The Scenario  Suppose I have a cylindrical beaker and a conical flask (which cross-sectional area is bigger at the bottom), each located on an identical digital weight scale. Both of them have the same area, $A$, at the bottom and both are weightless. I fill both of them with identical fluids so that the height of the fluid in each container is the same. Obviously, the conical flask will require less to do so. Assume equal atmospheric pressure and gravity.   The Inconsistency  According to hydrostatics, the pressure at depth $h$, independent of the container shape, is: $$P(h)=\rho gh + P_0$$  where $\rho$ is the density of the fluid and $P_0$ is the atmospheric pressure at the fluid surface. Both the cylindrical beaker and the conical flask have the same fluid height; therefore, both should have the same pressure at the bottom, regardless of their shape. Since they have the same area at the bottom, the force exerted on the weight scale should be equal ($F=PA$). Therefore, the weight scales should register the same weight for both the cylindrical beaker and the conical flask.   This is impossible, since the amount of fluid in each container is significantly different (approximately by a factor of $3$).   The answers to this  says that the additional weight of an inverted conical flask is due to the forces acting on the walls. However, I don't believe that it is possible for the water to act an upward force on the walls and thus lift the container upwards.  How does one explain this inconsistency?
Scenario description  Lets assume both containers have a capacity of 300 litres.  One is a vertical tube  as shown in pic 1  Other one is more or less a V shaped containers as shown in pic 2  Both are at ground level  Question  No doubt that whole weight of 300 litres will act on the base of the tube (pic 1). But will the weight of the whole 300 litres act on the base of the container as shown in pic 2?  I.e if you keep both the containers on a weighing scale, for sure, it will show a weight of approx. 300 kg each.  But what I'm asking is whether the weight of whole 300 litres acts on the base of container 2 (since the container's walls are slanting, as opposed to the walls of the tube in pic 1).  If the whole weight will not act on the base of the container, can you state the reasoning and also the principle, so that I can further get to know about it?  Pic 1             |         |                    |         |            |         |            |         |            |         |            |         |            |_________|   Pic 2           \              /           \            /            \          /             \________/
Could we please be a bit nicer to new users? How do I make ditto marks? In France, students are taught not to repeat the same text twice when there is little difference between a line and the one below. It's a quick way to take notes.  I reproduced this effect by tinkering:    The code is as follows:  \documentclass[aspectratio=1610]{beamer}  \usepackage[T1]{fontenc} \usepackage[french]{babel}  \usepackage{amsmath, amsfonts, amssymb} \usefonttheme[onlymath]{serif}  \begin{document} \begin{frame} Lorsque le \og \textit{carreau carré} \fg{}   mesure: \begin{itemize} \item $\rm 1\,cm$ de côté, l'unité d'aire est appelée le \og \textrm{centimètre carré} \fg{} et est noté $\rm cm^2$; \item $\rm 1\,dm$ \hspace{1mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}''\hspace{8mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{décimètre carré} \fg{} \hspace{2mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1.5mm} $\rm dm^2$; \item $\rm 1\,m$ \hspace{3mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}'' \hspace{7mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{mètre carré} \fg{}  \hspace{9mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1mm} $\rm m^2$; \item etc. \end{itemize} \end{frame} \end{document}   How can I get the same effect more simply than by tinkering like I just did? Feedback Request: New Timeline Question View There is an experimental timeline view for questions now available on meta ONLY! (Now working on SO, SF, and SU as well)  This is partially motivated by comments about how difficult it is to follow very active questions which have a lot of activity, and also the feedback on the API which was heavily dominated by "we need to know what happened in this time range" type responses.  It can only be accessed through URL hackery at the moment. To get to it, enter question URLs like so:  https://meta.stackexchange.com/posts/{id}/timeline  This is a chronological timeline of everything that happened on a question, including   initial question ask answers  revisions comments closure, deletion, reopen, undelete, etc votes   all based on when they happened in chronological order.  We are thinking about making this a fourth tab on the question, like so:  Timeline | Oldest | Newest | Votes  Please try it out and provide feedback. It is still a little rough, so we are not looking for highly detailed bug reports, just more general feedback.  Timeline view for this question: Is it better in C++ to pass by value or pass by constant reference? Is it better in C++ to pass by value or pass by constant reference?  I am wondering which is better practice.  I realize that pass by constant reference should provide for better performance in the program because you are not making a copy of the variable. How do you find all subclasses of a given class in Java? How does one go about and try to find all subclasses of a given class (or all implementors of a given interface) in Java? As of now, I have a method to do this, but I find it quite inefficient (to say the least). The method is:    Get a list of all class names that exist on the class path Load each class and test to see if it is a subclass or implementor of the desired class or interface   In Eclipse, there is a nice feature called the Type Hierarchy that manages to show this quite efficiently. How does one go about and do it programmatically? I am trying to run gedit from an SSH terminal on Windows, connected to an Amazon EC2 instance running Ubuntu 12.04 Server and I am getting this error:  Cannot open display:   How do I fix it? Change style of labels of Tikz nodes of a given style Java2D Performance Issues I'm having performance oddities with Java2D. I know of the sun.java2d.opengl VM parameter to enable 3D acceleration for 2D, but even using that has some weird issues.   Here are results of tests I ran:  Drawing a 25x18 map with 32x32 pixel tiles on a JComponent Image 1 = .bmp format, Image 2 = A .png format  Without -Dsun.java2d.opengl=true  120 FPS using .BMP image 1 13 FPS using .PNG image 2  With -Dsun.java2d.opengl=true  12 FPS using .BMP image 1 700 FPS using .PNG image 2  Without acceleration, I'm assuming some kind of transformation is taking place with every drawImage() I do in software, and is pulling down the FPS considerably in the case of .PNG. Why though, with acceleration, would the results switch (and PNG actually performs incredibly faster)?! Craziness!  .BMP Image 1 is translated to an image type of TYPE_INT_RGB. .PNG Image 2 is translated to an image type of TYPE_CUSTOM. In order to get consistent speed with and without opengl acceleration, I have to create a new BufferedImage with an image type of TYPE_INT_ARGB, and draw Image 1 or Image 2 to this new image.   Here are the results running with that:  Without -Dsun.java2d.opengl=true  120 FPS using .BMP image 1 120 FPS using .PNG image 2  With -Dsun.java2d.opengl=true  700 FPS using .BMP image 1 700 FPS using .PNG image 2  My real question is, can I assume that TYPE_INT_ARGB will be the native image type for all systems and platforms? I'm assuming this value could be different. Is there some way for me to get the native value so that I can always create new BufferedImages for maximum performance?   Thanks in advance... To prove that $(\mathbb{P(N)},d)$ is a metric space To prove that $(\mathbb{P(N)},d)$ is a metric space where $\mathbb{P(N)}$ is the power set of $\mathbb{N}$.  And $d:\mathbb{P(N)}\times \mathbb{P(N)} \mapsto\mathbb{R}$ is defined by $d(A,B)=\begin{cases} 0, &amp; \text{if A} \Delta \text{B=}\emptyset  \\ m^{-1}, &amp; \text{where m is the smallest member of} A\Delta B \end{cases} $.   Attempt: $x \in P\Delta Q=(P-Q)\cup(Q-P) \implies x\in (P-Q) \text{ or } x\in (Q-P) $. But $(P-Q)\cap(Q-P)= \emptyset \implies x \in P \text{ and} \notin Q \text{ or }x \in Q \text{ and} \notin P. \ \ \ $    (*)  To prove the triangle inequality:  Take any three sets $A,B,C \subset \mathbb{P(N)}$ such that none of them are equal to another. Now,  $\min A \Delta B  =m_1, \min B \Delta C  =m_2,  \min A \Delta C  =m_3   $. To prove $d(A,B) \leq d(A,C)+ d(B,C)$. By (*), $m_1 \in A$ or $m_1 \in B$ but not both.   Again,  $m_2 \leq m_1$  or $m_3 \leq m_1$. Either way, we are done. When $A \neq B$ and either $B =C $ or $A=C$ (not both), we have respectively $A=C$ , $B=C$ . Which satisfies the triangle inequality. When $A=B$ it is evident.   Symmetry: We know $A \Delta B =B \Delta A$. $d(A,B)= d(B,A)$  Non-negativity and $0 \iff A=B$:   $d(A,B)=0 \iff A \Delta B= \emptyset \iff A \subset B \text{ and } B \subset A \iff A=B$. By definition $d(A,B) \geq 0$  Is this okay? Please verify. MacTeX - TeX Live Utility broken after 2015 update Why isn't Harry Potter punished for using magic outside of Hogwarts in Prisoner of Azkaban? MSO Review Queue Privileges are Misleading When I visit Stack Overflow, I see the review option in the bar at the top of the screen.    However when on MSO, I don't see it. I assumed this was because I didn't have enough reputation to access the queue. I was curious what the requirement was on meta, so I moseyed on over to the privileges page. To my surprise, I saw that the privilege is listed as only requiring 500 rep and informs me I already have it:    Confused, I manually typed in meta.stackoverflow.com/review to see what would happen. The page did in fact load, but as you can see meta has no "First Posts" or "Late Answers" queue.    Seeing on that page that a minimum of 2k reputation is required to access any queues on MSO, I report the following bug:  1) On the privileges list on MSO, the 500 rep privilege of "Access first posts and late answers review queues" should not appear.  I also have the following feature request:  2) On the privileges list on MSO, it would be useful if instead there was a 2k privilege that informed you that you have access to the "Suggested Edits" and "Low Quality Posts" queues. Currently, the only way to link to a revision (clicking "link"), you just get  which shows what the post looked like at that revision:        Personally, I rarely use this and haven't ever found myself in a scenario (as far as I remember) where I would prefer the way it currently works to what I'm suggesting here.  Could we:   Add another link, or Change the current link   Such that it:   Displays the diff on a separate page (I'd prefer this, since the highlight and scroll thing doesn't always work properly - although perhaps it has something to do with loading images, so it might not apply here, or, if it doesn't, we could fix that instead), or          Highlights and scrolls to a diff, like what is done when you link to an answer () Came across this little practice exercise, and I couldn't properly convince myself of this relation:  Let $X,Y \subset \mathbb{R}^n$ and $g:X\times Y \rightarrow \mathbb{R}$. Show that $$\sup_{y \in Y} \inf_{x \in X}g(x,y) \leq \inf_{x \in X} \sup_{y \in Y} g(x,y).$$  My thinking was starting with $\inf_{x \in X}g(x,\overline{y}) \leq\sup_{y \in Y} g(\overline{x},y)$, but does that even hold for all $\overline{x} \in X$ and $\overline{y} \in Y$? Are employments in universities affiliated (or named) with a specific religion restricted to people with the same religion? I just saw an ad in mathjobs.org about an opening in a Catholic university, see . I am not christian. So I was wondering to be eligible for employment in a university or college affiliated with a specific religion, should the applicant  have the same religion, or other people from other religions (or even non-religious people) are eligible to apply as well? The plot is simply that aliens visit Earth and their interest in collecting cow pies (and just like other collectibles, special attributes make them more valuable) creates interest in humans in obtaining them to sell. Then the aliens leave and the market plummets. I do not recall the name of the story and also at the end I think some new object is of interest which maybe someone remembers. As silly as the premise sounds, if you look at what people really do collect and the amazing prices, the story kind of resonates. Digital crypto-kitties or whatever and more recent things selling for tens of millions or cryptocurrencies themselves seem not so different than cow pie collecting. Moreover, the fundamental theorem of collectibles is that to make a huge amount, paradoxically the collectible had to not only start out as more or less worthless but also something people tended to use/read and then destroy or at least throw away. Old Nat Geo magazines are worth almost nothing because everyone kept them; Action Comics #1 on the other hand, well moms could not wait to toss those when their son went away to college or got married. The stories I have in just my own family. Lost my APFS partition after using EaseUS partition manager on Bootcamp I used macOS mojave(APFS partition) and Windows10(Bootcamp). And I tried to expand Bootcamp partition with moving Windows OEM partition by EaseUS partition master in windows. After this, I can’t find APFS partition installed macOS.  I use MacBook Pro 2016.  I think “disk0s2” was APFS partition, but now it is “Windows Recovery” partition.  Do you have any ideas to solve this? (I am Japanese, so I'm sorry for my poor English)  I tried “gpt show” and “diskutil list” on macOS Recovery   Additional information  I tried dd if=/dev/disk0s2 count=1 bs=512 command in a Terminal app of macOS Utility from network boot, and the terminal says,  -bash-3.2# dd if=/dev/disk0s2 count=1 bs=512 | vis -c 1+0 records in 1+0 records out 512 bytes transferred in 0.005472 secs (93568 bytes/sec) )us??-ҵ?\^A\0\0\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^A\0\0\M^@\0\0\0\0NXSB\0\^P\0\0?\M^B?\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\^B\0\0\0\0\0\0\0"\^R???\M^_@}\M^Bvy57 ?(h?8\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^X\^A\0\0 l\0\0?\M^J\0\0\0\0\0\0\^R\r\0\0\0\0\0\0\a\0\0\0004*\0\0\^E\0\0\0\^B\0\0\0\^S*\0\0!\0\0\0\M^Qr8\0\0\0\0\0\M^U?\b\0\0\0\0\0\^A\^D\0\0\0\0\0\0\0\0\0\0d\0\0\0\^C\^D\0\0\0\0\0\0\M^T\M^N\^A\0\0\0\0\0\M^V\M^N\^A\0\0\0\0\0?0\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0-bash-3.2#   . How to change sign text color in Minecraft? I have gone through every single website and video to try to make a sign with colored text, but nothing works. Can anyone help me to get a sign to say:  Place Block(dark blue and bold text)  I really want this for a map I am making and I need help. Tags in spoilers are always visible, even if you don't put your mouse on the spoiler (on  for example). See the screenshot:      Looks a bit strange on this site too:        that needs ! What do you call a person who "shuts down" ideas?