The Fibonacci sequence is a sequence of construction. Take a square, place it against another square (1+1), add another set based on the previous operation (+2), take another just like the last two operations that connect them (+3), ...
Nothing you don't already know, but this is just a simple construction algorithm. What is interesting is how it builds the shapes and World in such an irrational (5^(1/2)) way, yet very organized. The Fibonacci sequence approaches the Golden Ratio, it defines the Golden Radio by its limit, but it isn't the Golden Ratio because it never has an end.
Then compare to a circle. Place another equal circle next to it and a third equal circle such that it touches both of the other two. Now you have an equalateral triangle. Keep building until there is one circle in the middle and six around its perimeter. A hexagon, made up of 6 equalateral triangles. From there you have the makings of snowflakes, quartz crystals, computer chips. Somewhere in there is a bee hive and again, the golden ratio.
This is still a mystery to me. Where is the Golden Mean in bees? If you set your compass heading to some northern angle, can you sail around the globe getting farther north and closer to the magnetic pole as you spiral in and transcribe the Golden Volute?
- Will (Dragonfly)