Fibonacci numbers and patterns in Cactus and Succulents ... 6/7


from previous page



The Golden Ratio


The Parthenon, Stars on Flags, the great pyramids in Egypt all exhibit the Golden Ratio


Dividing two sequential fibonacci numbers gives us:

1/1 = 1 , 2/1 = 2, 3/2 = 1.5 , 5/3 = 1.6666 , 8/5 = 1.6 , 13/8 = 1.625 , 21/13 = 1.615 , 34/21 = 1.619 .....

these divisions are converging, as you go further into the sequence, onto the number

1.618 or Phi (or 0.618 phi)

1.618034 is the golden ratio, golden section, golden mean or golden number as used by Greek Architects in building the Parthenon, the Egyptians in building the Pyramids, Leonardo Da Vinci and Salvador Dali in their paintings, it is used in musical harmony, it even (apparently) manifests itself in the share market cycle and its indexes, the spiraling pattern of a falcon while descending on it's prey and the orbits of the first 5 planets of our sun.



360 degrees in a circle multiplied by 0.618 = 225.5 degrees ( 137.5 degrees left over) - the Fibonacci angle.
this is the angle between each successive leaf etc on a plant.
This angle means that leaves above do not hide leaves below so ensuring maximum sunlight to all leaves, and rain is caught by the most leaves and channeled to the soil and hence roots.
In the sunflower flowerhead above, each new seed is phi (0.618) of a turn from the last one and there are Phi (1.618) seeds per turn.
In seed heads this angle gives optimal packing - no crowding in the centre and not too sparse at the edge.


continued on next page