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By Raymond Greiner
*Editors' Note: This piece was previously published in La Joie.
Today I have been thinking about geometric patterns and shapes, their intention and purpose, the obvious, the less obvious, and those which are more ambiguous. I’m thinking about geometry’s vast and profusely influential melding with Earth’s functions and living forms, as patterns and shapes release intentional, visual pulsations activating myriad energizing forces, which directly affect all earthly life forms.
Geometric designs are visible throughout nature. Some display distinct, symmetrical perfection while others are called fractals which are formed by fragmentation—splitting into parts—creating reduced-size copies of their original form, a process called self-similarity which can vary in degrees of duplication, often more abstract in shape and size, some forming less accurate duplications while others are more exact. Examples of fractals in nature include clouds, river networks, fault lines, mountain ranges, snowflakes, lightening, cauliflower, broccoli, systems of blood vessels, and ocean waves. Even coastlines may be loosely considered fractals in nature. Trees and ferns and also are clear examples of fractals. Artists are inspired by fractals; the renowned abstract artist Jackson Pollack often displayed fractals in his works.
I see spider webs daily in summer. A tiny creature on its mission of survival creates these devices. A single spider will often construct five webs each day, and then eats its web after serving its purpose in order to ingest protein-creating material for its next set of webs. These webs are images of beauty, especially when the morning sun strikes them glistening with dew revealing geometric design perfection.
Honeybees are master craftsmen; their cells are prefect hexagons, constructed in micro-tolerances with each cell positioned at a 13-degree list to prevent the honey from tipping out prior to sealing it with wax. These tiny hexagons cells may vary in size. Cell dimensions are engineered to exactly accommodate the number of cells allowable within the comb’s available construction site. Cell size variation is more common in wild hives because in manufactured hives the allotted construction space is uniform. Honeybees reflect evolutionary intelligence which functions throughout nature.
Geometry is vividly displayed throughout the earth in special application, often in a direct relationship with human interaction. Some geometric forms and structures are linked to metaphysical speculation, suggesting mystery, lacking clarity regarding specifics of origin and presence. The Great Pyramids are examples, the how and why of their construction is a source of endless debate regarding intended purpose. It’s a fascination that the Egyptians constructed these large, complex geometric structures displaying distinct, knowledgeable application of geometry.
The Romans struggled with geometry, which was problematic because of the difficulties associated with application of Roman numerals to solve complex calculations and were probably incapable of constructing such large precise pyramid structures. As a result of the Romans’ inability to assimilate the principles of geometry, the science stagnated for 2000 years, from the era of the Egyptian pyramid construction.
Finally, the Greek mathematician Euclid (325-265 BCE) conquered a clear understanding of Geometry. Conjecture is that Euclid was an intense student of Egyptian history and also lived much of his adult life in Alexandria, Egypt the speculation being that his ability to absorb and understand the principles of geometry was connected to his Egyptian interests. Greece and Egypt had a long period of trade and cultural connections, which may also have contributed.
The base measurements on the Giza pyramid, the largest, are within six-inch tolerances point to point; modern buildings of lesser dimension cannot hold such tolerances. The exactness of this large, complex structure continues to perplex modern architects. It does cause wonder.
The intricate design of many of nature’s critters is another source of mystery and fascination. The common box turtle displays unique and beautiful geometric markings, extending onto its shell’s lower flange. I pause when I discover one of these turtles to examine these patterns, such perfection. The chambered nautilus also characterizes living geometry with its expanding spiral of distinct markings all along the shell’s exterior, growing larger as the inhabitant of this shell moves to the next chamber, a true wonder of the deep. And if the shell is cut in half, it’s revealed that the chambers are equally spaced in a perfect equiangular spiral.
Flowers and plants are directly connected to soil, water and sunlight, displaying distinct and uniform geometric patterns, flourishing with color that attracts pollinators’, an intense bonding of sun, earth and organisms in rhythmical, omnipresent symmetry.
Geometric wonders are captivating, unfolding with infinite varieties of shape and scale. Geometry and nature are meshed, moving forward in unison, emulating the geometric Universe. The abundance of these observations offer continuing proof that all life forms on our planet, and likely others, are wholly fused ever evolving in a vast variety of patterns and shapes, intentionally geometric.
“The goal in life is to make your heartbeat match the beat of the Universe. To match your nature with nature.” -Joseph Campbell
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