9.8.2 Greatest hits from previous weeks

9.8.2.1 What does # mean in Mathematica?
9.8.2.2 How to make an inkblot?
9.8.2.3 Why round to even integers?
9.8.2.4 Mathematica 10.0.x freezes in Initializing kernels
9.8.2.5 How do I make a 3DPlot using cylindrical coordinates?
9.8.2.6 QR Code in shopping cart handle
9.8.2.7 How to add a vertical line to a plot
9.8.2.1 What does # mean in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19035

I asked Mathematica to compute the following 
 
 Solve[c (1-x)^2-x^(1/4) == 0, x] 
 
 
and it returned this: 
x = Root[#1^8 c^4 - 8 #1^7 c^4 + 28 #1^6 c^4 - 56 #1^5 c^4 ... 
[syntax] [core-language]
 
asked by ronanymous https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5730 Score of 45
answered by Dr. belisarius https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=193 Score of 76
9.8.2.2 How to make an inkblot?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=3345

How to effectively create a polygon that looks like a realistic inkblot? So far, I could come up with this (borrowing from Ed Pegg Jr.'s Rorschach demonstration): 
 
... 
[graphics] [performance-tuning] [image-processing] [generative-art]
 
asked by István Zachar https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=89 Score of 90
answered by Sjoerd C. de Vries https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=57 Score of 54
9.8.2.3 Why round to even integers?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=2116

According to the Mathematica help: 
Round rounds numbers of the form x.5 toward the nearest even integer. 
For example: 
 
 Round[{0.5, 1.5, 2.5, 3.5, 4.5}] 
 
 
gives 
... 
[numerics] [language-design]
 
asked by wxffles https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=427 Score of 86
answered by Per Alexandersson https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=488 Score of 53
9.8.2.4 Mathematica 10.0.x freezes in Initializing kernels

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=92931

Bug caused by paclet update and fixed by paclet update. 
I updated to Windows 10 and have been running Mathematica fine on it for over a month.  For some reason, it has just stopped working. I don't ... 
[bugs] [front-end] [system] [kernel-startup] [paclets]
 
asked by mitcheljh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=6783 Score of 80
answered by ilian https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=145 Score of 100
9.8.2.5 How do I make a 3DPlot using cylindrical coordinates?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=19076

I'm trying to plot a function of the form $z(r,\theta)$ where $r \in [0, R]$ for a finite R, $\theta \in [0,2\pi[$, and z is the third coordinate, a function of the first two. I couldn't find anything ... 
[plotting]
 
asked by Learning is a mess https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5643 Score of 20
answered by whuber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=91 Score of 29
9.8.2.6 QR Code in shopping cart handle

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=26268

This week, the market people from my work wanted to put QR codes in shopping cart handles, but when they tested it, the QR code did not work. I noted that the cylindrical curvature (even small) ... 
[image-processing]
 
asked by Murta https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2266 Score of 202
answered by halirutan https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=187 Score of 197
9.8.2.7 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 Score of 79
answered by Ajasja https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=745 Score of 96