Fibonacci in Nature

by Nikhat Parveen, UGA

The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

Plants do not know about this sequence - they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.

Why do these arrangements occur? In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space.

In the seeming randomness of the natural world, we can find many instances of mathematical order involving the Fibonacci numbers themselves and the closely related "Golden" elements.

Fibonacci in Plants

 Phyllotaxis is the study of the ordered position of leaves on a stem. The leaves on this plant are staggered in a spiral pattern to permit optimum exposure to sunlight. If we apply the Golden Ratio to a circle we can see how it is that this plant exhibits Fibonacci qualities. Click on the picture to see a more detailed illustration of leaf arrangements.

 

                                                                             Fig.2

By dividing a circle into Golden proportions, where the ratio of the arc length are equal to the Golden Ratio, we find the angle of the arcs to be 137.5 degrees. In fact, this is the angle at which adjacent leaves are positioned around the stem. This phenomenon is observed in many types of plants.

Abhishek K Das, Remnant of a supernova !

5.5k upvotes by Yash Sharma, Alok Pandey, Zlatan Stajić, (more)

Golden Mean, Golden Section, Divine Proportion are all common names for what is known as the Golden Ratio which is based off the number phi  discovered by Italian Mathematician Fibonacco. Phi ()is the ratio between the number sequence  etc. where the next number in the sequence is derived by adding  numbers together. So, , and  ,  and so on. When we divide two sequential numbers i.e.  and 

the ratio between these numbers soon become very close to  .

Some believe that it is the most efficient outcome, the result of natural forces.  Whatever you believe, the pervasive appearance of φ in all we see and experience creates a sense of balance, harmony and beauty in the design of all we find in nature. It should be no surprise then that mankind would use this same proportion found in nature to achieve balance, harmony and beauty in its own creations of art, architecture, colors, design, composition, space and even music. From the partheon to Monalisa , from the Egyptian Pyramids to credit cards,  has been there, always.

Now the amazing part , famous logos with golden ratios all over the place:

1. National Geographic

2. Pepsi