The question popped into my mind after reading  and the corresponding . From what I've understood (please correct me if I'm wrong), they wanted to redefine the Kilogram. So they made the roundest object on earth whose mass is exactly $1$kg. But why they went through all the trouble for making a $1$kg perfect sphere?  I mean, couldn't it be an easier-to-make shape? Or why it's shape should be perfect? From a layman's point of view, when you want to make something a perfect $1$kg and a perfect sphere simultaneously, these two perfectnesses may compensate each other. You may smoothen some surfaces to make it more round but instead you might lose some material, or vice versa.  Here are the reasons that I could think of, which did not sound totally convincing:   The object is intended to be a reference for kilogram, which is the base for all weight measurements. This kind of object is surely a special one, so it should be special in some other ways as well to make it unique. Being the roundest object serves this purpose. To illustrate some technological advancements. I mean, if they are showing their ability to make such a perfect silicon sphere, it indicates that they can handle making some ultra-sensitive devices as well, such as ultra-accurate gyros and other stuff. This would justify the expenses in the long (or even short) term. The molecular structure of silicon in its monocrystalline form is spatially symmetric. So the sphere shape is more compliant with this crystal form than other shapes. (Sorry for possibly inaccurate terms, I'm not so familiar with the details).   These reasons are not so related to physics except somehow the last one. Here are my questions:        Are there any other physics-related or technical reasons for the spherical shape of the kilogram reference?   Wouldn't it be better to put more focus on the accuracy of the weight and be less worried about its perfect shape?      P.S. Some side-notes:  I tried my best to add relevant tags, but since I am not so familiar with this site and this is my first question, some tags might be missing or irrelevant. Please feel free to edit and improve the question.  I am also having trouble understanding why the kilogram should be redefined at first place and what was wrong with the good old platinum-irridium alloy. Since this was not so relevant, I didn't mention it directly. But a really perfect answer may shed some light on this matter as well.
I can understand the choice of material, silicon 28, but why is it a sphere rather than (say) a cube? Article   I would have thought that a sphere would have been the hardest shape to machine accurately.
xticks steps using Pgfplots / dateplot TP-LINK TL-WN823N Unable to connect to network How can a computer with dynamic IP work as a webserver? How can a computer with dynamic IP work as a WebServer? System App Permissions I have an application that needs root permissions to run.  No biggie, all of my personal devices are rooted, so I am very comfortable with the process. The problem is that this application is to be used on company owned devices issued to certain employees and I don't want them to be able to uninstall the application nor do I want them having root access to the device.  I was thinking that the following process would accomplish my goals:   Root the device Install my app as a system app Launch the application and grant su rights to it Unroot the device   Since it would be a system app, and the device wouldn't be rooted, users would be prevented from removing the app.  What I am unsure of is whether or not that application would retain its root privileges once the device is unrooted?   Any feedback or insight would be greatly appreciated! itoa() is a really handy function to convert a number to a string. Linux does not seem to have itoa(), is there an equivalent function or do I have to use sprintf(str, "%d", num)? How to fix TikZ corners in 3D Am trying to draw a simple rectangle and there seems to be minor issue with two of the endpoints (f and d in the following). I tried line cap=rect as suggested by  but that did not seem to work.  The resulting image:    \documentclass{standalone} \setlength\PreviewBorder{5pt}%  \usepackage{tikz}  \newcommand*{\Width}{2.0} \newcommand*{\Height}{3.0} \newcommand*{\Depth}{1.0}  \begin{document} \begin{tikzpicture}%     \coordinate (A) at ( 0,       0,     \Depth);%     \coordinate (B) at (\Height,  0,     \Depth);%     \coordinate (C) at (\Height,  0,      0);%     \coordinate (D) at (\Height, \Width,  0);%     \coordinate (E) at ( 0,      \Width,  0);%     \coordinate (F) at ( 0,      \Width, \Depth);%     \coordinate (G) at (\Height, \Width, \Depth);%     \coordinate (H) at ( 0,       0,      0);%     %     \draw [blue, ultra thick,line cap=rect]%         (A) -- (B) -- (C) -- (D) -- (E) -- (F) -- cycle;%     \draw [blue, ultra thick,line cap=rect]%         (B) -- (G) -- (F) -- (E) -- (D) -- (G) -- cycle;%      \path (D)  [right] node {$d$};% Problem Point 1     \path (F)  [left ] node {$f$};% Problem Point 2 \end{tikzpicture}% \end{document}   This problem about  seems related, but I do not understand how to adapt that to my problem. For every vector space $V$ does there exist a linear functional $f$ ( a linear map from $V$ to $F$ the underlying field ) such that for some $ \vec v \in V$ , $f(\vec v) \ne 0$ ? If it does exist , can we prove the existence without the "axiom of choice " ? Is the existence equivalent to axiom of choice ? Looking for a (short?) story about a cryo ship looking for habitable planets Number of factors of a big number How to find the number of factors of $884466000$ without using a calculator? How to import Apple Mail archive files in Outlook 2013? I need to import Apple Mail archived files in Outlook 2013 on Windows, but every time I open the import wizard and reach the file selection step, I cannot select the archived file. It doesn't even show in the dialog box.  I don't know what the issue is. Is it the file size issue as the archive file is large (about 7 GB) or there is any other fault? Given a set $\{1,2,3,4\}$, how is the following relation $R$ antisymmetric?  $$R = \{(1, 2), (2, 3), (3, 4)\}$$  Note: Antisymmetric is the idea that if $(a,b)$ is in $R$ and $(b,a)$ is in $R$, then $a = b$. In my textbook  it says the above is antisymmetric which isn't the case as whenever $(a,b)$ is in $R$, $(b,a)$ is not. How to delete a file with a path too long to be deleted Command to run an application with Administrator privileges, but NOT AS administrator (prompt with UAC) What is the default 'backup' user for? I am setting up multiple-machine backup plan and I was hoping to use a user called 'backup' on each machine as the backup destination.   My problem is, there is already a user called 'backup' on my machine.  What is it for, and can I hijack it for my own purposes?  root@frodo:~# useradd backup useradd: user 'backup' already exists Partition a set into subsets of size $k$ Limits of dead reckoning using MEMS sensors I'm trying to track body parts relative to a person's torso. I see quite a few questions about using MEMS accelerometers and gyros for dead reckoning, and they confirm my suspicions that various factors greatly limit their usefulness for these sorts of applications, but I'm seeking clarification of these limits:   What exactly are these limits?  Other answers have addressed why these limits exist. Naturally the specifications the parts in the system in question and what is considered "acceptable error" for the system will both change the exact limits, but is there a single order of magnitude in time, or distance that I can expect dead reckoning to work? I'm well aware that over long distances (a few yards or so) the error becomes too large for most practical purposes, but what about within a few feet?  What can I do to improve these limits?  I'm currently looking at using an accelerometer and a gyro. What other sensors can I add to the system to improve the error rate? I know over longer distances a GPS can be used, but I doubt any consumer electronics grade GPS has fine enough resolution to help in my case.  Additionally, a general consensus seems to the only way to improve these limits past the point of improved sensors is to provide a reference not subject to error. Some systems solve this using cameras and markers.  What kind of reference points can a portable/wearable device provide?   I've seen the usage of radio waves to measure long distances accurately, but I can't tell if such a system could be accurate on such small scale (in terms of distance measured) using "off-the-shelf" components. I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I go about doing this using SPSS. $A$ is normal and nilpotent, show $A=0$ Given a matrix $A \in R^{n \times n}$ which is normal ($AA^H=A^HA$ where $A^H$ is hermitian of $A$) and nilpotent ($A^k=0$ for some $k$). Now we need to show that $A=0$. (This is essentially exercise 5(b) in sec. 80 on p.162 of Paul R. Halmos' Finite-Dimensional Vector Spaces.) I tried to show in the following way, we know that, $AA^H=A^HA$ pre-multiply by $A^{k-1}\implies A^kA^H=A^{k-1}A^HA$ Now, we have $0 = A^{k-1}A^HA$, since $A$ nilpotent. I am not sure how to proceed from here to show $A=0$. Can someone help me in this problem? How to set up USB for Virtualbox? general solution sum of two uniform random variables aY+bX=Z? is there a general solution to that? I have seen simple examples for Y+X=Z but I was wondering how this would be with rescaling?