Is there a general expression for the volume of an truncated elliptical cone, that is a cone in which both the base surface and top are elliptical and not circles? Both of the ellipses are parallel surfaces if that helps. I have managed to find a general expression for a normal truncated cone at $[\frac π 3(r_1^2+r_1r_2+r_2^2)h]$. Would it be possible to approximate by using the average volume of 2 normal truncated cones calculated by using the 2 sets of radii in the ellipses?
I wish to calculate the volumes of a truncated cone whith asymetry over all axes and ellipses as base and top - how do I do that?  I have height and radii of the corresponding ellipses. (I assume correctly I need the geometric means of the 2 radii describing the ellipsis.)  Kind Regards
What would be the right position of "substantially" in the following:     1). Before verb: These optimal values substantially contribute to the success of the methodology.      2). After verb: These optimal values contribute substantially to the success of the methodology.   Here is my issue:  Fact1: When I use Google Ngram, I get , 0 occurrence of option 1.  Fact2: I found an excellent Grammar book that discusses Adverbs, their types and prefered positions. The author defines some rules that I'll summarize as follows:   Connecting adverbs, eg: however, then,..., Position: Beginning of clause. Indefinite frequency, eg: always, usually,..., Position: Mid position (after auxilary verb, before other verbs) sometimes beginning of clause. Focusing adverbs, eg: mainly, only,..., Position: Mid position. Adverb of certainty, eg: clearly, obviously, Position: Mid position. Adverb of completeness, eg: almost, nearly,..., Position: Mid position. Adverb of manner, eg: fast, slowly, nicely,..., Position: End clause, mid and beginning. Adverb of place, eg: upstairs, around, Position: End clause, sometimes beginning. Adverb of time, eg: daily, weekly, ... Position: Mostly end clause, sometimes beginning and mid position.   I think that "substantially" is an adverb of completeness. Therefore, the right position is before the verb "contribute" (option 1). However, Google Ngam indicates that option 1 is not widely used.  What do you think? Any suggestions? Proving a Composition of Functions is Bijective If I have $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f$ is onto and $f\circ f\circ f = f$, how can I prove that $f$ is bijective? I know that I only have to prove that it is 1-to-1 because I'm given the fact that it's onto, but how can I use the fact that $f\circ f\circ f=f$ to prove that it is 1-to-1?  Thanks! Evaluate definite interval of normal distribution I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it.  However, I wonder if there is a a nice formula for $N(c_{-} \leq x &lt; c_{+}| \mu, \sigma^2)$. Or what the "state of the art" approximation for this problem might be. How to install specific Ubuntu packages, with exact version? I want to setup a new virtual machine with some specified packages (name and version), that are provided.  For example apache2 in version 2.2.20-1ubuntu1 with all dependencies. Even if there is a new version of this package on the servers this one should be installed.  The solution has to work/scale with multiple (n) "setups". Another virtual machine might need an older version of apache2.  I currently know of some possibilities that install the exact packages, but do not scale that good:   Copy all required *.deb to every virtual machine manually and enter: dpkg -i ... -> Could work, but it is very error prone. (Manual scripts etc.) Create and use a new Ubuntu repository for each setup. -> Does not work because I would need n repositories. Setup the machine once and copy the VM / create a snapshot. -> Does not work because I would need to store n VMs.   My problem could be labeled as patch management, but I do not want to update my packages to the current version. My goal is to install old packages. List contents of tarball in tree format Per the answers  I'm able to list the contents of my tarball in ls format. However, I'd like to be able to list them in tree format, i.e. something like the latter instead of the former:  With tar:  $ tar -tf foo.tar  foo/ foo/baz/ foo/baz/qux/ foo/baz/qux/hisfile.txt foo/bar/ foo/bar/myfile.txt foo/bar/yourfile.txt   With tree:  $ tree foo foo ├── bar │   ├── myfile.txt │   └── yourfile.txt └── baz     └── qux         └── hisfile.txt   Is it possible to do this without extracting the tarball? I'd prefer to have to avoid extracting the tarball due to their size. remote ssh tcpdump command, through a gateway, to be opened, in realtime, in Wireshark, on local machine I (Host A - Windows based using plink) am trying to connect to a remote linux server (Host C), through a gateway linux server (Host B), and run this tcpdump on Host C to be piped all the way back to Host A (through Host B I assume), and opened, in real time, with Wireshark on Host A:  Below is what I saw as the command when not using a gateway ("direct remote fetch").  So, how would I make this work going through my gateway host B scenario above?  Host A$ plink.exe -ssh -pw abc123 root@Host C "tcpdump -s0 -U -n -w - -i eth0 not port 22" | "C:\Program Files\Wireshark\Wireshark.exe" -k -i - , I shouldn't need to vote down or flag the answer, because the question itself is a dog.      Users should be allowed to also enable the "I'm done" button by down voting, close voting or flagging the question rather than directly taking action on the answer.    Currently, I have to click on the question's title, close or down vote it in the new tab, then go back to the review page, and click "Not sure" to continue on my adventure. Inline elements shifting when made bold on hover I created a horizontal menu using a HTML lists and CSS. Everything works as it should except when you hover over the links. You see, I created a bold hover state for the links, and now the menu links shift because of the bold size difference.  I encounter the same problem as . However, the post does not have proper solution. I've searched everywhere for a solution and can't find one. Surely I can't be the only one trying to do this.  Does anyone have any ideas?  P.S: I don't know the width of the text in menu items so I cannot just set the width of the li items.    .nav { margin: 0; padding: 0; } .nav li {      list-style: none;      display: inline;      border-left: #ffffff 1px solid;  } .nav li a:link, .nav li a:visited {      text-decoration: none;      color: #000;      margin-left: 8px;      margin-right: 5px;  } .nav li a:hover{      text-decoration: none;      font-weight: bold;  } .nav li.first { border: none; } &lt;ul class="nav"&gt;     &lt;li class="first"&gt;&lt;a href="#"&gt;item 0&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 1&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 2&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 3&lt;/a&gt;&lt;/li&gt;     &lt;li&gt;&lt;a href="#"&gt;item 4&lt;/a&gt;&lt;/li&gt; &lt;/ul&gt; Is Mana Weaving ok if it's followed by a thorough shuffle? My friends and I are relatively new to MtG. At some point, one of them introduced us to the idea of mana weaving, and we'd do this to declump our decks prior to a very thorough shuffling. However, at the Theros pre-release, one of us was asked not to do this, and we learned it was frowned upon and ceased to do it.  I just now came across , and it sounds like mana weaving's only bad if you use it to leave your deck in an even distribution, and it's OK if your deck is then thoroughly shuffled. In hindsight, the judge may have simply thought my friend wouldn't have shuffled afterwards, but at the time I came under the impression it was frowned upon even if you did shuffle afterwards.  So: is mana weaving my deck OK, if I shuffle it very thoroughly afterwards? What would you consider to be the best exception type to throw when an extension method is called on a null instance (where the extension method does not allow it)? Since extension methods are nothing but static methods you could argue that it should be ArgumentNullException, but on the other hand they're used like instance methods so it might be more natural to use the NullReferenceException. Let's take the following example:  public static string ToInvariantString(this IFormattable value, string format) {     return value.ToString(format, CultureInfo.InvariantCulture); }   This way a NullReferenceException will be thrown if the value parameter is null.   The other example would be:  public static string ToInvariantString(this IFormattable value, string format) {     if (value == null) throw new ArgumentNullException("value");     return value.ToString(format, CultureInfo.InvariantCulture); }   EDIT: In some of the answers you have pointed out that an extension methods can be called like a static method and in those cases a null reference exception would be wrong, which is a great point, and actually one of my concerns, not sure why I forgot to mention that in the question in the first place.   Someone also pointed out that it's wrong to throw a NullReferenceException, and yes, it is. That's why I don't throw it, I just let it happen (let the CLR throw it) by not guarding the method.  I think I favor the ArgumentNullException (that's what I've use so far) but I still think there is at least room to argue for an against the NullReferenceException since it seems more natural in most places where the method is going to be used. How do you concatenate matrices? And how do you make block matrices? Free GIS workshops, tutorials, and applied learning material This Q&amp;A lists free as in $0 workshops in GIS and related fields that have their material available to view or download online. The list is not limited to FOSS GIS, as GISers usually use a combination of open and closed source tools to accomplish their tasks. Some of these tools are easier than others and some are better documented. This list will be a great benefit to the community especially for new comers to the field. General GIS   from   from   from   from   Open-source GIS   from   from   from   from   from   ESRI Products   from   from   Transportation These links include either theoretical or applied transportation knowledge in transportation planning          Disaster Management    Databases   from   Geo Statistics    from How to prove that the center of the dihedral group $D_{2n}$ is $\{1,r^{n}\}$ and the center of $D_{2n-1}$ is $\{1\}$?  I don't know how to prove it in this general case. I am trying to pickle some mangoes the Indian way. I boiled the jar in hot water, dried it and then added the mixture of spices, salt and mangoes to the jars after the mixture had cooled. I made the mixture in a frying pan to try and remove as much water as I could. After it was cooled, I put it in the jar and heated some mustard oil till it just barely started smoking. I let that cool and poured it over the mango spice mixture.  For the first three days it was fine. On the fourth day, I opened it to test the taste and ended up adding more salt. Now, there seems to be gas forming in the jar. I've noticed it a few times now. When I open the jar, I hear a whooshing noise as air escapes. It's quite a lot, since I opened the container about 3 times in a 10 hour period and each time gas escaped. Has this pickle gone bad? Or is this something that's normal? jQuery Event Handler created in loop How to move a visible file to a hidden folder? I've only been using Ubuntu for two weeks and have been able to find answers to any problem I had, however this one defies my searches.  I want to move a visible programme file (wallch) to a hidden directory ./config/autostart.  I have been able to enter this directory and the subject file is not there and I want to have this program start at bootup.  Can anyone assist?  Thanking you `--no-install-recommends` only specified packages I want to install xfce4-goodies but I don't want Midori Browser. With --no-install-recommends I don't know how to specify only Midori. I want the rest of packages. How to do that? Thanks! Font size setting is missed in iPhone application Can you add a setting for choosing font size in iPhone mobile app?   It's hard to read questions. I get double question marks when referring to labels inside figures I need a non trivial  examples of group isomorphism that maps $G\to H$ such that   $G/H \cong G$.