8.3.2 Greatest hits from previous weeks

8.3.2.1 Are you interested in purchasing David Wagner's "Power programming with Mathematica"?
8.3.2.2 How to add a vertical line to a plot
8.3.2.3 How to calculate contour integrals with Mathematica?
8.3.2.4 Multivariable Taylor expansion does not work as expected
8.3.2.5 Drawing a square root spiral
8.3.2.6 Is there an open source implementation of Mathematica-the-language?
8.3.2.7 How to make the digits of  go around in a spiral like this?
8.3.2.1 Are you interested in purchasing David Wagner's "Power programming with Mathematica"?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=16485

I recently contacted McGraw-Hill to see if they have a mechanism in place for printing out-of-print books that are still of interest.  Specifically, I asked about "Power programming with Mathematica" ... 
[reference-request]
 
asked by Todd Allen https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=249 164 votes
answered by Todd Allen https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=249 239 votes
8.3.2.2 How to add a vertical line to a plot

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3561

In the plot below I would like to add two vertical lines at $x = \frac{\pi}{15} \pm \frac{1}{20}$. 
How can I do that? 
 
... 
[plotting]
 
asked by sjdh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=515 73 votes
answered by Ajasja https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=745 89 votes
8.3.2.3 How to calculate contour integrals with Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=34073

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand? 
[calculus-and-analysis] [complex]
 
asked by user64494 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7152 43 votes
answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 65 votes
8.3.2.4 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)... 
[calculus-and-analysis] [series-expansion]
 
asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 70 votes
answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 78 votes
8.3.2.5 Drawing a square root spiral

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=66969

Here is a start. I'm looking for a nice way to draw it. 
 
... 
[graphics] [geometry]
 
asked by matrix89 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 24 votes
answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 23 votes
8.3.2.6 Is there an open source implementation of Mathematica-the-language?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=4454

I've seen questions before such as "What is the best open-source equivalent for Mathematica?", but that specific question (and that line of inquiry in general) cares more about the computer algebra ... 
[programming] [open-source]
 
asked by sblom https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=178 125 votes
answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 88 votes
8.3.2.7 How to make the digits of  go around in a spiral like this?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=109982

Here is a start. 
 
 MapIndexed[Text[Reverse[First[RealDigits[Pi,10,252]]][[Tr@#2]],#]&, 
Table[{t Cos[t],t Sin[t]},{t,0,16Pi,0.2}]]//Graphics 
 
[graphics] [formatting] [generative-art]
 
asked by matrix89 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 57 votes
answered by Martin Ender https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2305 73 votes