Take the square $[0,1]^2$ we take $n$ random lines through the square. You can choose random lines by choosing a point on one of the sides of the squares and randomly choosing a different point on any of the other three sides and then drawing a line connecting them.   What is the probability that after $n$ of these random lines the largest region is greater than or equal to $0.5$?  Any tips or cases help, thanks.
Say you have a stick which breaks randomly into three pieces (we can choose the points randomly). What is the probability that the area is greater than or equal to $0.4$?   I can see it has something to do with Heron's formula but I just can't put t together.
Broken "Network profile" link when Area51 is their only account Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$ Someone edited my message on StackOverflow, but it really bugs me out.  I'm not sure what's wrong with it:   As you see, the bigger the circle becomes, the more vertices I need for hiding the straight lines. As you see, the bigger the circle becomes, the more vertices I need to hide the straight lines.   The latter (corrected) sentence just bugs me out for some reason. It would sound better if there was a comma after the word "need", perhaps, but I guess that would be even worse in means of grammatical correctness.  Can someone explain why is the first sentence bad and the second sentence correct? And could there even be better solution to fix the first sentence? limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$ Installing 64-bit geoprocessing of ArcGIS for Desktop? I am trying to install 64-bit processing to ArcGIS 10.2, but the ESRI .  One similar question on this exchange  that shows an option to include this, but my setup installation program (which I downloaded) does not show this installation window, but instead goes straight to selecting features to install as shown below.  I can't find any other documentation for running 64-bit geoprocessing on ArcGIS version 10.2.  Can anyone show me how to do this? or is it best to just try to install the service pack 1 version of it? Why don't we pluralize "foot" in measurements? This is how I'm approaching it: let $R$ be a finite integral domain and I'm trying to show every element in $R$ has an inverse:   let $R-\{0\}=\{x_1,x_2,\ldots,x_k\}$,  then as $R$ is closed under multiplication $\prod_{n=1}^k\ x_i=x_j$,  therefore by canceling $x_j$ we get $x_1x_2\cdots x_{j-1}x_{j+1}\cdots x_k=1 $,  by commuting any of these elements to the front we find an inverse for first term, e.g. for $x_m$ we have $x_m(x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k)=1$, where $(x_m)^{-1}=x_1\cdots x_{m-1}x_{m+1}\cdots x_{j-1}x_{j+1}\cdots x_k$.   As far as I can see this is correct, so we have found inverses for all $x_i\in R$ apart from $x_j$ if I am right so far. How would we find $(x_{j})^{-1}$? Cancellation of Direct Products Multiple (diamond) inheritance compiles without "virtual", but doesn't with I see more and more servers that have no domain defined in the /etc/resolv.conf file.  Only a search entry. In what cases is this setup used ? Are there any cases where it must not be used ?  nameserver xxx.xxx.xxx.xxx nameserver yyy.yyy.yyy.yyy nameserver zzz.zzz.zzz.zzz  search domain1 domain2 domain3 ... Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for these? How many orders have specific names?  In this case, I'm dealing with NURBs curves, so the "tangency" and "curvature" related words are to be preferred over "velocity" and "acceleration" words. Should my canonical URLs have only the ID with no slug so that they don't change? Our URLs will be created by the user's content.  Eg:  www.example.com/bar-1234/i-went-to-baz-4321  The "i went to baz" portion is user generated, included with the aim of being helpful to the person viewing the URL and also to possibly contain useful keywords for search engines.  However, the string that forms that portion is user editable. So it could become:  www.example.com/bar-1234/we-drove-to-baz-4321  AFAICT the canonical URL should be:  www.example.com/bar-1234/4321  The string portion is discarded by the controller, which means that there's potential for duplicate content from limitless URLs!  So, my question is, does it matter if my canonical URL is 'non SEO friendly'?  It seems logical to me to provide search engines with the "id only" version of the URL which is always consistent, but the canonical URL is the one that appears in search results, so is there any benefit from trying to use more 'SEO friendly' URLs? Mandatory excerpt for custom post type Solve differential equation, $x'=x^2-2t^{-2}$ Solve differential equation:  $x'=x^2- \frac{2}{t^2}$  Maybe is it sth connected with homogeneous equation? I have no idea how to solve it. Jewish Law prohibits the  However, butter, a milk product, is a kitchen staple for most cooked emulsions (eg. pan-sauces, sauces béchamels, or roux-based sauces). While I use appropriate cooking fats for making non-dairy versions for meat dishes, this frequently doesn't work.  What is a non-dairy fat which may be used to as an emulsifier or roux ingredient? Ubuntu 16.04 VIM without python support! Although Ubuntu 16.04 release notes mention that:  The default VIM package has been built against python3 instead of python2.  Yet after I installed vim with the following command:  sudo apt-get install vim   And checked:  vim --version   It showed:  -python -python3   Is it a bug? How do I get vim with Python support? How to find files containing two strings in different lines Does anyone know how to find the radius of convergence of the series $\sum\ z^{n!}$, where $z$ is a complex number?  I tried to use the definition: $$\frac{1}{R}=\limsup\left|\frac{a_{n+1}}{a_{n}}\right|$$ but I wasn't successful. How to check if a process is running via a batch script Convert char to int in C#