Fibonacci is a recursive sequence and has an astonishing persistence in nature.  Which suggests its importance as an essential representation of how life works.  Although it is not in all things living, the reoccurrence of the pattern in nature makes people look closer.

Also know as the Golden Rule it is a simple pattern of numbers where each number is the sum of the previous two numbers.

###### Everything Starts Out Small

The spiral is common place in nature.  From flowers to weather, to shells you can find it.

###### From the Universe to the Microscope

The milky way is a spiral galaxy that gets further apart as the distance increases from the sun. DNA is a spiral of molecules measuring 34 angstroms long by 21 angstroms wide; the way a pinecone grows; seeds in the center of a sunflower; the shape of an egg are all examples of constant similar proportions.

###### Pay Attention to the Details

1,1,2,3,5,8,13,21…rings. The sequence is growing with the tree, and flowers are also hold the same pattern.

###### Who discovered the Fibonacci sequence?

The Fibonacci sequence was introduced to the western world by Leonardo Pisano who was an Italian mathematician. He wrote a book on how to do calculations, and published it in 1202. Each number is dependent on the two previous numbers, and can be seen in different spirals.

###### Other places you can spot a spiral!

Fibonacci sequencing can be seen in ocean waves and the spirals of hurricanes. Also, in the spiral of draining water. When you make a fist and your skin spirals, plants and animals. Not all spirals fit the sequencing perfectly. But it is fun to think about the possibilities.

###### Photographer’s opinions

Susan Wagner is a person that loves to take pictures of all things nature.  I asked her what she thought about finding the pattern in some of her images seen below. Susan said “the angles draw the eyes into then center of the swirl.  Photographer’s should capture images to be pleasing to the eye.”

James Troublefield, a local photographer, states, “the fact that the sequence exists is a display of mans ability to visualize math and that we have the ability to distinguish it. A reason we are at the top of the food chain.”

###### Conclusion

Fibonacci can be found throughout nature and it is a perfect example of artwork. The sequence continues to grow at the same angles with the same ratio. It is the photographers dream of exactness because the rule continues for eternity. Actually the sequence is found on people’s faces! This proves Math is a part of nature’s beauty, and is all around us….

The was a fun topic for me to research. I have been a photographer for 20 years, and finally understand why my eyes are attracted to certain things. I found that I was talking about the Fibonacci sequence to anyone that would listen. Nature is beautiful! Now I can say, so is math! I would encourage everyone to take the time and try to find a little math in nature!

###### References

https://sites.google.com/a/saintannsny.org/peerpoints-vol-3/fibonacci-numbers-in-nature

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_College_Mathematics_for_Everyday_Life_(Inigo_et_al)/10%3A_Geometric_Symmetry_and_the_Golden_Ratio/10.04%3A_Fibonacci_Numbers_and_the_Golden_Ratio

Susan Wagner and James Troublefield – local photograhers