# Seven Brothers

Following up on Contours, A Mathematical Coloring Book, here's another contour plot for coloring:

The PDF version is here. The copyright is Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International.

Like the other contour plots in the book, this plot was created using Sage. Here's the Sage notebook code, in case you want to play with the plot.

```
a = exp(2*pi/3*I)
f(z) = sin(z^7 + a)
f = fast_callable(f, domain=CDF, vars='z')
def ff(x, y):
return f(CDF(x, y)).real(), f(CDF(x, y)).imag()
def iterate(func, n):
def g(x, y):
for i in range(n):
x, y = func(x, y)
return abs(CDF(x,y))
return g
G = Graphics()
for j in range(1, 6):
G += contour_plot(iterate(ff, j), (-1.8, 1.8), (-1.8, 1.8),
contours=[0.2, 0.5, 1], fill=False)
G.show(frame=True, axes=False, aspect_ratio=1)
```

# Three Logicians

Taken from Spiked Math.

# Contours: A Mathematical Coloring Book

Here is a mathematical coloring book I recently made. It contains black and white pictures generated by mathematical formulas which you color in for fun. Best printed on size A4 paper or bigger. Enjoy and share!

# Asymptotics of Coefficients of Multivariate Generating Functions

Last week i improved the design and functionality of `amgf.py`, the (open-source) Sage module i wrote to compute asymptotics of coefficients of multivariate generating functions.
If you'd like to try out the module, goto my R&D page to download it or the corresponding Sage patch which is awaiting review.
Let me know if you find any bugs or have any constructive criticism.
Thanks.

# Leinartas Partial Fraction Decompositions

I wrote some notes on Leinartas multivariate partial fraction decompositions and Sage code to compute them. If that sounds useful to you, check out the notes and code on my R&D page. Extra points if you review the Sage patch :-)

# Top 5 Reasons Why Math Is Hard

Mathematics, the science of patterns, is a beautiful and fascinating subject, but it ain't easy.

- The field is vast and the chains of dependency long
- Everything has to be so "correct"
- Accompanying fame, fortune, and fast cars distracting
- Objects of study exist in mysterious, separate universe inaccessible by physical means
- Hole in left parietal lobe (power drill)
- Can't count

**Why no comments?**
I used to do public comments but found that moderating and maintaining them took too much time in front of the computer, time better spent playing outdoors.
So these days I only do private comments, that is, you can email me comments regarding a post by clicking the 'Comment' link at the bottom the post.