8.34.2 Greatest hits from previous weeks

8.34.2.1 How to create animated snowfall?
8.34.2.2 How do I plot $x^2+y^2=1$ in 3D?
8.34.2.3 How to build a bvh (a motion capture file format) player in Mathematica?
8.34.2.4 How to express trigonometric equation in terms of of given trigonometric function?
8.34.2.5 Multivariable Taylor expansion does not work as expected
8.34.2.6 How can I create an empty JSON object?
8.34.2.7 How to find the position of elements in a list satisfying criteria
8.34.2.1 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
8.34.2.2 How do I plot $x^2+y^2=1$ in 3D?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=10710

How would I plot $x^2+y^2=1$ in 3D (it would form a cylinder)? Since there is no $z$ in the equation, I can't solve for it and use  Plot3D . Or can I just put the ... 
[plotting]
 
asked by diracdeltafunk https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2282 Score of 7
8.34.2.3 How to build a bvh (a motion capture file format) player in Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=60292

How to build a bvh player that can be used to visualize human motions in Mathematica? Any 
idea or sample code would be appreciated. 
... 
[graphics3d] [import] [animation] [visualization] [code-request]
 
asked by Putterboy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=16069 Score of 49
answered by Sjoerd C. de Vries https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=57 Score of 97
8.34.2.4 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
8.34.2.5 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 Score of 75
answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 Score of 83
8.34.2.6 How can I create an empty JSON object?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=50727

For creating non-empty object, I use following syntax 
 
 ExportString[{"key" -> "value"}, "JSON"] 
(*{"key" : "value"}*) 
 
 
But how can I create an empty object? ... 
[export] [conversion] [json-format]
 
asked by molekyla777 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=11981 Score of 10
answered by jkuczm https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=14303 Score of 11
8.34.2.7 How to find the position of elements in a list satisfying criteria

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=180

Say I have a list  x={2,4,6,8,10}  and I want to find out the positions of the elements that are greater than 7. 
 
... 
[list-manipulation]
 
asked by PeterR https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=140 Score of 72
answered by J. M.'s persistent exhaustion https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 Score of 70