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Sunday, November 17, 2013

Geometric cell division

Take a square and add a similar square to one of its sides and remove the shared edge. What remains is a rectangle.

Take an octagon and add a similar octagon to one of its sides and remove the shared edge. What remains is the following polygon.

 Take an n-gon and add a similar n-gon to one of its sides and remove the shared edge. At infinity the n-gons will divide into two circles. Unfortunately my computer is too slow to effectively record this in a video.
n=12

n=32

n=64

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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.)