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Sunday, October 28, 2007

Pascal's Triangle as a Matrix Exponential

For me, this is an amazing result. When I read about it in "Accessing Bernoulli-Numbers by Matrix-Operations, Gottfried Helms 3'2006 Version 2.3" I immediately started Mathematica and tried it myself. The picture above is the result. It's what I call some deep mathematics, although the formula for calculating the Matrix Exponential is easily understood.

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(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.)