This airplane's propellers are both rotating anti-clockwise. But as you see, they are seem like rotating clockwise seen from front (nose) side. This phenomenon is known as optical illusion.  My question is, how to explain it? This occurs at certain rotation speed only. When the rotation is put slower, we will see the actual rotation, so does when it put higher. Need to know the range of rotation speed when it will be seen revert the rotation.
Sometimes you see a video of a fan or a propeller spinning very fast, and the apparent rotation is distorted. The fan can appear to be moving in the opposite direction of rotation, or even stationary. This optical illusion is known as the wagon-wheel effect. If I understand correctly, this occurs because the camera framerate is slower than the frequency at which the fan makes one rev, so stroboscopic effects should be expected.   Does the wagon-wheel effect occur only in videos, or can we observe it just with the eye?
Logistic regression vs. LDA as two-class classifiers 1) a ten years old boy is sitting on the couch.      2) a ten year old boy is sitting on the couch.      3) a ten-years old boy is sitting on the couch.      4) a ten-year old boy is sitting on the couch.   Which is correct? Concurrent and Blocking Queue in Java I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... User group (company) page that shows summary of all user accounts belonging to the same company/user group Why do I have to enter my password to log in? Using the Stack Exchange login, why do I have to enter my password again and again to log in? Wasn’t the whole purpose of OpenID to do away with this?  This doesn’t even only happen when visiting a new Stack Exchange site – it also happens for sites where I already have an account but which I don’t visit regularly. Here’s what I mean:    Of course I don’t remember my password (it’s a long random string). And so I have to go to my password manager and manually copy the password from openid.stackexchange.com’s account into the login form. – And incidentally, this is what my password manager looks like now:    (And, by the way, those are the only entries in my keychain so far, but by far not the only SE sites where I have an account.)  … I feel that this defeats the purpose of site-wide login and OpenID. In the olden times when MyOpenID was still working properly, I’d simply enter my OpenID on the login form, and the software would take care of the rest – namely, redirect to the OpenID service, (automatically) verify that I was authorised to use it, and redirect back to the original website, having logged me in. It was literally one button click for me. It’s substantially more work now, and I’d like to understand why this regression is necessary.  (Note: of course once a site’s password has landed in my password manager I (probably?) won’t have to enter it again. But still: wasn’t site-wide login and OpenID supposed to solve this already?) OpenLayers low resolution and/or shifts in QGIS print composer? How do I enable Cortana after the Anniversary Update (1607)? I use to run  $s =~ s/[^[:print:]]//g;   on Perl to get rid of non printable characters.   In Python there's no POSIX regex classes, and I can't write [:print:] having it mean what I want. I know of no way in Python to detect if a character is printable or not.   What would you do?   EDIT: It has to support Unicode characters as well. The string.printable way will happily strip them out of the output.  curses.ascii.isprint will return false for any unicode character. According to the original paper of , there is no key validation needed when using Curve25519 for Diffie-Hellman Key Exchange. However, where does this property come from? Is there any proof or argumentation available in order to understand this really practical property of Curve25519? Does this mean that each $x$ coordinate could belong to a point $P=(x,y)$ from Curve25519? Is that even possible? I gave a quick answer to part of  which had not been covered by previous answers, trying to clarify the reason you would say time of decoding but not decoding’s time. I said it was ’s usually indicates possession, but of course there were several counterexamples that would have occurred to me after a moment’s consideration, and these where helpfully supplied:   Britain’s climate two days’ time  a day’s work  the sun’s rays   I am still of a mind to say that possession of some sort is what allows the ’s. Even though the sun does not have title to its rays, they do belong to the sun. Now, at the risk of duplicating the original question and/or being pigheaded, I am curious as to why time of decoding but not decoding’s time is correct, if not for the reason I gave. How to mount and unmount hard drives under Windows (the unix way) Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$ MySQL is giving weird result Is every complex (smooth) manifold a scheme? The question in the title doesn't quite make sense. I was always wondering if the scheme is the generalization of manifold. The precise statement should be like following:  If $X$ is a complex (smooth)manifold, is there a scheme $Y$ over $\mathbb{C}$ such that the corresponding analytic space $Y^{an}$ isomorphic to $X$?  I guess if $X$ is projective, then this is Chow's theorem. And I doubt the question has an affirmative answer if $X$ is non-compact (I guess that $X: y-e^x=0$ in $\mathbb{C}^2$ might be an example, but I do not know how to show this).  Edit 1:  There are also example (as @hunter pointed out) of a complex torus but not an abelian variety shows that a compact manifold might not be a variety, however, is it possible to be a scheme ?(according to Hartshorne, the category of varieties is a subcategory of quasi-projective, integral, separated scheme. But could there be some non-quasiprojective scheme($Y$ has to be integral, separated in our case according to GAGA, I guess) )?  Edit 2: Another question I think of is: is (Artin) Stack a generalization of manifold? I really want to know if manifold could be think of some subcategory of some category of with "algebraic objects". How to programmatically create a WPF window in a WinForm application Cursor hitting "border" between differently sized monitors I'm not sure if I'll be to explain this right. I have a dual monitor display on Windows 7 and my left monitor (laptop) has a lower vertical resolution than the right monitor (regular LCD monitor). So obviously, if I stick these monitors together, there's a part in the upper-left corner of my LCD monitor where cursor cannot go to the other monitor. I remember there was a trick to make this gap disappear, and make it seem like the monitors are of equal height.  Any suggestions?  By the way, I am also using UltraMon. Kind of a strange question, but say something has spoiled, i.e. smells bad, tastes bad, etc.  Will it actually always make you sick? Like for instance spoiled dressing, let's say it tastes sour, smells nasty and you eat it, will it make you sick?  If so what actually makes you sick? The toxins/bacteria? or it just being unappetizing?  I ask because I tried a TINY bit of ranch and while it tasted mostly fine (it was a bit tangy) it smelled quite tangy but looked fine. I also saw . Why didn't the Seons change? In the book Elantris, the Reod was caused by a giant earthquake opening a chasm which changed the shape of all the Aons. The Seons, which are basically living Aons, were presumably unchanged, since nobody noticed the change, which should have been obvious on the simpler Aons.