This is a practical problem born while folding a paper.  We can bisect a paper by using only hand.      $\star$ Easy, fold it so that the two ends (of the length) coincide and press   the paper to get the bisector of the length.   Repeating the $\star$ again and again we can divide the paper into $2^n$ (where $n\in\mathbb{N}$) parts using only hand.  But how can we divide the paper into some other(I mean other than $2^n$) number of parts .And particularly,       How can we divide the paper into three parts? Using only hand and instruments like ruler, compass, protractor etc and cutting away any piece of paper is banned.   I would recommend the reader to take a paper and try it!, it's really interesting!.
This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on eye estimate where to fold. Then I turn the letter over and fold bottom to top. Most of the time ending up with three different areas. There must be a way to do this exactly, without using any tools (ruler, etc.).
I recently submitted an application to the AppExchange, only to have it not pass the security check due to "Insecure Storage of Sensitive Data Vulnerability." The problem is that my app accesses an external API, for which it has its own API Secret and API Key. These are static, and specific to the Salesforce App- they will be the same for all users, all installations, etc.  Perhaps stupidly, I stored them as private properties of the class that uses them.  private static String apiSecret = 'superS3|&lt;R37'; private static String apiKey = 'sameHerebutdifferent';   It is a Managed app, so users cannot see them. As such, I am puzzled as to 1. why this is insecure and 2. how better to store these values, given that we are apparently operating under the assumption that having them in the text of the class itself is insecure. Is there a portable version of Chrome for Ubuntu? Error installing Apache2 Server I'm looking to clarify the differences/overlaps between the three and, if the terminology isn't accurate establish the correct terminology Create a hexadecimal colour based on a string with JavaScript Meaning of "kernel" In analysis, there are at least three kinds of "" concepts:   In probability theory, there is a concept called , also called probability kernel, from one measure space $X$ to another $Y$. It is actually a family of measures on $Y$, indexed by members of $X$. It can transform a measure on $X$ to a measure on $Y$, in terms of integration.  A special case is  of probability density function in statistics, where the  is actually a probability kernel. In real/complex analysis, there is a concept called  from a product space $X \times Y$ to $\mathbb{R}$ or $\mathbb{C}$. It can transform some special function: $X \to \mathbb{R}$ or $\mathbb{C}$ to another one:$Y \to \mathbb{R}$ or $\mathbb{C}$. This is used for defining integral transformation In Hilbert space theory, there is concept called , which is a family of bounded mappings for a family of Hilbert spaces. For every two Hilbert spaces $X$ and $Y$ in the family, there are exactly two members of the kernel, one mapping from $X$ to $Y$ and the other from $Y$ to $X$.   I wonder    Are they related concepts, since they seem to share some indescribable similarity? Can they be unified?   In particular, the first two are similar to each other as the kernels induce transformations on measures and on functions in terms of integrals.  It is however not obvious to me how the third one, i.e. the Hilbert space one, is related to the second one. Are they related to the  concepts? Or even to the  concept?   I feel like some insights and references for catching the general ideas shared across as many kinds of "kernels" as possible.  Thanks and regards! QGIS apply style to shapefile Help proving the primitive roots of unity are dense in the unit circle. I'm having difficulty understanding how to prove that the primitive roots of unity are in fact dense on the unit circle. I have the following so far:  The unit circle can be written $D=\{x\in\mathbb{C}:|x|=1\}$. The set of primitive $m$-th roots of unity is $A_m=\{\zeta_k:\zeta_k^m=1,\zeta_k\text{ is primitive}\}$.  Hence, the set of all primitive roots $A$ is given by the union of $A_m$ over $m=1,2,3,\ldots$. But I can't seem to get started on how to prove that $A$ is dense in $D$. Is editing sources.list a good idea? This doubt is hitting me since 2-3 days, so I decided to test it myself. What I did is I installed Ubuntu 16.04.4 in VMWare and edited /etc/apt/sources.list and replaced xenial with bionic using:  sudo sed -i 's/xenial/bionic/g' /etc/apt/sources.list   Then I ran  sudo apt-get update &amp;&amp; sudo apt-get upgrade    I was able to upgrade to 18.04, confirmed by using lsb_release -a. However, I encountered some problems like:   apt does not have a stable CLI interface. Use with caution in scripts. unmet dependency of  python3-aptdaemon.pkcompat Release 'bionic-backports' for 'appstream' not found Broken Unity   I solved all the errors and installed gnome and gdm3.   So, I just want to know is it a good idea to edit sources.list? I know that my system might broke but is there any other specific reason not to use this.  Note: I tested this on Ubuntu 16.04 in VMWare to clear my doubts only. How can I initialise a static Map? How would you initialise a static Map in Java?  Method one: static initialiser  Method two: instance initialiser (anonymous subclass) or some other method?  What are the pros and cons of each?  Here is an example illustrating the two methods:  import java.util.HashMap; import java.util.Map;  public class Test {     private static final Map&lt;Integer, String&gt; myMap = new HashMap&lt;&gt;();     static {         myMap.put(1, "one");         myMap.put(2, "two");     }      private static final Map&lt;Integer, String&gt; myMap2 = new HashMap&lt;&gt;(){         {             put(1, "one");             put(2, "two");         }     }; } I applied for a standard visitor visa to the UK for seven days. I earn £278/month and have been working at the same organization for more than a year. I have saved up enough funds for the trip and I attached bank statements to prove it. The ECO refused my visa stating:      I note that you stated that your trip to the UK will cost you £1100, this is approximately 4 times your monthly income. I do not find it credible that you spend this amount on a trip.   I am a single woman, with no financial responsibilities and I saved up for this trip because I really wanted to visit the UK.  How do I prove to the ECO and the authorities that spending £1,100 for my trip wouldn't have caused me any financial harm neither would I have had to access UK government funds?    Another concern of mine is that if I reapply without the partial funding of my father or get sponsored by a different person, does the amount given by my father previously cause hindrance in my visa application?  Won't they still reject it on the basis of my pay being too insignificant? Converting to upper and lower case in Java What is the use of percent signs (%) at the end of lines? (Why is my macro creating extra space?) I see that the code in many packages and examples contains percent signs % at the end of (many) lines. What are they used for? Do they affect the parsing of those lines? ［I'm Done］ button is available after ［Save Edits］ even when nothing was edited in First Posts queue My question is whether $x/x$ is always equal to $1$. I am mostly intersted in real numbers and particularly wonder whether $x/x$ is defined at $x=0$.  On one hand the division should simplify to $1$, on the other hand you should not be allowed to divide by zero.   I have been trying to find whether the simplification 'goes first' or whether the division causes trouble first, but it has proven impossible for me to find usefull search terms.     Note that this question arose after reading  and its first comment. Proving an inclusion related to algebraic sets and interpreting it Is AncestryDNA match of 1,655 cM a half sibling? Shared DNA: 1,655 cM across 46 segments.   Can someone that shows this as one of my matches on AncestryDNA be a half sibling? Stop iPhone alerting me when I'm in a phone call When I'm in a phone call, I still get alerts for emails and texts. The noise will play and, if the phone is on Speaker, it will vibrate -- often leading the person I'm talking to wonder what that weird noise was.  Surely there must be a way to silence the phone while you're talking on it. It's very distracting to have beepings going off right next to your ear! Testing a UPS by unplugging it from the wall At an Not For Profit/Charity I volunteer for occasionally we were very fortunate to be provided (donated) with a brand new 3Kva APC UPS. This is total overkill for our modest server rack (four mid-range servers and a switch!) but hey, I'll take what I can get!  Pressing the TEST button on the front indicates that yes, the UPS does work. Brilliant. But it only tests it for about 15 seconds.  My question is - will I degrade the UPS by unplugging it from the wall to see how long it will last? My plan is to unplug it, and wait until the battery meter reaches its last LED before plugging it back in, so that I know about how long I will have in the event of a power outage.  Do people do this on a regular basis? I'm guessing no (Lead Acid is very different to Li-Ion batteries)... but what kind of harm would it do if this were to happen (on purpose) every 6 months? Best practices for storing UI settings? we're currently planning a larger WPF LoB application and i wonder what others think being the best practice for storing lots of UI settings e.g.   Expander States Menu orders Sizing Properties etc...   i don't like the idea of having dozens of stored values using the delivered SettingsProvider (i.e. App.config file) although it can be used to store it in an embedded database using a custom SettingsProvider. being able to use some kind of databinding is also a concern. Has anyone had the same problems?   What did you do to store lots of ui user settings?