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Only the other day I saw a brief clip (no explanation of what it was - it was background to a song, I think) which showed a missile going in through the square window of a bulding - but what came out was a circular smoke ring.

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Clear examples of geometry (and Golden Mean geometry) in Nature and matter:

* Crystals, natural and cultured.
* The hexagonal geometry of snowflakes.
* Creatures exhibiting logarithmic spiral patterns: e.g. snails and various shell fish.
* Birds and flying insects, exhibiting clear Golden Mean proportions in bodies & wings.
* The way in which lightning forms branches.
* The way in which rivers branch.
* The geometric molecular and atomic patterns that all solid metals exhibit.

Another, less obvious, example of this special ratio can be found in Deoxyribonucleic Acid (DNA) - the foundation and guiding mechanism of all living biological organisms. link