Meaning in context - "if not where that curiosity comes from,at least how you can best satisfy it"
What does "if not" mean in the given sentence
Prove the definitions of $e$ to be equivalent How to prove that the following definitions of $e^x$ are equivalent, with as simple tools as possible and without any knowledge of $e$ or logarithms ?  $$\sum_{n=0}^{\infty} \frac{x^n}{n!}=\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n$$  Also preferably, prove that this is $a^x$ for some real number $a&gt;0$. How do I rotate an object along it's own axis (windmill) I'm trying to rotate the blades of a windmill for an animation but the windmill is already at an angle. When I keyframe it on it's own axis (after pressing control + alt + space) and rotate it the blades spin inwards during the animation before coming back at the end. I've tried locking the other axis but that keeps the blades from rotating back to the right orientation. Also, whenever I rotate the object 360 degrees it turns the 360 into a really small number (0.0001) so it plays forward hallway then backwards (with a 180 degree keyframe halfway). Any help would be appreciated!. Determinant of a $2\times 2$ block matrix I would like to know the proof for:  The determinant of the block matrix $$\begin{pmatrix} A &amp; B\\ C&amp; D\end{pmatrix}$$ equals $$(D-1) \det(A) + \det(A-BC) = (D+1) \det(A) - \det(A+BC)$$ when $A$ is a square matrix, $D$ is a scalar, $C$ is a row vector and $B$ is a column vector.  I appreciate your help. Total of attribute field of point layer per polygon layer I have a polygon shapefile of many lakes, I also have a point shapefile of locations on those lakes where fish were caught.  The point shapefile contains the attributes: Fisherman_iD, Fish_Caught, Lat, Long.  The polygon shapefile contains the attributes Lake_name, Points_per_polygon(PNTCNT)  Each point obviously has differing entries under the fish_caught field.   What I want to get is the average fish caught per lake (polygon).  So I need to have a total number of fish caught, per individual polygon, and then I can divide that by the PNTCNT file I create using the Points in a Polygon tool.  Ideas? I am relatively new to QGIS. Title page line spacing I have a simple problem but I didn't manage to find any answer for it. In my title page, I just used  \title{Name of the title}   then  \hrule height 0,1cm \leavevmode \\[0,5cm]     {\Huge{\textbf{\@title}}}\\[0,5cm] \hrule height 0,1cm \leavevmode \\[0,5cm]   to print the title of my document. But it takes more than 3 lines on the PDF file, and I have a different spacing between the 1st and 2nd line compared to the 2nd and 3rd, which is a bit frustrating.   Anyone got an idea of why ? How loud/obvious is a wizard casting a spell? Some spells have somatic and vocal components, that's well known.  How loud must a wizard talk? How obvious/wide should his gestures be?  Some spells that would be awesome would be fairly limited if you need to shout them (ex: mage hand, range 30ft). Inductive proof of the closed formula for the Fibonacci sequence Fibonacci numbers $f(n)$ are defined recursively:  $f(n) = f(n-1) +f(n-2)$ for $n &gt; 2$ and $f(1) = 1$, $f(2) = 1$. They also admit a simple closed form: $$\sqrt 5 f( n ) = \left(\dfrac{1+ \sqrt 5}{2}\right)^n- \left(\dfrac{1 - \sqrt 5}{2}\right)^n \tag1$$  How to prove (1) using induction?  Remarks One could get (1) by the general method of solving recurrences: look for solutions of the form $f(n)=r^n$, then fit them to the initial values. But there should be a more concrete proof for this specific sequence, using the principle of mathematical induction. How exactly do DLL files work? There seems to be an awful lot of them, but I don't know what they are or how they work.  So, what's the deal with them? Installing particular versions when repo has newer versions? "Show desktop" keyboard shortcut in Mac OS X I am using a MacBook Pro with Mac OS X 10.5. Is there a similar function to "show desktop" (shortcut is WIN+D) on a Mac?   It should hide all applications and show a clean desktop. Proving a relation between inradius ,circumradius and exradii in a triangle Prove that in a triangle $$r^2+r_1^2+r_2^2+r_3^2=16R^2-(a^2+b^2+c^2)$$ where the symbols have their usual meanings. I am looking for a smaller or elegant proof using trigonometry. A geometric proof would be super cool. I did prove it but it took me ages to do the calculation. Thanks. How to ask the position(?) of a president (like 10th) of a country, correctly? Difference between the i386 download and the amd64? What is the difference between standard i386 download and the amd64 download of Ubuntu 11.04? I am currently running the i386 on an amd machine, would my system work better with the amd64 download instead? (my machine was running Windows 7 64bit, but I neglected to look at that prior to installing Ubuntu). Calculating centroids of polygon using ArcPy? I am trying to calculate the centroids of a polygon and add the x- and y-coordinate to their respective fields:  arcpy.env.workspace = r"C:/..."  input_fc = "shapefiles/precincts_v.shp" arcpy.AddField_management(input_fc, "X", "DOUBLE") arcpy.AddField_management(input_fc, "Y", "DOUBLE")  arcpy.CalculateField_management(input_fc, "X", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[0]", "PYTHON")  arcpy.CalculateField_management(input_fc, "Y", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[1]", "PYTHON")    but I an invalid syntax error. Where is the mistake?  Edit: exact error message  Traceback (most recent call last):   File "C:\Users\mquentel\Dropbox\PLSS\CA voting data\Python\CONSTRUCT_merge_voting_and_census.py", line 17, in &lt;module&gt;     arcpy.CalculateField_management(input_fc, "X", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[0]", "PYTHON")   File "C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcPy\arcpy\management.py", line 3360, in CalculateField     raise e ExecuteError: ERROR 000539: SyntaxError: invalid syntax (&lt;expression&gt;, line 1) Failed to execute (CalculateField). Energia/MSP-EXP432 Issue: Analog In Pin removing voltage from Voltage Divider In the circuit below, I want to measure the voltage going to the ADC (output from the voltage divider consisting of a fixed resistor and photoresistor) using an MSP-EXP432; however, the MSP-EXP432 "Analog In" pin is lowering the output voltage (i.e. the voltage going into the ADC from the voltage divider drops when the "Analog In" pin is connected).  I set the analog pin as an input in the code shown below in Energia.  Is there any way to fix this?    const int bitsOfADC = 14; // 14-bit ADC Launchpad //int maxVal = 2^N -1;  // 2^14-1 int maxVal = 16383; float FSV = 5.0; // Supply to 0804ADC float LaunchPadResolution = FSV/maxVal; int D7 = A13; int D6 = A14; int ADCInput = A6; boolean D7_State = LOW; boolean D6_State = LOW; void setup() {   delay(1000);   Serial.begin(9600);   pinMode(D7, INPUT);   pinMode(D6, INPUT);   analogReadResolution(bitsOfADC);   pinMode(ADCInput, INPUT); } Unable to upgrade Windows 10 edition from Home to Pro I have a Lenovo laptop which upgraded from Windows 8.1 Home to Windows 10 Home.  I have a (legitimate) Windows 10 Pro key which I ran through the "Change Product Key" wizard.  After a reboot I get an error which states "We couldn't upgrade your edition" and asks me to try again or seek help from my system administrator (me!) or Microsoft.  There is nothing in the event logs except Info entries in the Setup log stating it failed to change the installed state to Pro Edition with a hex error code (I don't have access to the laptop right now, I will update later with the full log details)  Googling the hex error code led me to a Windows 7 KB Article regarding Windows Update failure due to locked files. The article stepped through using MSCONFIG to perform a clean boot which I did, but still got the error.  Any pointers on how to upgrade this laptop? Or will I have to get the sledgehammer out and do a clean install? Boy asks 'How about pie?' I am looking for the title of a 1950s science fiction movie, involving an astronomer trying to decode some extraterrestrial signal, where the juvenile (male) character asks 'how about pi?' which all the adults interpret as a foolish 'how about pie?' question. Xbox Game bar after uninstalling UWP and disabling UAC It looks like the  update  from Microsoft.  I have  and  UWPs as much as I can, along with Cortana and Edge.  Yet today I saw a weird green bar popup saying something about "Press Win + G to bring up the game bar".  I figured it would have to do with the Xbox UWP app, which I have previously uninstalled.  I presume this is UWP functionality, but I'm not sure how to find out for certain.  Can this app or program exist outside of the UWP ecosystem?  Is it a part of the Xbox app?  What method(s) are there to remove it?  Is there a prophylactic to prevent such things in the future?  I'm currently stuck in Windows Home, even though I  (not me, but gives you context).  I will be fixing that sometime soon. Why isn't Harry Potter punished for using magic outside of Hogwarts in Prisoner of Azkaban? Is it possible to get the sheetname?