Why does this hyperboloid change into a surface?
What geometric object is given by this equation?
What does general relativity say about the relative velocities of objects that are far away from one another? What does general relativity say about the relative velocities of objects that are far away from one another? In particular:--  Can distant galaxies be moving away from us at speeds faster than $c$? Can cosmological redshifts be analyzed as Doppler shifts? Can I apply a Lorentz transformation in general relativity? Perhaps this is trivial: how does one prove that the work done by a homogeneous gravitational field on a system of particles is equal to the work done on a point mass with the total mass of the system, located at the center of mass of the system. Is anti-gravity (i.e. repulsive gravity) possible in theoretical physics? Is  (i.e. repulsive gravity) possible in string theory?  I have read some articles about scientists making assumptions about the existence of anti-gravity, but is it possible in string theory? Exposing database IDs - security risk? I've heard that exposing database IDs (in URLs, for example) is a security risk, but I'm having trouble understanding why.  Any opinions or links on why it's a risk, or why it isn't?  EDIT: of course the access is scoped, e.g. if you can't see resource foo?id=123 you'll get an error page. Otherwise the URL itself should be secret.  EDIT: if the URL is secret, it will probably contain a generated token that has a limited lifetime, e.g. valid for 1 hour and can only be used once.  EDIT (months later): my current preferred practice for this is to use UUIDS for IDs and expose them. If I'm using sequential numbers (usually for performance on some DBs) as IDs I like generating a UUID token for each entry as an alternate key, and expose that. Finding the limit of $\left(\frac{n}{n+1}\right)^n$ Find the limit of: $$\lim_{n\to\infty}\left(\frac{n}{n+1}\right)^n$$   I'm pretty sure it goes to zero since $(n+1)^n &gt; n^n$ but when I input large numbers it goes to $0.36$.  Also, when factoring: $$n^{1/n}\left(\frac{1}{1+\frac1n}\right)^n$$ it looks like it goes to $1$.   So how can I find this limit? Adding only specific text from a file to an array list, part 2 - Java Immigration officer placed a standard Leave to Enter stamp when I have Indefinite Leave to Remain. What do I do? I travel on a NZ passport and have lived in the UK since 2006. I travelled to Canada in June 2016 to begin a 2 year Canadian working visa but on a trip back to the UK in July I received a 6 month visa stamp in my passport despite having an Indefinite Leave To Remain Visa in my old passport (I haven't got a biometric card yet but plan to apply for one before I return to the UK to live. What should I do about this? Any good resources for Lagrangian and Hamiltonian Dynamics? I'm taking a course on  and  Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics.  So far at my university library, I have found many books on both subjects, but not ones with good practice questions and answers. I have Schuam's outline of Lagrangian Dynamics, but didn't really find a lot of practice questions.  Any suggestions would be greatly appreciated! Are there any examples of subspaces  of $\ell^{2}$ and $\ell^{\infty}$ which are not closed? How were the number of rounds for different key sizes of AES selected? The number of AES rounds increases with the key length. Why increase the number of rounds at all, and how were these round counts chosen? How does a circular lens produce rectangular shots? Apple Magic Trackpad multitouch configuration Enabling CORS in GeoServer (jetty)? Batch normalize audio volume on .ogg-files Are there any simple tools to normalize an .ogg-library of 10'000+ songs so that the volume is the same throughout all songs?  Terminal or GUI doesn't matter, it only need to be simple.  One caveat though, I don't want soft interludes/intermissions and ballads blown out of proportion.  Preferably the process should find the overall gain of the album (I have all my CD's ripped into separate folders) and normalize the level thereafter. Does a word rhyme with itself? Coloring a black and white PDF graphic I have a graphic in PDF format (originally converted from an SVG) that is monochromatic (black on white). Is it possible using TikZ or PSTricks but not (Illustrator or Inkscape) to include this image in a different color?  Example:    While it lasts (there seems to be no long term way to host a pdf), you can .  Edit: Simple was perhaps a bit of a misnomer - the pdfs are cropped and monochromatic, but to intricate to redraw on my own. The above example is a character from a font (which I can recolor), but it gives a good example of what shapes I am talking about. Why did Voldemort stop employing Occlumency against Harry in Deathly Hallows? I have the two PGF nodes foo and bar positioned in a row.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document}   \begin{tikzpicture}[node distance=0.2cm,mynode/.style={rectangle,draw}]     \node[mynode] (foo)                {foo};     \node[mynode] (bar) [right=of foo] {bar};   \end{tikzpicture} \end{document}   How can I create a third node below those two nodes with the width of foo, bar and the node distance between them? Is there a way to do this with the fit library or is this the wrong approach? How would I prove there is no smallest positive rational number? what is the best method to prove this statement? Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$ What is the result of  $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$ . I tried to do couple of algebraic manipulations, but I didn't reach to any conclusion.  Thanks a lot.