How does Tex layout engine work
How does TeX actually work?
Seeking QGIS tutorials and web resources? This morning, I had eggs for breakfast, and I was looking at the pieces of broken shells and thought "What is the surface area of this egg?" The problem is that I have no real idea about how to find the surface area.    I have learned formulas for circles, and I know the equation for an ellipse; however, I don't know how to apply that.   The only idea I can think of is to put an egg on a sheet of paper and trace it, and then measure the outline drawn, and then try to find an equation for that ellipse and rotate that about the $x$-axis.  Now, my problem is how I can find the equation of the ellipse from the graph, and will my tracing method really be the edge of the egg?  Also, can I use the ? Will I have to use some techniques to solve the integral that are not covered in the ?  There has to be a better method for finding the surface area. Please, help me understand how to find the surface area of an egg; i.e., how to use my mathematical knowledge for something other than passing exams. Check out the below program.   try {     for (String data : Files.readAllLines(Paths.get("D:/sample.txt"))){         String[] de = data.split(";");         System.out.println("Length = " + de.length);     } } catch (IOException e) {     e.printStackTrace(); }   Sample.txt:   1;2;3;4 A;B;; a;b;c;   Output:   Length = 4 Length = 2 Length = 3   Why second and third output is giving 2 and 3 instead of 4. In sample.txt file, condition  for 2nd and 3rd line is should give newline(\n or enter) immediately after giving delimiter for the third field. Can anyone help me how to get length as 4 for 2nd and 3rd line without changing the condition of the sample.txt file and how to print the values of de[2] (throws  ArrayIndexOutOfBoundsException)? Is "Five dollars is all I have" correct? I want to emphasize that I only have 5 dollars, so can I use the sentence:     Five dollars is all I have.   Or must it be:      Five dollars are all I have.   Please give the explanation as well. "wait more than" vs. "wait FOR more than" If you make him wait (for) more than ten minutes, he'll just walk away.  I found both instances on Google Books:  and . So I'm a bid confused. Has Marvel commented on the extra Infinity Gauntlet? Add Item to Finder Sidebar I have read that watchdog timer pushes microprocessor/controller into reset state whenever it experiences any software anomaly like executing in infinite loop. and after some time a very senior prof told us that after reset the processor resumes operation from the next instruction to the erroneous one.  when watchdog timer resets the processor, from where does the processor start its next execution?  I just wanted to know what is correct or if some other concept is employed? Can you make a non-polar electrolytic capacitor out of two regular electrolytic capacitors? How do you disable an application specific hotkey, for example, "Command-P"? In many applications, Command-P is used to print.  My fingers are accustomed to emacs settings and reflexively press Command-P not for printing but for browsing history. It's annoying to see the print pop-up window every time when I press Command-P. I don't need a shortcut to print. How do you block a shortcut globally? If we look at light as a collection of little particles, we can say that dimmer light has its photons more spread out.  But if we look at light as a wave, then there no gaps unless specifically placed there on purpose.  So how can one interpret the formation of gaps between the photons? What are the major differences between ANSI C and K&R C? How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$? This question came from the prelim exam I took last month. I have a proof that seems a bit unwieldy to me (posted as an answer), so I'm opening it up to ask if there are other ways of showing this.     Let $x$ be any positive real number, and define a sequence $\{a_n\}$ by   $$ a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} $$   where $[x]$ is the largest integer less than or equal to $x$. Prove that $\displaystyle{\lim_{n \to \infty} a_n = x/2}$. Subgroups of finitely generated groups are not necessarily finitely generated I was wondering this today, and my algebra professor didn't know the answer.      Are subgroups of finitely generated groups also finitely generated?    I suppose it is necessarily true for finitely generated abelian groups, but is it true in general?  And if not, is there a simple example of a finitely generated group with a non-finitely generated subgroup?  NOTE:  This question has been merged with another question, asked by an undergraduate.  For an example not involving free groups, please see Andreas Caranti's answer, which was the accepted answer on the merged question. Velocity Maxwell-Boltzmann distribution for dummies I have a volume with $N$ molecules; I need to assign to each particle a velocity vector: $$|\mathbf{v}_{i}|=[v_{x}, v_{y}, v_{z}]^{T}$$ for the $i$-th molecule; the velocities must follow the Maxwell-Boltzmann distribution; here is the question: I know the definition of the M.B. distribution, how do I extract the velocities that I have to assign to each molecule? Basically what I want to know is how to calculate $$v_{x}=?$$ $$v_{y}=?$$ $$v_{z}=?$$ for each molecule. I'm having a hard time finding the solution of the following equation:  $$0 = x\cos(x)+2$$  This is part of showing that $f(x):= x^2e^{\sin(x)}$ has 3 extremas in $[-\frac{\pi}{2},\frac{\pi}{2}]$. ibus Avro in Ubuntu 14.04 LTS I used the instructions given  to install ibus Avro in my ubuntu 14.04 LTS (64 bit) but ibus avro was not installed. Can anyone help me to solve this case? After giving the commands in terminal nothing happens. In Random forest algorithm, Breiman (author) constructs similarity matrix as follows:   Send all learning examples down each tree in the forest If two examples land in the same leaf increment corresponding element in similarity matrix by 1 Normalize the matrix with number of trees   He says:     The proximities between cases n and k form a matrix {prox(n,k)}. From their definition, it is easy to show that this matrix is symmetric, positive definite and bounded above by 1, with the diagonal elements equal to 1. It follows that the values 1-prox(n,k) are squared distances in a Euclidean space of dimension not greater than the number of cases.    In his implementation, he uses sqrt(1-prox), where prox is a similarity matrix, to convert it to distance matrix. I guess it has something to do with the "sqaured distances in a Euclidean space"-quoted above.  Can somebody shine a little light on why it follows that 1-prox are squared distances in a Euclidean space and why he uses squared root to get distance matrix? Possible Duplicate:          Let $X$ be a compact metric space and $f$ be an isometric map from $X$ to $X$. Prove $f$ is a surjective map. Adding PDF (especially GeoPDF) to ArcMap as data? I receive a lot of PDF maps (vector, image, with georeference and without) and I am having to convert them to an image file before I can add them to ArcMap and georeference.    I can't see any obvious out-of-the-box utility that would allow me to add and georeference a PDF directly without having to convert to an image file first.   Any ideas?  I would prefer to add a PDF to map directly without any prior "pdf to image" conversion