It's now repeating itself:  systemd-resolved[3195]: message repeated 4 times: [ Server returned error  NXDOMAIN, mitigating potential DNS violation DVE-2018-0001, retrying transaction  with reduced feature level UDP.]   I've looked online for a solution and nobody is reporting this issue. Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$ How can we prove that? $$\sum_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}=\frac{1}{3}e^{\frac{-x}{2}}x\left(e^{\frac{3x}{2}}-2\sin\left(\frac{\pi+3\sqrt{3}x}{6}\right)\right).$$  I think if we write the taylor expansion of $\sin(u)$ and $e^u$, we can arrive from RHS to LHS, but I am looking for a way to prove it from LHS. How do Stack Overflow questions appear in Google search results in seconds? Possible Duplicate:          I have noticed that when I ask a question on Stack Overflow and I go into Google and search for the question, it comes up in Google in just a minute or so.  How do they do this? I want the secret!  I am a web developer and I know about most things that you can do for SEO, but I have no idea how these questions appear in Google this quickly!  I think it's amazing! I just graduated, and I'm starting a new job soon. My employer has pretty good policy for matching 401(k) contributions, so I want to invest as much as possible, especially during this first year.  My question is: should I invest in a traditional 401(k), a Roth 401(k), or some combination of the two? On the one hand, tax rates may be much higher when I retire, and I might be in a higher tax bracket, so a Roth 401(k) would be good. On the other hand, I might be in a lower tax bracket when I retire, so a traditional 401(k) might be better. It's hard to know where I will stand in 30 years.  Is this the same trade-off as with a traditional / Roth IRA, or is there any other tax difference I should know about? Is there a way to disable access to certain Settings components?