Category: Plant Ally Cards

Pine Trees and The Fibonacci sequence

3/12/2021

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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

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

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PALO VERDE TREES, FROM ELDER TO THE NEW GENERATION: IN YOUR OWN TIME.

7/17/2020

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During a special season in the desert, the trees take their turns in creating blossoms for all the pollinators. One of those trees is the Palo Verde Tree. One may think that the blooms occur all at once and then the period is over; however, I have observed that clusters of the Palo Verdes take turns.

There is this lovely communication of Palo Verdes throughout the area that are first in bloom and display these electric honey yellow blossoms. It is dazzling and beautiful with such a contrast against the green bark of the tree. It is their time to lure the pollinators in this spring celebration!

This year, there is a subtleness to their order of blooming that may replicate an almost forgotten order of family hierarchy. The older trees are first to bloom before the newer generation get their turn. The fuller, stronger, more mature trees are able to present themselves to the pollinators and have their moment. However, the mature trees are the not the only ones to get their time to shine. The younger generation is then transferred this power to be able to stand out amongst the desert trees as well. It is such a beautiful dance of transition that allows all ages of the Palo Verdes to have their bloom. What a wonderful gesture to offer to the pollinators to get both blossoms of maturity and new generation to provide diversity.

So how could we use this way of taking turns in our own lifespan? I feel that when we are younger adults, we want to peek at our success in life early on. I have felt that there is this race to be highly successful at such a young age. We might also envy the more matured adults in their success and how they flourish. It is through this hierarchy that we often miss out on, that we can all have our blossoming moment in our own time. There is so much experience, work, and time that goes into a peek moment that we often strive for. This also happens in seasons of each chapter of our lifespan. To wait a little longer for my time to bloom, I look at the ones before me and sit in awe of their “electric yellow honey” shining light that took so many seasons to get here.

Celebrate in someone else’s shining moment, observe how many dry and rain seasons they lived through, and know that your shining moment will come in your own time too.

Many Blessings,

Christina Grossman, M.A, C.A.
Founder of Sacred Reminders, LLC

All Content and Photos on www.sacredreminders.com are
Property of Sacred Reminders, LLC and Christina Grossman
Copyright 2016-2020 All Rights Reserved

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Mathematically Botanical

Pine Trees and The Fibonacci sequence

PALO VERDE TREES, FROM ELDER TO THE NEW GENERATION: IN YOUR OWN TIME.

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