Fibonacci Numbers - Golden Angle

Fibonacci Phyllotaxis
   
 

In spiral phyllotaxis, the number of visible spirals, called parastichies, are most often two successive elements of the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...
where each number is the sum of the previous two. When this occurs, the angle between successive leaves or botanical element is close to the Golden Angle - about 137.5o, related to the golden mean.

The Aonium on the right exhibits 3 spirals winding in one direction, 2 in the other. The angle between leaves 2 and 3 and the angle between leaves 5 and 6 are both very close to 137.5o.

 

 

 

 

It was estimated that, among plants displaying spiral or multijugate phyllotaxis, about 92% of them have Fibonacci phyllotaxis.

   
           
 
Fibonacci Numbers vs. Golden Angle
       
 

Golden angle <-> Golden Mean, Golden Mean is a limit of quotients of Fibonacci numbers.

To find out more about the Fibonacci numbers and the Golden Mean, visit Ron Knott's website