I have a world map divided into zones and need to compute the area for each polygon. I tried using Vector > Geometry Tools > Export/Add geometry columns and successfully get the area and perimeter but I don't know the units of this measurement.     I assumed this was in square meters because the Layer CRS is WGS84 and I have 'Units for area measurement' in Project > Project Properties set to square meters but it seemed off by couple orders of magnitude. If I assumed these measurements were in square kilometers the sum of all the areas is still off by about 20% from the earths surface area.
How do I calculate areas of an area shapefile in square meters (m²) or in acres (ha)? I didn't find that functionality in the Vector Tools.
Why do Lambertian Reflectors Privilege the Observer? Fibonacci Sequence and series limits 1) Let $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$.   How do you prove that  $$\sum_{n=2}^\infty \frac1{F_{n-1} F_{n+1}} = 1$$   $$\sum_{n=2}^\infty \frac{F_n}{F_{n-1} F_{n+1}} = 1$$   Do you even use the formula $n(n+1)/2$?   I tried using $F_{n-1} = F_n - F_{n-2}$ and $F_{n+1} = F_n + F_{n-1}$ and then trying to figure out how to substitute those, but I've been going around in circles. How would you solve this? What tips can you give me to solve this? Is there any website that teaches this? I tried searching google and youtube but none were helpful.   2) Let $s_x = \tan(2/x)$. Where does this become nonincreasing? While using monotonic limits to establish there is a limit.   I was guessing you need to use upperbound and lowerbound but doesn't it go to infinity? rsync and symbolic links I want to backup my home directory to an external drive nightly using a cron job to execute rsync.  I am unsure of the exact behavior of rsync's symbolic link flags.   rsync's -a flag includes the -l flag (i.e. "copy symlinks as symlinks").  Does this just mean it will copy the link or that it will follow the link and copy everything in the link-to directory?  I want to avoid that because I have links to directories full of media files that would involve copying hundreds of gigabytes I don't need to back up. Fearing (but not certain) that rsync -a would copy all those media files I instead added the --no-links flag.  This does not seem to be behavior I want.  It just ignores copying any link which is problematic because I do have links I want copied (e.g. links to common header files from different project directories). Assuming #1 above (without the --no-links flag) is what I really want and it just copies the link without copying the linked-to files, will the links break when they are backed up?  For example I may rsync source directory /home/me/projects/misc to /media/extdrive/backup/home/me/projects/misc.  In this case I assume rsync is not smart enough nor does it try to correct the contents of symlinks for the relative directory changes.  Is this correct?  This is okay, it doesn't matter if the links are broken in the backup directories so long as they would be fixed and working if such time comes when they need to be restored. MacBook Air: What taking up all my hard drive space I am trying to pass a reference to a two-dimensional array to a function in C++. I know the size of both dimensions at compile time. Here is what I have right now:  const int board_width = 80; const int board_height = 80; void do_something(int[board_width][board_height]&amp; array);  //function prototype   But this doesn't work. I get this error from g++:  error: expected ‘,’ or ‘...’ before ‘*’ token   What does this error mean, and how can I fix it? Fourier series identity "reflect" vs "reflection on" or "reflection of" The bride's elegant dress reflected her good taste. The bride's elegant dress is a reflection on her good taste. The bride's elegant dress is a reflection of her good taste.  Would you tell me if they mean the same thing? If they would mean the same thing, what about the following question--link--? or I mean how could we distinguish such a distinction between these functions? Similarly, what about these:  A student's grades reflected her teacher A student's grades are a reflection on her teacher A student's grade are a reflection of her teacher  When, where or in which situation don't they mean the same? How can we distinguish such a distinction? Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$ How to replace one char with another in all filenames of the current directories? What is the best filesystem to use cross-platform (Linux, Windows, OS X) which supports disk sizes of at least 2TB and file sizes >4GB?  I'm planning to use it on a USB drive on different computers.  Are there any filesystems that can be used on all the named OSes without installing additional drivers? Conjugacy classes in $A_n$. Suppose $n$ is a non negative integer $\geq 4$ and $\sigma\in S_n$ a permutation. Conjugacy classes in $S_n$ are completley determined by the cycle structure of $\sigma$. If we let the alternating group $A_n$.act on $S_n$ by conjugation, the orbits coincide with the conjugacy classes in $S_n$ except for those (even) permutations whose cycle structure is composed of even cycles (which corresponds to cycles of uneven length) of distinct order (fixed points are treated as cycles of length $1$.) See   For instance a $3$-cycle in $A_4$ has cycle structure $[3,1]$ which fits the bill, and a $5$-cycle in $A_5$ or $A_6$ works too, since the cycle structure is $[5]$ and $[5,1]$ respectively. On the other hand, a $3$-cycle in $A_5$ will does not satisfy the criteria as it has cycle structure $[3,1,1]$ with two fixed points.  In this case, the conjugacy class of $\sigma$ inside $S_n$ splits in $2$ orbits of the conjugation action of $A_n$, and if $\tau$ is any odd permutation, for instance $(12)$, then we have $$\mathrm{Conj}_{S_n}(\sigma)=\mathcal{O}(\sigma)\coprod\mathcal{O}(\tau\sigma\tau^{-1})$$  My question is How can we differentiate between the two orbits? Does it have geometric meaning?    I can see that this information can be useful when looking at representations of the alternating groups, since there are as many irreducible representations as conjugacy classes. As for some geometric interpretation, I ask because there is one for the three cycles in $A_4$. If $S_4$ is understood as the group of symmetries of a regular tetrahedron, then $A_4$ is the subgroup of direct symmetries, and a $3$-cycle corresponds to a rotation of angle $\frac{2\pi}{3}$ or $\frac{4\pi}{3}$ with axis passing through one of the vertices. Conjugacy classes inside $A_n$ preserve the angle, and that's how we can tell them apart. In this case the computations are so simple we don't really need this picture, but I think it is a nice way to understand the fact $3$-cycles in are not all conjugate inside $A_4$... Best way to run scheduled tasks Today we have built a console application for running the scheduled tasks for our ASP.NET website. But I think this approach is a bit error prone and difficult to maintain. How do you execute your scheduled task (in an windows/IIS/ASP.NET environment)  Update:   Examples of tasks:   Sending email from an email-queue in the database Removing outdated objects from the database Retrieving stats from Google AdWords and fill a table in the database. How can I "normalize" the scale of what seems to be either an infinitely large or infinitely small object I'm having issues with an obj file I've imported into Blender. At first I thought the import was broken in some way because the import would go smoothly, but there was no model to be seen. Eventually I figured out that I could snap my view to the object by pressing . on the numpad and it was in fact there, just extremely small or large (I can't tell). I've tried scaling, but the sizes are so extreme that it doesn't seem to be working. Also due to the extreme nature of the object I can only see certain parts of it at a time depending on the angle in which im viewing it at it starts to de-render the parts not directly in front of the camera. What bike+equipment for a long daily urban commute? In the (distant) past I commuted 6 km (more than half an hour) each way, on a cheap bike with big knobbly tyres.  Soon I'll have a new commute: 18 km each way, daily. That's much further than I've done in the past, and I don't want it to take 2 hours each way; but  suggests that it's feasible:      Most people who reside 10 to 20 kilometres away will also find it quite easy to cycle to work, although the distance in the high end of this range will become a little more demanding.   If I can do it in 80 minutes or even less each way, that would be ideal. I'm 49 years old, 6 foot tall, and weigh 170lb, and I want to commute by bike because otherwise I'd be getting no exercise in my week at all.  I've never bought or ridden anything but a cheap bike.  What equipment should I buy then, to commute 11 miles each way through a city (Toronto) on  flat, paved roads, shared with cars:   Wheels? Tyres? Clipless pedals and shoes? Gears? Handlebars (e.g. flat or dropped)? Frame (size, shape, material)? Mud-guard/fender? I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. Are there rules for disassembling a slain creature, especially dragon? Started new job. Rollover previous employer 401k to new 401k, IRA or Roth IRA? I recently started a new job and have a 401k from my previous employer that I don't know what to do with.  Should I roll it into my new employer's 401k, a traditional IRA or a Roth IRA? Negative pressure Sum of (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on) Is spacetime absolute? As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is truly at rest (absolute space). Hence the concept is physically meaningless, and the positions of (and distances between) physical objects, events, etc. are relative to the frame in which one is observing them from. Advancing on to Special Relativity, by postulating that the speed of light (in vacuum) is constant in all frames of reference, we are forced to conclude that time is relative also (as if it weren't then different observers would observe a different speed of light (in vacuum)). This leads to the result that the concepts of space and time are no longer completely separate and independent of one another and instead intertwined (as an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame). Hence they should be considered as should be considered as a single entity, called spacetime.  Sorry for the waffling so far, just want to check that my understanding is correct up to this point?!  My main question is, given that space and time are (individually) relative quantities, is spacetime itself relative, or can it be considered absolute (as after all, it is the mathematical space of all possible events and exists independently of the physical events that occur within it)?