Novel about developing anti-gravity by fooling scientists I'm trying to remember the name of a novel I remember reading in the 90s about attempting to develop anti-gravity. General Googling hasn't brought up anything, I guess it was probably not well-known (I can't even remember how good it was, just very vague memories!) and likely well out of print. Not sure when it was written though, may well have been 70s or 80s. The premise as I remember it was the US government gathered together some of their best scientists and mathematicians, and told them (incorrectly - on purpose) that the Soviets had developed some form of &quot;anti-gravity&quot;, and that they needed to re-create it for the US in a form of &quot;Manhattan project&quot;.
Government investigating home library of missing inventor This is a short story from the 50s or 60s.  A scientist or inventor has invented either teleportation or a space drive and has disappeared - leaving no documentation or clues except his extensive home library.  The government gathers all types of scientists to attempt to duplicate his research.  Several months later, as they are about to launch the first space drive space ship, the officer in charge reveals that there was no 'disappeared inventor'.  The greatest step toward a new impossible concept is knowing that it has already been done.
I would like to find all ellipses which contain 2 given points and has one focus at origin (zero). All in 2D plane.   There are several possible approaches but I'm not sure which is the best - both looks quite difficult to solve algebraically.   using polar equation relative to focus with $(R_1,\phi_1),(R_2,\phi_2)$, being coordinates of points $$ R_1 = \frac{a(1-e^2)}{1-ecos(\phi_1-\theta)} $$ $$ R_2 = \frac{a(1-e^2)}{1-ecos(\phi_2-\theta)} $$ then for given $\theta$ solve for semimajor axis $a$ and eccentricity $e$ using deffinition of elipse as a set of points of the same distance from both foci. Given 2 points of cartesian coordinates $(x_1,y_1),(x_2,y_2)$ and one focus in origin $(0,0)$. For each given distance parameter $L$ solve for coordinates of second focus $(x_f,y_f)$, $$ L = \sqrt{x_1^2 + y_2^2} + \sqrt{(x_1 - x_f)^2 + (y_1 - y_f)^2} $$ $$ L = \sqrt{x_2^2 + y_2^2} + \sqrt{(x_2 - x_f)^2 + (y_2 - y_f)^2} $$ I can also first rotate the coordinate system (or my input points) by given angle (which is my arbitrary parameter) and then use some simplified equation of ellipse which has major axis parallel to x-axis which has just 2 degrees of freedom. But even after this rotation I don't see much simplification of algebraic solution.    Or is there any better way?    The resulting equations are quite difficult to solve. I wonder if there is some trick to simplify it and make it more elegant.  Also, because I would later to implement it into computational code where it would be computed manytimes per second, I would prefer solution inf form which is fast to evaluate numerically ( prefferably without goniometric or any transcedental functions )    Why I'm interested ? - I need it for some optimalization of orbital transfers for spaceship orbiting the Sun. I asked also in physics.stackexchange, and people recomand me that I should rather go to math section. Could there be a body of water the size of a planet? Show that if $x$, $y$, $z$ are integers such that $x^2 + y^2 = z^2$, then at least one of them is divisible by $2$, at least one is divisible by $3$, and at least one is divisible by $5$.  I know that $x,y,z$ are sides of a right-angled triangles. If I start putting values, then I can show, but have no clue about mathematical approach.  How do I solve it mathematically, using modular arithmetic? Taking advantage of one-time pad key reuse? Suppose Alice wants to send encryptions (under a one-time pad) of $m_1$ and $m_2$ to Bob over a public channel.  Alice and Bob have a shared key $k$; however, both messages are the same length as the key $k$.  Since Alice is extraordinary lazy (and doesn't know about stream ciphers), she decides to just reuse the key.  Alice sends ciphertexts $c_1 = m_1 \oplus k$ and $c_2 = m_2 \oplus k$ to Bob through a public channel.  Unfortunately, Eve intercepts both of these ciphertexts and calculates $c_1 \oplus c_2 = m_1 \oplus m_2$.     What can Eve do with $m_1 \oplus m_2$?     Intuitively, it makes sense that Alice and Bob would not want $m_1 \oplus m_2$ to fall into Eve's hands, but how exactly should Eve continue with her attack? Prove $\sin^2\theta + \cos^2\theta = 1$ How do you prove the following trigonometric identity: $$ \sin^2\theta+\cos^2\theta=1$$  I'm curious to know of the different ways of proving this depending on different characterizations of sine and cosine. n tasks assigned to n computers, what is the EX value of a computer getting 5 or more tasks? Say a central server assigns each of n tasks uniformly and independently at random to n computers connected to it on a network. Say a computer is ‘overloaded’ if it receives 5 or more tasks.  Q: Calculate the expected number of overloaded computers.  I thought of doing [1 - Pr(a computer is not overloaded)] but that leads me to a complicated expression of: $$1 - PR(NotOver) = 1 - \sum_{i=0}^4  \left( \frac{1}{n} \right)^{i} { \left( \frac{n-1}{n} \right)}^{n-i}$$ multiplying this by n would(hopefully) give the Expected value. But the answer seems not very elegant atall, is there something I'm missing or an easier way to tackle this? Thanks! Currently, if you access a deleted question you will get a short message informing you that the question has been deleted. However, if you click on a direct link to a deleted answer or comment (which you can get via notifications), nothing is displayed.  This is naturally quite confusing as you will get the message about a new answer or comment via notifications, click on the link and simply see nothing.  Therefore, I propose to display some sort of message to the user, informing her/him that the answer or question has been deleted. Note that this is different from always showing a deleted answer/comment, as I specifically request it in case you access the specific URL.  One example for a comment would be:   One example for a deleted answer is:   This question is related to ,  but requests a feature to circumvent the problem altogether. Is "each" singular or plural? You goes with are. Does the presence of each change this?  How satisfied are each of you with the time you've spent in your respective  universities. How satisfied is each of you with the time you've spent in your respective  universities I just purchased a D5100 and I am  slowly learning the basics.  I mostly shoot landscape/scenery shots.    I have been trying to capture the full moon unsuccessfully.  It looks focused in the viewfinder and I've experimented with slow shutter speeds and large apertures but the resulting image always comes out as a bright glare.  I'm never able to see the details of the moon.  How can I improve my shots? I have a framed picture about two feet by three feet in size that weighs about one pound (not a sheet of paper). I want to hang it onto a wall that is of full-blown hard concrete and covered with paper wallpaper (not vinyl - just paper).  The default way would be to drill the concrete and insert an anchor but that would damage the wall surface.  Is there a way to hang such picture onto such wall without damaging the wall? Decrease Backlight Below Minimum I have this laptop that doesn't handle the backlight very well.  In /etc/default/grub, I have added a acpi_backlight=vendor function to get it to work at all. Which is cool, and the backlight now actually works, but the minimum backlight setting is still pretty high.  Is there any way to decrease the backlight below minimum? I don't mind having to type in the terminal to do that, as I won't need to do it often (just at night etc.) Turning vector grid into individual shapefiles using QGIS? I am using QGIS and I created a vector grid on a crop field in order to cut it into plots. I want to save each grid cell into individual polygon shapefiles automatically.  Here is an example of a vector grid I would like to split into 117 shapefiles:    Eventually, I did it manually with the selection tool and "Save as" but it is really time-consuming when there are more than 100 plots to save.    Is there any way to do it faster and more automatically?  Each plot as an attribute named "Plot" that can discriminate against them (basically being id + 1). It's the attribute used here to label them. round in PHP shows scientific notation instead of full number I'm trying to do an echo of a variable containing 1400000.  so there is written: echo round(1400000); this gives 1,4E+6 instead of the full number. Anybody an idea on how to display it fully? SQL: Get records created in time range for specific dates Roots of a functionwith condition $\int_0^\pi f(x) \sin x dx = \int_0^\pi f(x) \cos x dx =0.$ Let $f:[0,\pi] \rightarrow \Bbb R$ be a continuous function which satisfies $\int_0^\pi f(x) \sin x dx = \int_0^\pi f(x) \cos x dx =0.$ Show that $f$ has at least two roots. Why did I receive a message saying I have been granted a privilege, yet I don't have enough reputation? The site shown a message saying I have been granted a privilege, but the reputation required for that privilege is higher than the one I actually have. What happened? Easiest way to add a text to the beginning of another text file in Command Line (Windows) What is the easiest way to add a text to the beginning of another text file in Command Line (Windows)? Ghost Schedulable Classes Blocking Deployment Why are mirrorless cameras much slower than DSLRs? This is a follow-up to a .  I've been comparing cycle times (or shot to shot times in single shot mode) of mirrorless cameras with interchangeable lenses with traditional DSLRs and all of them, even the highest end ones (like the Olympus OM-D EM-5 or Panasonic GH3) are slower than even entry level DSLRs.  How's that possible? The electronics should be the same and they don't have the burden of a mirror going up and down between each shot. I think that there must be a technical reason for that (maybe some cpu time is going to feed the live-view before the image is encoded?), because from a commercial point of view it does not make sense.  I've seen the cycle times under the performance tab in the reviews pages of .  The average CSC has cycle times around 0.7~1.2s, the flagship ones around 0.5s. The average DSLR has cycle times around 0.4s and the flagships around 0.25s. After trying to delete apache and tomcat, and now trying to reinstall apache 2, I am missing the init.d/apache2 file to start/stop my server.  I am not sure if the new install actualy worked, and my apt-get purge apache2 didn't remove everything in the first place!  How can I get the init.d/apache2 file to test if server starts / is installed properly (I had removed files and directories manually)?