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## Wednesday, December 29, 2010

### Continued Fractions

I started studying continued fractions..., a vast subject. ( 'new land!' )

Here I calculate the Extended GCD of $9976$ and $6961$ using Blankinship's matrix method. A by-product of the calculation ( column 1 ) are the numbers for expressing $\frac{9976}{6961}$ as a finite continued fraction.
$\left( \begin{array}{cccc} - & - & 9976 & 6961 \\ - & 9976 & 1 & 0 \\ 1 & 6961 & 0 & 1 \\ 2 & 3015 & 1 & -1 \\ 3 & 931 & -2 & 3 \\ 4 & 222 & 7 & -10 \\ 5 & 43 & -30 & 43 \\ 6 & 7 & 157 & -225 \\ 7 & 1 & -972 & 1393\\ & 0 & 6961 & -9976 \\ \end{array} \right)$

$\frac{9976}{6961}=1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\frac{1}{6+\frac{1}{7}}}}}}$

## 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.)