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                    When Fibonacci was asked why he studied these numbers and their ratios he replied: "Someday these numbers will unlock the secrets of nature and will explain why a drone bee does not have a father." It is evident by this statement that Fibonacci was aware that Phi and its associated Fibonacci numbers are found expressed in the shapes and proportions of life forms such as: humans, animals, and plants.

           Is the divine number's (1.618) appearance in nature some great mystery, or is it simply a function of practicality?  The fact that nature must grow in the most efficient manner to survive may explain why a sunflower head is shaped in a spiral but does it explain why we have 2 hands, 3 sections per finger, 5 digits per hand, and 8 fingers?
 
 

      "The law of Golden Proportion reveals itself in quantitative division of the human body in accordance with the Fibonacci numbers. The number of the bones of the trunk, limbs, and the skull can be taken by way of example here. There are three osteal systems in the trunk skeleton: vertebral column, its costal department, and sternum. Sternum includes three bones (manubrium, body, and xiphoid process). Vertebral column comprises of 33 (34) vertebrae with 12-13 pairs of ribs branching off them.

    Cranium consists of eight bones. Either side of upper and lower jaws contains eight alveoli and roots of eight teeth respectively. 

     Skeleton of the upper limb consists of 3 parts (shoulder, forearm, and bones of hand). Hand contains 8 wrist bones, 5 metacarpal bones and bones of 5 fingers. Each finger except for the thumb has 3 phalanges. In this way, morphogenesis of the hand including two neighboring terms of the Fibonacci series, in particular 8 bones of the wrist and 5 bones of the metacarpus, approaches the GS 1.618, because 8/5 = 1.6."
 
 

     When we look at the way Fibonacci numbers appear in nature we see a pattern of growth evolving. If we look at plants and consider why the leaves appear at certain turns of the plant, why the stems branch off at a certain sections, or why seed pods are distributed a certain way, we should be able to discuss and figure out why.
 
 

" Phylotaxis is the study of the ordered position of leaves on a stem. ( Phyllos-leaf taxis order) (filo pastry-- thin leaves of pastry) With particular reference to their repetition in the same alignment,
the Fibonacci sequence has been observed in phylotaxis and extensively studied in three different spiral arrangements ."

       Two remarkable things about the placement of leaves on stems are the fact that it is irrelevant of the species, and there are a few common angles of rotation. The most common angle of rotation seems to be ~137.5 degrees. The leaves further up the plant are placed above gaps below the plant so it can receive the maximum exposure to sunlight. The golden ratio in some form appears in the placement of leaves as viewed from overhead, in the number of turns between leaves, and in the ratio of the degrees of placement.

       The spirals found in certain flowers are so obvious they do not need to be pointed out, but in others you may need some guidance to see it.

         Whatever your decision, divine number or practicality, does it support the number of petals on a flower being a Fibonacci number?

       This could be a coincidence, does it seem like people just looking to find a connection? There are many more connections to be made in our natural surroundings.  In fact there are so many that coincidence gets ruled out.  I will end this with some more pictures and you can see if you can spot the Fibonacci numbers, Golden Ratio, or spiral involved.