I am trying to build a flow chart using TikZ. I would like the horizontal and vertical spacing to be different. Thus, I am using node distance=2.5cm and 1cm. However, the second distance (1cm) is ignored and the 2.5 cm are used for the horizontal and vertical node distances.   In addition I tried to vary the second value, but still all nodes stay 2.5cm apart.  MWE:  \documentclass[]{article} \usepackage{tikz} \usetikzlibrary{decorations.pathreplacing,shapes,arrows,positioning} \usetikzlibrary{calc}  \usepackage[]{xcolor} \usetikzlibrary{positioning} \begin{document}  \definecolor{tmp}{RGB}{173, 198, 16} \tikzstyle{block} = [rectangle, draw, fill=tmp!80,      text width=5em, text centered,  minimum height=4em] \begin{figure} \small \begin{tikzpicture}[node distance=2.5cm and 1cm]     \node [block] (A) {A};     \node [block,right of=A] (B) {B};     \node [block,right of=B] (C) {C};     \node [block,right of=C] (D) {D};     \node [block,right of=D] (E) {E};     \node [block,below of=E] (F) {F};     \node [block,left of=F] (G) {G};     \node [block,left of=G] (H) {H};     \node [block,below of=A] (I) {I};     \node [block,below of=I] (J) {J};     \node [block,right of=J] (K) {K};     \node [block,below of=H] (L) {L};     \node [block,below of=G] (M) {M};  \end{tikzpicture} \end{figure} \end{document}   I searched the internet and I believe that I am using the node distance=2.5cm and 1cm correctly. But why doesn't it work?
In the PGF/TikZ manual, sometimes I see the option right of=somenode instead of right=of somenode. They look very similar, but the effects are different.  The distance between nodes positioned with the latter option is boundary-to-boundary, as stated in the manual. However, with the first option, it seems that the distance is shorter. I couldn't find any explanation of the first option in the manual.  My question is: what is the difference between the two options? Is there any explanation in the manual that I missed?
Fantasy novel: magic school, talking rabbit, character bites off another character's fingers The plotline as a whole is completely lost to me, but it was a big inspiration to my preteen self at the time and has shaped my creative development up to now. I'll list some of the big points that I can recall from it, if anyone has the vaguest idea what book I am referring to I would be so appreciative for any guess! I just want to reread it.   Main character is a delinquent of sorts, goes to a magic school. I don't remember there being any pictures in this book. There is a threesome between the main character and his two friends I believe it is a talking rabbit that says something along the lines of "My dear child, you are incensed", followed by one of the characters saying something like "Damn right I am!" A character that had been mentioned earlier but never made an appearance (he was banned for doing bad magic I think) shows up to fight and he bites off another character's fingers. 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However, in the case of illuminance, there's only actual perception if your eye happens to be the surface in question.  I can basically grasp this, but then I come across charts saying things like "family living room: 50 lux". Wait, hold on! Does that really mean that the typical lights in a house are that bright, or is it just confused and wrong, or am I confused and wrong?  If you're not taking pictures of light sources directly, why would an incident light meter reading ever be useful in photography? Reflected light recorded on film or by a sensor is usually what makes a photograph. So, if I have an incident light meter, how does that reading relate meaningfully to my camera settings?  Since incident light meters are sold and used, this implies that there must be some useful conversion. But this is where my brain explodes. Google tells me that 1 lumen equals 1 candela, so therefore 1 lumen/m² (i.e. 1 lux) must equal 1 candela/m2 (i.e. 1 nit). But clearly something is missing from this. There's something called a "steradian". Cones are involved. I'd never heard of this before; how does it fit in? I can see how it might be determined when calculating the usefulness of LED home lighting, but for a photo, I'm at a loss.  Some part of my (exploded, from the last paragraph) brain is trying to relate this to the difference between flash metering with TTL and with an incident meter. But how can the incident meter work without knowing the reflectance properties of the objects in the scene? Is this what the "C" in the  is all about? Is it just an average-this-probably-will-work value, or is there more to it than that? And if it is just an average, what knowledge is necessary for compensating for off-averages scenes? (As with the , where the photographer simply judges if the scene should be rendered brighter or darker than the average given by the meter.)  So yeah, so much confusion. In short:   What's the difference? 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For a given inner product space $V$, I would like to prove the inequality $$\|\mathbf{x}+\mathbf{y}\|^2 + \|\mathbf{x}-\mathbf{y}\|^2 = 2(\|\mathbf{x}\|^2 + \|\mathbf{y}\|^2).$$  We see that $$\|\mathbf{x}+\mathbf{y}\|^2 + \|\mathbf{x}-\mathbf{y}\|^2 = \langle\mathbf{x}+\mathbf{y},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{x}-\mathbf{y},\mathbf{x}-\mathbf{y}\rangle,$$  which by linearity $$=\langle\mathbf{x},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{y},\mathbf{x}+\mathbf{y}\rangle + \langle\mathbf{x},\mathbf{x}-\mathbf{y}\rangle - \langle\mathbf{y},\mathbf{x}-\mathbf{y}\rangle.$$  I've been trying to figure out how to go about this proof using linearity in the second argument of an inner product, but my textbook does not say that linearity necessarily holds in the second component. If it does, how would I go about the rest of this proof? If not, should I be potentially using some aspect of conjugate symmetry to prove this statement? 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