I rendered a 1200x800 image, but it's just the transparent texture thing:    I used Cycles for this image. In a test in Blender Render, it worked perfectly, although the materials were made in Cycles so you obviously couldn't see them as you were supposed to.
A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [
One of is followed by plural noun/pronoun and singular helping verb What happens when you put a Portable Hole inside a Bag of Holding while on the Astral plane? What would happen if someone were to place a Portable Hole within a Bag of Holding while being within the Astral Plane? Would it be the reverse effect? \textcite macro produces "Author (year)" correctly but colours first paren with hyperref I have to find an easy ring which this ring is isomorphic with.  I can prove that $5 = (2+i)(2-i) \in (2+i)$ but this doesn't help me further.  My book says the answer is $\mathbb {Z_5} $ In Robert Dixon's Mathographics, a regular pentagon is constructed with straightedge and compass only.  It is the pentagon $ABCDE$ pictured below.   I am having trouble seeing why the central angles are all $72^\circ$, though. Can anyone provide the proof?  Also, does anyone know who this construction is due to? I haven't seen it anywhere, other than in Dixon's book; is it Dixon's result?     The result appears much more impressive without all the labels (which are slightly misplaced, please excuse this); however, I provided those so that answering would be easier. Also, it makes it easy to describe the steps in the construction:  1) Draw a circle (the red one)  with center $h$.  2) Draw the perpendicular lines $\ell_1$ and $\ell_2$ through $h$. Locate the points of intersection $f$, $B$, and $g$ with the red circle.  3) Bisect the line segment $gh$. Denote the center by $a$.  4) Draw the green circle with center $a$ and radius $ah$.  5) Draw the other green circle (as in (3) and 4)).  6) Draw the line segment through $f$ and $a$.  7) Locate the points of intersection $b$ and $c$ of the line segment with the circle constructed in step 4).  8) Draw the blue arcs (both have center at $f$ and the radii are $fb$ and $fc$).  9) Locate the points of intersection $A$, $C$, $D$, and $E$.   I actually have the solution to the first question, and will post it unless a more elegant explanation is provided (which is probably likely).  However, I find this construction particularly   beautiful, and would like to know who it is attributed to (Dixon doesn't say, explicitly). Plotting several 2d functions in a 3d graph I am trying to reproduce a similar figure to the following one. My first guess was to use pgfplots but I didn't find any example that I could use as a starting point. At the moment I am unsure if pgfplots is actually the right package or I should rely on something else e.g. TikZ.   Since I don't really know where to start, I would appreciate any piece of code that points me in the right direction.    EDIT  Here is some dummy data for the plots.  plot1   plot2   plot3   plot4 0       0       0       0 3.466   2.058   0       0 4.262   2.976   0.001   0 3.822   3.168   0.006   0.008 2.953   2.936   0.019   0.063 2.065   2.492   0.046   0.265 1.332   1.977   0.092   0.734 0.797   1.478   0.164   1.508 0.443   1.045   0.268   2.44 0.228   0.698   0.412   3.219 0.107   0.438   0.598   3.524 0.046   0.256   0.831   3.219 0.017   0.138   1.109   2.44 0.006   0.067   1.429   1.508 0.002   0.029   1.78    0.734 0       0.01    2.141   0.265 0       0.003   2.479   0.063 0       0.001   2.736   0.008 0       0       2.808   0 0       0       2.465   0 0       0       0       0 DataView.Sort - more than just asc/desc (need custom sort) is exactly what I'm looking for. I want my description environment to produce this:  Label is long   text  lab2            blalballalaa label3          possible second rule label four      hello world   Someone offered this:  \newenvironment{mydescription}[1]                                                   {\begin{list}{}%    {\renewcommand\makelabel[1]{##1:\hfill}%    \settowidth\labelwidth{\makelabel{#1}}%    \setlength\leftmargin{\labelwidth}    \addtolength\leftmargin{\labelsep}}}   {\end{list}}   Which works great (the parameter is the longest label), except I think the enumitem should be able to do this. Unfortunately, the documentation for it is extremely confusing to me. Could someone show me how to achieve the same result with enumitem? There are many times when I curse the autocorrection mechanism for changing what I typed, but overall, much of the corrections are welcome so I don't really want to disable it. I do want to have it do it's work but alert me when it makes each change so I don't have to proofread everything or focus with perfect attention to the screen to see the momentary red and/or blue underlining that alerts me to the machine override.  I would love a way to turn on an audible beep (customizable of course) so that I also get a warning each time my typing gets corrected (and only when autocorrection occurs). How to clear current “read-only” state on a USB flash drive I setup with Rufus? I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong Python, Unicode, and the Windows console When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016). Suppose I want a strong 20-bit blockcipher.  In other words, I want a function that takes a key (suppose the key is 128 bits), and implements a permutation from 20 bits to 20 bits.  The set of permutations should be close to a randomly-chosen subset of size $2^{128}$ of all $2^{20}!$ permutations on 20 bits.  I don't want you to build a new blockcipher from scratch.  Instead, assume you have a "strong" blockcipher like AES (128-bit blocksize, 128-bit keysize) and use this to build your 20-bit cipher.   Of course, your construction should be practical (i.e., you should be able to run it in both directions with reasonable amounts of time and memory). Is this valid for convergence? Does $\sum_{n=1}^{\infty} \sqrt[n]{3} - 1$ converge or diverge?   Hints please  I have that $0 \le \sqrt[n]{3}  - 1 \le 1$  Does this help? Image of Jacobson Radical is the Jacobson Radical I'm stuck on the following problem:      Let $R$ be a commutative ring with $1$, and suppose $R$ is semilocal with maximal ideals $\mathfrak m_1, ... , \mathfrak m_s$.  Let $\mathfrak a$ be an ideal of $R$. The problem is to show that under the usual surjection $\pi:R \rightarrow R/\mathfrak a$, the Jacobson radical of $R$ is sent to the Jacobson radical of $R/\mathfrak a$.   My attempt: suppose that $\mathfrak m_1, ... , \mathfrak m_t$ contain $\mathfrak a$, but $\mathfrak m_{t+1}, ... , \mathfrak m_s$ do not.  Then $Jac(R/\mathfrak a) = (\mathfrak m_1/ \mathfrak a) \cap \cdots \cap (\mathfrak m_t/ \mathfrak a)$.  Obviously $\pi Jac(R) \subseteq Jac(R/ \mathfrak a)$, and the converse inclusion is equivalent to the following claim: if $x \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_t$, then there exists a $y \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_s$ such that $x - y \in \mathfrak a$.    This should be some application of the Chinese remainder theorem, but I'm not seeing it.  All I have to go on is that there exist $m_i \in \mathfrak m_i$ ($t+1 \leq i \leq s$) with $m_i \not\in I$.  I also haven't found out a way to use the fact that $\mathfrak m_1 ,... , \mathfrak m_s$ are all the maximal ideals of $R$.  I was also thinking about looking at some explicit maps.  If we let $\Gamma$ be the composition $$\frac{(R/\mathfrak a)}{Jac(R/ \mathfrak a)} \xrightarrow{\cong} \frac{(R/\mathfrak a)}{(\mathfrak m_1/\mathfrak a)} \oplus \cdots \oplus \frac{(R/\mathfrak a)}{(\mathfrak m_t/\mathfrak a)} \xrightarrow{\cong} R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t$$ then we have a commutative diagram $$\begin{matrix} R/Jac(R) &amp;  \rightarrow &amp; \frac{(R/\mathfrak a)}{Jac(R/\mathfrak a)} \\ \downarrow &amp; &amp; \downarrow \Gamma \\ R/\mathfrak m_1 \oplus \cdots R/\mathfrak m_s &amp; \rightarrow &amp; R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t \end{matrix}$$ where the vertical arrows are isomorphisms, and the horizontal arrows are surjections. Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction? primes whose difference is a multiple of $n$ If $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set. In ZFC set theory, every element object is a set. We know or feel that if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.  My question is: Why if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set? What's a good beginner resource to learn group theory? Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$.   This is an unsolved question in my lecture notes. I can only seem to prove the converse direction for this. Would appreciate a solution for the other direction.     For converse direction:   Let the number, in lowest terms, be given by $\frac{l}{m}$ where $m = 2^ \alpha 5^\beta$, for some positive integers, $\alpha$ and $\beta$.    If $\alpha &gt; \beta$, let $k = 5^{(\alpha-\beta)}$. If $\alpha &lt; \beta$, let $k = 2^{(\beta-\alpha)}$.   Then $\frac{l}{m} = \frac{kl}{k2^\alpha5^\beta}=\frac{kl}{10^q}$ where $q = \max(\alpha,\beta)$.   Hence $\frac{l}{m}$ is a terminating decimal.