Fibonacci Numbers Identity ${F_n}^2 + {F_{n+1}}^2 = F_{2n+1}$
Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
Is there any difference between "color" and "colour"? What is the difference between color and colour? I'm trying to write a blog post which includes a code segment inside a &lt;pre&gt; tag. The code segment includes a generic type and uses &lt;&gt; to define that type. This is what the segment looks like:  &lt;pre&gt;     PrimeCalc calc = new PrimeCalc();     Func&lt;int, int&gt; del = calc.GetNextPrime; &lt;/pre&gt;   The resulting HTML removes the &lt;&gt; and ends up like this:  PrimeCalc calc = new PrimeCalc(); Func del = calc.GetNextPrime;   How do I escape the &lt;&gt; so they show up in the HTML? Getting javax.crypto.IllegalBlockSizeException: Input length must be multiple of 16 when decrypting with padded cipher? EDIT: Summary  I think I've found the best definition of what I want thanks to the discussion with @M. Tibbits:  When I open or refresh the SO, I get a notification of new activities that are of interest to me. Today these are (hard-coded): answers to my questions and comments addressed to me. I want a bit more control over it, that's all.     Yes, I've read  and , but I think I add new (good :) ) reasons for re-asking it:  The first question was answered before this so handy "inbox" notification feature was implemented. So now using favorites for "watching" a question is wrong, IMHO, for 2 reasons:   it splits essentially the same functionality (of getting notified when there is an activity you are interested in) between 2 very different user interfaces it's cumbersome - I need to: 1) add question to favorites; 2) click on my profile dropdown; 3) click on the "favorites" line; 4) see all my favorites with recent activity; 5) select the one I watch; 6) repeat this process occasionally to get updates; and 7) possibly remove the question from favorites at the end. All this as opposed to this little red button when there are news.   Favorites are different in nature that watching. I add a question to Favorites when I find the answers useful to me in my work, so I may want to have it handy in the future. By watching an interesting question I will be able to decide whether I want it in faviorites, after I see the answers.  EDIT: I see that I was not clear enough.  I want to add a question to Favorites when:   it has some good answers the question and answers are relevant in my work I want to keep them handy as my long-term (persistent) knowledge base   I want to watch a question for short while (matter of days/weeks) when:   it is interesting / relevant I want to follow it to see what are the answers. Then I can decide whether I want it in my favorites   As you see, the main differentiators are good answers and long/short term. For short-term, automatic notification is better.  Bottom line, all I ask is "watch this question" checkbox (which may expire after say a week if there is a need to free resources) Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. How do I calculate the instantaneous acceleration, rotational acceleration, and trajectory of this object, assuming it starts from rest? Declaring variables inside or outside of a loop How to preserve non-ASCII characters in ogr2ogr import? I define a shell keybinding in my ~/.bashrc like so:  bind -x '"\e\C-w":"/usr/bin/reset"'   This does make Ctrl-Alt-w launch the reset executable. However, it leaves the terminal in a state that resembles the one you get into by pressing Ctrl-v. So, for example, if immediately after resetting in this way I press Ctrl-p, instead of invoking the action of that shortcut (repeat previous command) I get ^P printed.  Any idea what's causing this problem and how to fix it?  EDIT: I am attaching a Python program that reproduces the messed-up terminal state I am trying to fix with the reset. I encounter this condition very often while debugging multi-threaded applications:  import pdb, thread, time  def interrupt():     time.sleep(2)     pdb.set_trace()  thread.start_new_thread(interrupt, ()) raw_input('? ')   To reproduce the messed-up state, just run the code above, and press Enter when you see the debugger invoked (it will print a bunch of text, ending with pdb.set_trace(), about two seconds after you run the program and the initial prompt appears). Placing items before \documentclass When looking in books or at sample code, I always see \documentclass appearing first. Is that absolutely necessary?  I have created some test code which seems to compile fine:  \def\SetClass{article} \documentclass{\SetClass} \begin{document}     This is some text. \end{document}   Is there any problem with placing other items, such as \input, \usepackage, or such details before the \documentclass? If I upload my brain into a computer is it still me? I think the answer is yes but I know a lot of people disagree. So, I would like to ask these people when exactly does it stop being me.  Let's say I want to upload my brain into a computer using the following procedure:  I have each of my neurons replaced by electronic neurons. By electronic neurons I mean chips with the necessary hardware and software to perform the exact same function that the neuron being replaced was performing. This means that given the same inputs that the biological neuron was given it would produce the same outputs. Then I connect that electronic neuron to all the neurons that former biological neuron was connected to.   At the end of this process is it still me? If not when did it stop being me? When one neuron was replaced? When 1,000 were replaced? When 1,000,000 were replaced?  (assuming it is still me)  Then, I divide these electronic neurons into groups and for each group I perform the following:   Write software to simulate the group of electrical neurons in my computer such that given the same inputs that go into the group of electronic neurons in my brain, it will produce the same outputs. Replace each group of neurons with another chip that communicates with my computer. Each of the chips will communicate to the corresponding software module in order to determine how to transform its inputs into the necessary outputs. Connect all of the inputs and outputs of the group of electronic neurons to that new chip.   At the end of this process is it still me? If not when did it stop being me? When one group was replaced? When 1,000 were replaced? When 1,000,000 were replaced?  (assuming it is still me) Now, what I have is a bunch of these new chips in my head, connected to each other and for each of these chips I have a small neural network software module in my computer. So, now for each pair of chip/software module I do this:   Transfer all connections going into and out of the chip into the computer version (i.e. connect the software module to the other software modules that represent the other chips that this chip is connected to) Disconnect the chip from the other chips and remove it   At the end of this process is it still me? If not when did it stop being me? When one of the new chips was replaced? When 1,000 were replaced? When 1,000,000 were replaced?  If it is still me then I have successfully moved my brain into a computer without ceasing being myself.  So, again the question is if at the end it is not me anymore when exactly does it stop being me and why does it stop being me?  EDIT: This question assumes that our universe and everything in it (including ourselves) follows the (testable) laws of physics. As it stands it also assumes that neuroscience is mostly right, although the question could also be considered without that requirement if instead of neural simulations we were to implement physics simulation of the brain. Of course this is a lot less practical. However, if your view is that our minds have a supernatural component then the question does not make any sense.  It was also pointed out that this is related to the Ship of Theseus, i.e. is something still the same if all its parts have been changed. With regards to that I think it is useful to consider that most of the cells in our body (not including brain cells) are regularly replaced anyway and some people even get entire organs replaced. Yet, we don't say that they stopped being themselves. Note, however, that if you are assuming a supernatural component of the mind that this explanation is not really adequate or relevant. Edges on an even number of Hamilton cycles Is using 15 amp components on a 20 amp breaker against code? Copy a file back to local system with ssh If I'm logged in to a system via SSH, is there a way to copy a file back to my local system without firing up another terminal or screen session and doing scp or something similar or without doing SSH from the remote system back to the local system? Why does sudo change the PATH? Seeking podcasts related to geospatial technologies? An improved \rowstyle that takes the cell contents as an argument It is possible to format the column entries of a tabular in an argument-style fashion using the lrbox environment to   store the column cell in a box (say) \mybox; and supply \mybox as an argument to some other macro.   Here is a short example illustrating this fact*:  \documentclass{article} \usepackage{array}% http://ctan.org/pkg/array \begin{document} \newsavebox{\mybox} \begin{tabular}{c&gt;{\begin{lrbox}{\mybox}}c&lt;{\end{lrbox}\fbox{\usebox{\mybox}}}c}   One &amp; Two &amp; Three \\ \hline   1 &amp; 2 &amp; 3 \\   4 &amp; 5 &amp; 6 \\   7 &amp; 8 &amp; 9 \\ \hline \end{tabular} \end{document}     The above example uses the  to achieve this column-specific formatting. More specifically, each cell in the column is supplied as an argument to \fbox. Does there exist an equivalent automation that would yield    \documentclass{article} \begin{document} \begin{tabular}{ccc}   One &amp; Two &amp; Three \\ \hline   1 &amp; 2 &amp; 3 \\   \fbox{4} &amp; \fbox{5} &amp; \fbox{6} \\   7 &amp; 8 &amp; 9 \\ \hline \end{tabular} \end{document}   without having to specify \fbox for each entry in the row?  As a start, I know that the  provides \rowfont[&lt;alignment&gt;]{&lt;font specification&gt;}. However, this only applies macros &lt;font specification&gt; to each cell in a row and these macros can't take the cell contents as an argument. Moreover, you need to use the tabu environment in order to use this. So that's a little restricting. Also, trying to decipher the  macros for colouring a tabular or array row is just confusing.  The UK TeX FAQ entry on  modifies the row entries via column specifications and therefore requires the addition of "subtle" identifiers like  \begin{tabular}{|$l|^l|^l|}   to initiate $ and propagate ^ whatever row style is defined. Is there a way around this or at least a cleaner alternative that doesn't use columns to format entries in a row? In particular, a solution should provide an lrbox-style flexibility, since the contents of the cell in the to-be-styled row could be anything, even a paragraph (say).  * There are other alternatives, as indicated by the post . Query Activity for ORDER BY xxx DESC LIMIT Convert a comma delimited list of numbers to a hyphenated list or range I'm having a problem with author display for a statute - the author is 'City and County of San Francisco' but the output (using the apalike.bst style file provided by Elsevier) gives the author as 'City and San Francisco', missing the 'County' in the authorname.  Any suggestions? text processing rows to columns for a block