4.46.1 Top new questions this week

4.46.1.1 The fastest thing since sliced cubes?

https://mathematica.stackexchange.com/questions/160527/the-fastest-thing-since-sliced-cubes

 
I've fallen down a rabbit hole recently, and need a reality check. 
 
Suppose you have an arbitrary unit vector, $u \in \mathbf{R}^3$, and you cut up the unit cube into slices orthogonal to $u$ with  ...
 

- asked by aardvark2012 (18 votes), answered by ybeltukov (7 votes)

4.46.1.2 Mathematica does not respect linearity of integral

https://mathematica.stackexchange.com/questions/160655/mathematica-does-not-respect-linearity-of-integral

 
I have the following issue, trying to evaluate an integral. Mathematica tells me 
 
Integrate[x^2 (1 + x^2)^(1/2) + y + z, {x, y, z}  Sphere[{0, 0, 0}, 1]] 
 
(* 1/2  (3 Sqrt[2] - Log[2 (2 + Sqrt[2])])  ...
 

- asked by Simone Melchiorre Chiarello (14 votes), answered by Itai Seggev (8 votes)

4.46.1.3 How to obtain the cell-adjacency graph of a mesh?

https://mathematica.stackexchange.com/questions/160443/how-to-obtain-the-cell-adjacency-graph-of-a-mesh

 
Given an arbitrary mesh region, how can I efficiently obtain the graph describing the adjacency structure of mesh cells? 
 
For example, given the following mesh, 
 
SeedRandom[123] 
pts = RandomReal[1,  ...
 

- asked by Szabolcs (10 votes), answered by Henrik Schumacher (11 votes)

4.46.1.4 Can a symbol have both OwnValues and DownValues?

https://mathematica.stackexchange.com/questions/160740/can-a-symbol-have-both-ownvalues-and-downvalues

 
Mathematica Version 11.2 desktop / Windows 10 Pro 64-bit 
 
I am trying to understand if a symbol can have both OwnValues and DownValues. 
 
Is this acceptable or not acceptable? 
 
As an experiment, I  ...
 

- asked by John (10 votes), answered by m_goldberg (11 votes)

4.46.1.5 Differences between DSolve and NDSolve

https://mathematica.stackexchange.com/questions/160560/differences-between-dsolve-and-ndsolve

 
I have a question about the difference in the solution between DSolve and NDSolve. 
 
I want to solve the Friedmann equation of 
 
\begin{align} 
3\left(\frac{\dot{a}^2}{a^2}+\frac{k}{a^2}\right)=8\pi  ...
 

- asked by user85503 (10 votes), answered by Michael E2 (10 votes)

4.46.1.6 How to check if a vector is an eigenvector of a matrix using mathematica?

https://mathematica.stackexchange.com/questions/160801/how-to-check-if-a-vector-is-an-eigenvector-of-a-matrix-using-mathematica

 
Here is a vector 
 
$$\begin{pmatrix}i\\7i\\-2\end{pmatrix}$$ 
 
Here is a matrix 
 
$$\begin{pmatrix}2& i&0\\-i&1&1\\0 &1&0\end{pmatrix}$$ 
 
Is there a simple way to determine  ...
 

- asked by Conor Cosnett (8 votes), answered by Michael E2 (5 votes)

4.46.1.7 How do I read values from photocells connected to analog pins of Arduino Uno?

https://mathematica.stackexchange.com/questions/160761/how-do-i-read-values-from-photocells-connected-to-analog-pins-of-arduino-uno

 
Generally, I need to connect my Arduino Uno to Mathematica and read 3 analog values from A0, A1, A2 in real-time. 
 
As I understand, I have 2 ways of connecting Arduino to Mathematica: 
 
First: I have a  ...
 

- asked by Aleksandr Berezutskii (8 votes), answered by Suba Thomas (2 votes)