Converting a scientific notation number to a normal number in PHP
Is floating point math broken?
Is there a word that describes when you are unable to remember the word you want to say? How to use a flyback diode on a +/-12V motor I've got a motor hooked up to +12V on one side and -12V on the other, being driven in both directions by a Motor controller (). We were getting voltage spikes in the common ground after sending big impulses to the motor, so we put a flyback diode from the negative cable to the positive cable. However, this caused the motor to be less responsive in the reverse direction. How do we correctly prevent voltage spikes in the ground from this type of motor? Let $\mathbb{S} = \{ (X,Y,Z) \in \mathbb{R}^3 :X^2 + Y^2+Z^2=1\}$ denote the Riemann sphere. The following problem is taken from Gamelin "Complex Analysis" chapter one:     What is the image of the spherical cap $ C := \{(X,Y,Z) \in \mathbb{S} : A \leq X \leq 1\}$, where $A$ is some fixed real number between $-1$ and $1$, under the stereographic projection $ \pi(X,Y,Z) = \frac{X+iY}{1-Z}$?   Here is my work so far:  ( The case $A=1$ is trivial, so assume $A &lt;1$)  We want to find $\pi(C) = \{z \in \mathbb{C} \mid \exists(X,Y,Z) \in C: \pi(X,Y,Z) = z \}= \{z \in \mathbb{C} \mid \pi^{-1}(z) \in C\}$, where the last equality holds by $\pi$ being a bijection. Write $z=x+iy$.  Here, $ \pi^{-1}(z) \in C\iff A\leq \frac{2x}{1+x^2+y^2} \leq 1 \iff (\star) :A \leq \frac{2x}{1+x^2+y^2}$, since the inequality $2x \leq 1+x^2+y^2$ holds for all $x,y \in \mathbb{R}$.  $A=0$: $( \star)$ reduces to $ 0 \leq x$, so in this case the image is $\{z \in \mathbb{C} \mid \Re(z) \geq 0 \}$.   $A &gt;0$: Since $A \neq 0$ in $(\star)$ we have,  $ \frac{2x}{1+x^2+y^2} \geq A \iff Ax^2-2x+Ay^2+A \leq 0 \iff (x-\frac{1}{A})^2 +y^2 \leq \frac{1}{A^2}-1$. Thus the image is the interior and boundary of the circle centered at $\frac{1}{A}$ with radius $\sqrt{\frac{1}{A^2}-1}$. Note $\frac{1}{A^2}-1 \geq 0$ as $A \in (0,1)$.  $A &lt;0$ : By symmetry and the above, here the image is $ \mathbb{C} / \{ $ interior and boundary of circle centered at  $  \frac{1}{A}$ with radius $\sqrt {\frac{1}{A^2}-1} \}$.  Is my working correct? Many Thanks! How to set metadata for music files? In windows music files have metadata like artist name, album name associated with them. How is this metadata stored. Is it stored in file system like other file attributes or is it part of MP3 data that Windows Explorer extracts using a MP3 reader plugin?  Is it possible to read/change this information in Linux? Is it possible with commandline?  (I know these attributes can be set using Rhythymbox or some music player but I'm curious if these could also be set directly. Like in Windows the windows itself shows you artist information if you right click the file and open properties dialog) How do I convert seconds to hours, minutes and seconds? Let $\sim$ denote the equivalence relation on the $n$-sphere $S^n$ defined via   $$ (x_1,\dots,x_n,x_{n+1})\sim(x_1,\dots,x_n,−x_{n+1})\:\text{ for all }\: (x_1,\dots,x_{n+1})\in S^n. $$      Show that the quotient space $S^n/\sim$ is homeomorphic to the $n$-disc $D^n$.   I know that Ii have to show that there exists a bijective function $f: (S^n/\sim) \to D^n$ that is continuous and that the pre-image $f^{-1}$ is continuous as well, but I can't advance from here, any tips? sci-fi book where a meteorite gives 3 different kinds of telepathic powers to people who then vie for control 3 groups of telepaths each with different powers.  They received their powers from a meteorite.  One group is the strongest and are kind of in control.  Another group wants to gain control.  One group, I believe the strongest, have telepathic battles to determine the strength of one another conjuring up swords, walls, etc. in their minds. It was written by a lawyer.  Could have been written in the ‘80s, or earlier. Submit Buttons on the Left or the Right? We have been puzzling over where to put the submit button, on the left or the right. In researching, we noticed that many sites put buttons on the bottom right in dialogue boxes, and on the bottom left in forms.  It makes sense: in a dialogue box it seems to denote finality, being in the endpoint of the window for left–right readers; in a form, the bottom right could be in a different position relative to the rest of the form if the window is resized.  It seems to be a convention, but I don't see anyone talking about this specific phenomenon in the following questions, nor the articles referenced therein:        So, is this level of button position optimization worth it if it creates an inconsistency in button placement? Is this a good way to go? Why don't I need to install any Drivers for Ubuntu How can I get this symbol without using bbold? I am trying to find a book (young adult) where the devil is the protaganist, and other gods appear as characters I believe it was written by a teenager, and might have a sequel.   It has been many years since I read it, but I believe it had the devil acting like a regular human. He wasn't evil. I think it incorporated a lot of (gods/characters) norse, roman, Christian, and pagan. If the dual spaces are isometrically isomorphic are the spaces isomorphic? Casting a function pointer to another type Let's say I have a function that accepts a void (*)(void*) function pointer for use as a callback:  void do_stuff(void (*callback_fp)(void*), void* callback_arg);   Now, if I have a function like this:  void my_callback_function(struct my_struct* arg);   Can I do this safely?  do_stuff((void (*)(void*)) &amp;my_callback_function, NULL);   I've looked at  and I've looked at some C standards which say you can cast to 'compatible function pointers', but I cannot find a definition of what 'compatible function pointer' means. Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots. /review tab not accessible on a private beta This code in JS gives me a popup saying "i think null is a number", which I find slightly disturbing. What am I missing?    if (isNaN(null)) {   alert("null is not a number"); } else {   alert("i think null is a number"); }     I'm using Firefox 3. Is that a browser bug?  Other tests:    console.log(null == NaN);   // false console.log(isNaN("text")); // true console.log(NaN == "text"); // false     So, the problem seems not to be an exact comparison with NaN?  Edit: Now the question has been answered, I have cleaned up my post to have a better version for the archive. However, this renders some comments and even some answers a little incomprehensible. Don't blame their authors. Among the things I changed was:   Removed a note saying that I had screwed up the headline in the first place by reverting its meaning Earlier answers showed that I didn't state clearly enough why I thought the behaviour was weird, so I added the examples that check a string and do a manual comparison. "Always on Top" Windows with Java In Java, is there a way to have a window that is "Always on top" regardless if the user switches focus to another application?  I've searched the web, and all of the solutions lean to some sort of JNI interface with native bindings.  Truly this can't be the only way to do it?.. or is it? If $(a,b)=1$ then prove $(a+b, ab)=1$. Is there console mode in Mac OS X? Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing Given the sequence $a_0 = 1$, $a_{n+1}= \sqrt{2+a_n}$, how can I show that it is monotonically increasing?  I need it to show, that the sequence converges. I already proved boundedness but I can't figure out this last part.