# The beauty of Mayavi

Four charges with different magnitude plotted in 3D using Mayavi

In one of my earlier posts about Mayavi, I wrote about how you could visualize 2D field line plots using the flow function. At the end of that post I added that Mayavi is actually best at 3D plotting, and to follow up on that I’ll show you some of these plots with a few example Python scripts you might try out on your own.

### Now, Enter 3D!

The way you do your plots in Mayavi depends on what you want to express. Most likely, you would prefer to show some simple plots giving just the necessary amount of information to tell you how the electric field behaves around your charges. A simple example of this is shown below:

# Sweet first proof

Carl Friedrich Gauss (1777 – 1855) by G. Biermann (1824-1908)

Earlier today, enjoying a warm cup of coffee with a friend of mine,we got into a discussion about some math and ended up contemplating on how to prove the sum formula for the n first natural numbers.

The proof is rumored to first have been done by Gauss when he was only a child.

Let $S_n = 1 + 2 + 3 + . . . + (n-2) + (n-1) + n$

just rewriting the terms backwards we get

$S_n = n + (n-1) + (n-2) + \ldots + 3 + 2 +1$

now adding these two expressions for the sum we obtain

$2 S_n = (n+1) + (n+1) + (n+1) + \ldots+ (n+1) + (n+1) + (n+1)$

and since we had n terms in the original sum we now have $n \cdot (n+1)$‘s, so

$2 S_n = (n+1) + (n+1) + (n+1) + \ldots+ (n+1) + (n+1) + (n+1) = n(n+1)$

so..

$S_n = \frac{ n(n+1) }{2}$

Neat. On a computer this would severely reduce the number of operations that would have to be done to compute such a sum. Imagine having to sum up the first million natural numbers and let’s suppose the computer requires one operation for adding, multiplying, dividing and so forth. Then implementing this formula would reduce the numbers of operations from $10^6$ to 3.