re: Fibonnacci -
Whilst on the topic of fibonacci, some of the greatest intellects of the ages profoundly appreciated the value of the number series, Phi, and the Golden Ratio & Golden Spiral.
For example, Newton had the Golden Spiral carved on the headboard of his bed. Egyptian engineers also used the Golden ratio in the Great Pyramid by giving its faces a slope height 1.618 times half its base, so that the vertical height of the pyramid is at the same time the square root of 1.618 times half its base