## A Suspicious Series

30/12/2014

Does the series

$\displaystyle \sum_{k=1}^\infty \frac{\sin k}{k}$

converge?

At first, you may be reminded of the harmonic series that diverges, because of the divisor $k$ following the same progression, and may conclude that this suspicious series diverges because its terms do not go to zero fast enough. But we need to investigate how the $\sin k$ part behaves.

## Fibonacci rabbits as a rewrite system

23/12/2014

In my discrete mathematics class, I often use the Fibonacci rabbits example, here to show how to resolve a recurrence, there a variant where some rabbits go away, here again for rewrite systems.

What are rewrite systems? Not unlike context-free grammars, they provide rules generate “words” in a “language”. Turns out the Fibonacci rabbit population problem is super-easy to model as a rewrite system.

## Trébuchet!

16/12/2014

Lately, a side research project asked me to devise a mechanical prototype, something I haven’t done in quite awhile. But to the difference that it asked for gears, motors, and all that. Turns out that LEGO is a good way to prototype these things.

Taking a break, I accidentally a trébuchet.

## Lissajous Curves.

09/12/2014

Many of this blog’s entries seem … random and unconnected. This is another one, despite it being quite connected to some research I’m presently conducting. This week, we discuss Lissajous curves.

We’ll see the formulas, and how to select “nice” parameters.

## Stirling’s series

02/12/2014

Last week, we had a look at how g++ handles tail-recursion. Turns out it does a great job. One of the example used for testing the compiler was the factorial function, $n!$.

We haven’t pointed it out, but the factorial function in last week’s example computed the factorial modulo the machine-size (unsigned) integer. But what if we want to have the best possible estimation?