Pine Trees and The Fibonacci sequence

Ponderosa Pine Needle Cluster Mount Lemmon, Arizona 2020

Pine Cone of Ponderosa Pine Mount Lemmon, AZ 2020

Fibonacci Spiral https://commons.wikimedia.org/wiki/File:Fibonacci_spiral.svg

     Fibonacci, an Italian Mathematician, was not the first person to discover the number patterns in Nature, but he was most likely the first to publish the information and have his documentation accepted (Just putting this out here).  What was documented were patterns in Nature, in the growth patterns of animal populations, or even in the number of petals of a flower to the Pine needles in a cluster.  
     In documenting these numbers over a period of time, these numbers repeatedly manifested in the Natural world to where Fibonacci expressed this in a sequence. This sequence, the Fibonacci Sequence, is the sum of the prior two numbers, beginning with one and zero.  Pine trees, especially, are wonderful examples of further supporting the sequence.  The number of clusters of Pine needles in various Pinus species also produce a number that is included in the Fibonacci number sequence. The sequence and examples of needles clusters are depicted below: 

Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ... *

·     Ponderosa Pine (Pinus ponderosa var. scopulorum) has a needle    
      cluster of 3. 
·     Piñon or, also known as Pinyon Pine (Pinus edulis), has needle clusters of  2 in a bunch.
·     Limber Pine (Pinus flexilis) has a needle cluster of 5.
·     Southwestern White Pine (Pinus strobiformis) has a needle
      cluster of 5. *

      Charles Bonnet, is another person who spent many times out in Nature to observe.  If you have ever identified a plant by the leaf arrangement, then you have Charles Bonnet to thank.  In working to identify an unfamiliar plant, look at the leaf arrangement as one of the characteristics. Leaf patterns can be opposite, or alternating, along the stem, for example. He also studied the seed patterns on Pine cones and spiral patterns of Pine cones. Further observations in the seed patterns were also made.  
     What was observed, was that the seed patterns were made up of opposite spinning spirals.  While counting the number of parallel spirals in each direction produced consecutive numbers along the Fibonacci series.  The ratio of clockwise to counterclockwise spirals is an approximation of Phi, the Divine Proportion, or Golden Ratio. The spiral, in the diagram above, comes from the arrangements of squares of the numbers in the Fibonacci Sequence.
     What is fascinating is that our plants and trees on the mountain and in the desert grow this way for their own survival and wellbeing. Each new part and new growth will keep within the Fibonacci sequence and keep with the expression of Phi, the Golden Ratio. It is a pattern that is part of health, their wellbeing. Before you venture out into the Forests, think about wandering.  Make observations and find more stories that Pinus spp. want to share about how you and they live in the patterns of Mathematics in Nature. 

Many Blessings, 

Christina Grossman, MA, CA
www.sacredreminders.com 
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References: 

​Hemenway, Priya. (2005). Divine Proportion: Phi in Art, Nature, and Science.( pg. 137). 1st edition. Sterling Publishers.

Rose, F. (2012). Mountain Trees of Southern Arizona: A Field Guide. (pgs. 22-25). Tucson, AZ: Arizona-Sonora Desert Museum Press.

http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html
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https://commons.wikimedia.org/wiki/File:Fibonacci_spiral.svg