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Amateur Naturalist: The Mathematical Symmetry Of Pine Cones

on December 2, 2017 - 7:55am
The shape of the pinecone bracts create eight spirals going outward and counter clockwise. Photo by Robert Dryja
 
The Mathematical Symmetry of Pine Cones
By ROBERT DRYJA
Amateur Naturalist
 
 
The shape of the pine cones lying on the ground below a tree provides a kind of predictability that is the complete opposite to predicting the youthfulness or maturity of a tree. A cone grows overlapping bracts that protect the developing seeds within. When the seeds mature, the bracts open. The seeds then may flutter away to germinate or become food for some animal or insect.
 
What immediately catches a person’s attention is the symmetry of the bracts. They grow in spirals around the core of the cone. Two kinds of spirals are apparent. One spiral goes clockwise while the other goes counter clockwise. Further, these spirals incorporate a mathematical pattern that is startling. A cone will have eight spirals in one direction and thirteen spirals in the other.
 
Careful observation of larger cones shows another set of twenty one spirals starting further up from the base.
 
The spirals come to an end at the top of cone. They merge together by becoming smaller and meeting at a pair of bracts at the top of the cone. Careful observation of the top shows there is a single central column. It is composed of two bracts that have not separated from one another.
 
Another set of two bracts then folds away from the column as the cone matures. A set of three bracts next surrounds the two bracts. Finally, five bracts can be identified that surround the set of three bracts. The spirals coming up from the base now can be more easily seen.
 
Students may remember learning about the Fibonacci number series in their math class:
 
A number is calculated by adding together the two immediately preceding numbers.
 
 
The spirals on the pine cone are following the Fibonacci series. This is a remarkable visual surprise. A bit more math sleuthing shows that this is the most effective series of numbers for the bracts to follow while growing. The maximum amount of sunlight then is received by a growing cone. There are no gaps among the bracts where sunlight may be lost.
 
Thirteen spirals go outward in a clockwise pattern and also are created by the bracts. Photo by Robert Dryja
 
One central column is created by two bracts remaining together, (white). Two other bracts then are folded around the central column while growing, (red). A set of three more bracts next are folded around the set of two, (green). A set of five bracts then are folded around the set of three, (pink). Photo by Robert Dryja
 
Bracts spiral to the center of the top of the pinecone. Photo by Robert Dryja
 
The folded bracts are positioned in relation to one another in a spiral without gaps to receive the most sunlight for growth. Photo by Robert Dryja

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