Distance between the foci
A circle has the same center as an ellipse and passes through the foci $F_1$ and $F_2$ of the ellipse, two curves intersect in $4$ points.
Getting percent sign into an URL in a footnote I'm using the url package. Now, I have some some url with a percent sign in it and want to place it in a footnote. When I let the % where it is, I get a comment, and the whole thing fails to compile because of some unmatched brackets. When it's at the end of a line, it doesn't show up at all in the result. When I write \% instead, this gets literally into the output—but I want the url to be displayed correctly.  What could I do? I am trying to calculate the sum of this infinite series after having read the series chapter of my textbook: $$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$$  my steps:   $$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}=\sum_{n=1}^{\infty}\frac{2}{4n^2-1}-\sum_{n=1}^{\infty}\frac{1}{4n^2-1}=..help..=sum$$  I am lacking some important properties, I feel I am coming to the right step and cannot spit that out.. How do I edit PDF files produced by LaTeX in Illustrator? Fonts are not found When I try to use Adobe Illustrator (CS4) to edit a PDF file produced by LaTeX with several equations in it, Illustrator complains that it can't find the fonts:  The font CMBX10 is missing.  Affected text will be displayed using a substitute font. The font CMMI10 is missing.  Affected text will be displayed using a substitute font. The font CMMI6 is missing.  Affected text will be displayed using a substitute font. The font CMMI7 is missing.  Affected text will be displayed using a substitute font. The font CMMI8 is missing.  Affected text will be displayed using a substitute font. The font CMMIB10 is missing.  Affected text will be displayed using a substitute font. The font CMR10 is missing.  Affected text will be displayed using a substitute font. The font CMR7 is missing.  Affected text will be displayed using a substitute font. The font CMSY10 is missing.  Affected text will be displayed using a substitute font. The font CMSY6 is missing.  Affected text will be displayed using a substitute font. The font CMSY7 is missing.  Affected text will be displayed using a substitute font. The font MSBM10 is missing.  Affected text will be displayed using a substitute font. To preserve appearance, some text has been outlined.   How do I find &amp; install the necessary fonts? Why isn't the gamma function defined so that $\Gamma(n) = n! $? Why Java needs Serializable interface? Is Stack Overflow merging two different accounts by email without the user's consent? I had one account through Google with email X and another account through myopenid.com. I happened to add the same email X to this myopenid.com account. My intention was to stop using the Google account in favor of the new myopenid.com account.   After some time asking and answering questions with my openid.com account I am astonished to find out that it is now merged into my Google account. That creates all kinds of privacy issues. I thought the email on my Stack Overflow account was private. Did I miss anything here?  To be clear, I wanted to preserve my privacy in the second account, but now since all my recent questions were transferred to the old account, my privacy is completely lost.  And it looks like there is no verification for the email field in my profile, so if Stack Overflow is using that info to merge, there is a very serious security bug. If it is merging based on something else, that's even worse. I think your account belongs to that user here. Let me merge it. Terrible! Eeeek! Code blocks are misbehaving! So code blocks in questions and answers on the android app (inline included) seem to be scared of me putting my finger in them. When I poke them, they only move over two columns!  (For clarity, these are the code blocks that overlap the TextArea view because they've been eating too much)  The intended behaviour here is that when I press my finger into a code block, the touch event should register a drag; at current, I try to scroll inside a code block and I end up switching to question or answer view instead, over and over.  EDIT:  Something tells me this is status-bydesign because the text is deliberately cut off (probably inviting you to click on the code block and expand it; UX Decision?): Space ship manned by only AI returns home to a different earth, back in time Is "performance" singular or also plural? What is a wizard that makes them non-Muggle? Or, more directly, what ancestry does the witch/wizard gene follow? Is there a patriarchal wizard (or matriarchal witch) that Muggles have no part in? Elves perhaps? Stop reading here.  Purpose of the Question/History/Don't Read There seem to be solid consequences associated with being Muggle, or Muggle-related. A dominant theme in the novels is discrimination against the non-gifted race, but, when read into, the wizard bloodline doesn't appear all that well defined. JKR indicates that wizard-ness is genetic, or inherited:  &quot;Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places.&quot;  By the above, it stands that a family that produces a squib (non-magical born of magical parents) must be a half-blooded family in some way, since half-blooded only requires one non-magical ancestor. Of course, we are dealing in magic genetics. Any other form of genetics would make this inherited, seemingly recessive trait (or squibs couldn't exist), never appear at all. Unless they were XMen. If it is so important, what does the wizard-bloodline follow? Other Mythos In other literature a wizard can be nearly anything, but magical powers are typically inherited as well as learned. Merlin of the Arthurian Legend (also mentioned in HP) is Cambian, meaning he is born of demonic intervention; this explains his source of enchantment. Gandalf of Middle Earth is a Maiar, as are all Wizards of Middle Earth. Wizards in Harry Potter seem to follow a bloodline, and it has been mentioned (in the question Gabe linked) that genetics have a heavy play in it, meaning that squibs and parents of Muggle-born wizards should have identical genetics. This bloodline must come from somewhere. Magical Creatures In Harry Potter it is common for magical creatures to &quot;mingle&quot; with humans, these beings are typically somewhat magical. Elves have been described to have very strong magic, but are for some unreasonable reason subservient to humans. I may be mistaken, but believe it was hinted that elves and the wizarding lineage had intersected at one time. Maybe I'm imagining this. Genocidal Allusions Voldemort hates muggles, and half-bloods, and whatever else is non-wizard. The presence of this theme, suggests that this wizardly bloodline must be at least defined if the main antagonist is so obsessed with keeping that mysterious bloodline pure. Since Slytherin himself was said to be a supremacist (circa a really long time ago) it suggests that this bloodline should have existed long before he was around, especially if he founded a school with people he was not related to, but were also magical. How to translate and rotate the heading of landscaped pages? Accidently deleted boot option on Dell laptop Movie Identification: People record their experiences on reel-to-reel I know that this sounds like Strange Days, which I haven't seen, but from the Wikipedia description I don't think that's it.  I saw this back in the early-to-mid-90's on TV, pretty sure it was a premium channel. It follows a research group who develops a way to record experiences. Not thoughts, but at least the sights, sounds, smells, touch, etc. They record it onto this reel-to-reel tape, it looked striated and golden in color. The protagonist is the head of the research team.  I don't remember a great deal of the plot, but there were conspiracies surrounding the invention. The lab clown decides to give it a whirl by putting the bike-helmet-sized apparatus on his head and going out to have a little fun, in the classic wine, women, and song fashion. Once he returns, an older member of the team finds the tape and finds a section where the clown is having sex. Later on, the protagonist, who is the lead researcher, finds the older member shut up in his house seemingly for days and nearly comatose. The older researcher had the playback device over his head and is non-responsive. Worried, the protagonist removes the helmet and puts it on himself, only to find that the older researcher had snipped a few seconds of tape and had them running on a non-stop loop; the moment of orgasm for the clownish researcher. The older researcher eventually comes to and awkwardly apologizes.  I think there were also experiments in recording the sensorum of a lab monkey, and that played into the plot. I remember the plot seemed fairly thin and dull for what seemed to be a pretty neat idea. I don't desperately feel the need to watch the movie, but I'm mildly curious if my impressions would differ 20 years later now. If a prime divides a product then it must divide a factor of the product [Euclid's Lemma] We have $q, p$ prime and $tq = (p-1)(p+1)$ for some positive integer $t$. The book I'm reading says that because $q$ is prime, it divides $p-1$ or $p+1$.   Question: Why exactly does it matter that $q$ is prime here? How can I prohibit putting figure after the footnote? I have pretty simple LaTeX code that has a lot of figure environments, and I see the figure is inserted after the footnote.   \documentclass[10pt, onepage]{article}  \usepackage{graphics,graphicx} \usepackage{hyperref}  ... dependent code\footnote{You should use at least JRE 1.5 or later, but I highly recommend using JRE 1.6 or later}, you can safely use the JRE 1.5 or later.   \begin{figure} \centering \includegraphics[width=0.5\textwidth]{pic_install/4_configure_build_path.png} \caption{Configuration menu} \label{fig:config_build} \end{figure} A person who cannot understand that there may be other perspectives I'm searching for a word to describe a person who cannot understand that there may be different perspectives. I initially thought of single-minded, but that pertains to determination.  One example of several perspectives could be the difference between a process and an action. Please assume that a process is composed of several actions. A process may be composed of other processes, but these processes would be actions in this greater process.  If you accept my definitions, then depending on the holistic or granularity level, we may consider something a process or an action, depending on whether we are considering its parts or how it's part of a greater thing.  A person may have trouble understanding that it's not true or false that something is a process or an action, it depends on how it relates with everything else from the perspective that we take. From one perspective it's a process, from another it's an action. For some people, things seem to be in one and only one absolute way, which is wrong, IMHO.   Is there a word to describe this kind of problem that some people seem to have?  PD: It's like . But I don't think most people know the word monist.  Here are some other, superficially similar terms that actually mean something quite different. A racist is (approximately) someone who considers other races inferior. A narrow-minded person considers other perspectives wrong or irrelevant, or may not consider them, but is aware that they exist. A monist would not even understand that there is more than one race or multiple perspectives; there is simply one reality, and that's it. Do I have to code each case of this Grid full of plots separately? How to include a PDF image into a PDFLaTeX document I am generating a PDF file using pdflatex and need to include another PDF file. The reason is that I have a graphMl file which I exported from yEd graph editor to a PDF file, named sample.pdf. The TeX code to be compiled with pdflatex is given below. I need to include that file at the start of the document.   \documentclass[a4paper,leqno,twoside]{article}  \usepackage[latin1]{inputenc} \usepackage[english]{babel} \usepackage{multirow}  \begin{document}   [% FOREACH st IN Service %]    Name,Id:   [% st.Id %], [% st.Name %]     des:   [% st.Description %]    Customers:  [% FOREACH softservice IN st.Customers %]   [% FOREACH swid IN softservice.SW %]  [% swid.Service %]   [% FOREACH st IN Service %][% IF swid.Service == st.Id %]     ([% st.Name %])     [% END %] [% END %][% END %][% END %]    Suppliers:    [% FOREACH shservice IN st.Suppliers %]    [% FOREACH sw IN shservice.SW %][% sw.Service %]     [% FOREACH st IN Service %][% IF sw.Service == st.Id %]([% st.Name %])      [% END %][% END %][% END %]    [% FOREACH hw IN shservice.HW %][% hw.Type %][% hw.Nr %][% END %]   [% END %]   \newpage   [% END %] \end{document} I don't know which buttons I have to click or what key combination to type to calculate a cube root. How can I show that if some group $G$ has only one subgroup $K$ of order $n$, then $K$ is a normal subgroup? Would that mean that it only has one subgroup total? If so then I guess that makes sense.