As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Thursday, August 25, 2011

### Continued fractions (1)

Generating functions are "mathematical data structures" that can store an infinite amount of data.

For example $$\frac{1}{1-x} = \left\{ 1,1,1, \cdots \right\}$$ and $$\frac {1}{1-x-x^2} = \left\{ 1,1,2,3,5,8,13, \cdots \right\}$$ nicely represents the Fibonacci series. ( The existence of tools like the GF's made me sort of addicted on mathematics. ) If you think this is the most compact way to describe the Fibonacci series, then let mathematics surprise you. The most compact way to describe the Fibonacci series is $$\left[ <1> \right]$$ which means $$1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots }}}.$$ Objects like this are called continued fractions, more on these and why $\left[ <1> \right]$ is related to the Fibonacci series in the next post.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)