8.15.2 Greatest hits from previous weeks

8.15.2.1 How to express trigonometric equation in terms of of given trigonometric function?
8.15.2.2 How can I draw the Olympic rings with Mathematica?
8.15.2.3 How to create animated snowfall?
8.15.2.4 Mathematica 10.0.x freezes in Initializing kernels
8.15.2.5 How do I get the inverse of a homogeneous transformation matrix?
8.15.2.6 Are you interested in purchasing David Wagner's "Power programming with Mathematica"?
8.15.2.7 Positioning axes labels
8.15.2.1 How to express trigonometric equation in terms of of given trigonometric function?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=434

How can I express a trigonometric equation / identity in terms of a given trigonometric function? 
 
using following trigonometric identities 
 
... 
[functions] [trigonometry]
 
asked by Prashant Bhate https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=99 Score of 30
answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 Score of 37
8.15.2.2 How can I draw the Olympic rings with Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=8885

How can I draw the 5 interlocking Olympic rings with Mathematica? 
(SVG version) 
Edit 
 
Hard choice, but some pretty cool answers here. I didn't have 3D answers in mind when I posted the question, but ... 
[graphics] [generative-art]
 
asked by Mike Honeychurch https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=77 Score of 46
answered by cormullion https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=61 Score of 23
8.15.2.3 How to create animated snowfall?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=16881

Well, the title is self-explanatory. What sorts of snowfall can we generate using Mathematica? There are two options I suggest to consider: 
 
1) Continuous GIF animations with smallest possible number ... 
[dynamic] [random] [animation] [generative-art]
 
asked by faleichik https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=219 Score of 41
answered by Simon Woods https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=862 Score of 54
8.15.2.4 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
8.15.2.5 How do I get the inverse of a homogeneous transformation matrix?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=106257

I want to get the inverse of this homogeneous transformation matrix: 
 
 iab = { 
{1, 0, 0, 0}, 
{0, 0, -1, 0}, 
{0, 1, 0, 3}, 
{0, 0, 0, 1} 
} 
 
 
using the ... 
[matrix] [linear-algebra] [inverse] [geometric-transform] [rotation]
 
asked by andrestoga https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=37677 Score of 5
answered by march https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=29734 Score of 13
8.15.2.6 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 Score of 164
answered by Todd Allen https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=249 Score of 239
8.15.2.7 Positioning axes labels

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=87388

I need to change the position of my axes labels such that the y-axis label is in the middle and parallel to the y-axis. I'd also like the x-axis label to be in the middle of the x-axis rather than ... 
[plotting] [graphics]
 
asked by John_dydx https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7849 Score of 15
answered by Virgil https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=27697 Score of 17