10.30.2 Greatest hits from previous weeks

10.30.2.1 Solving $L=\frac 3  2  \sqrt 4 \pi ^2 A^2+W^2 -\frac \sqrt 5 W \sqrt 4 \pi ^2 A^2+W^2 +6 \pi ^2 A^2+3 W^2   \sqrt 2  +\frac 3 W  2 $ for $W$
10.30.2.2 Finding Limits in several variables
10.30.2.3 Drawing a square root spiral
10.30.2.4 How do I get the inverse of a homogeneous transformation matrix?
10.30.2.5 Is there an open source implementation of Mathematica-the-language?
10.30.2.6 How can I create an empty JSON object?
10.30.2.7 How to find the position of elements in a list satisfying criteria
10.30.2.1 Solving $L=\frac 3  2  \sqrt 4 \pi ^2 A^2+W^2 -\frac \sqrt 5 W \sqrt 4 \pi ^2 A^2+W^2 +6 \pi ^2 A^2+3 W^2   \sqrt 2  +\frac 3 W  2 $ for $W$

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=57763

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) 
 
... 
[equation-solving] [functions] [approximation]
 
asked by J.D'Almbert https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=19257 Score of 8
answered by Alexei Boulbitch https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=788 Score of 15
10.30.2.2 Finding Limits in several variables

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=21544

Is there a way to find a limit of a multivariable function, like 
 
$$\lim_{(x,y)\to (0,0)} f(x,y)$$ 
with Mathematica? 
 
When $f$ is continuous, we can use 
$$\lim_{(x,y)\to (0,0)} f(x,y)=\lim_{(x,0)\... 
[functions] [calculus-and-analysis]
 
asked by Dominic Michaelis https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5899 Score of 34
answered by whuber https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=91 Score of 44
10.30.2.3 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 matrix42 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 Score of 26
answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 Score of 25
10.30.2.4 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 7
answered by march https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=29734 Score of 15
10.30.2.5 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 Score of 131
answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 Score of 95
10.30.2.6 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
10.30.2.7 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 76
answered by J. M.'s missing motivation https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 Score of 80