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Sacred Geometry finds its roots in nature. In the ancient world, Greek and Roman philosophers theorized that Sacred Geometry was the blueprint for life. These scholars believed a god had a geometric plan to create the universe, and it formed the basis of all matter. They argued that specific geometric shapes and proportions have symbolic or spiritual meanings.

Today, scientists have found evidence that Mother Nature does use principles similar to Sacred Geometry. Living organisms and natural objects adhere to universal mathematical constants like Phi (1.618), or the Golden Mean. 

Snowflakes, flowers, and nautilus shells, and other natural constructions conform to the mathematical constant of Phi, or 1.618. Even the helical structure of deoxyribonucleic acid, or DNA, adheres to this value. In today's Phidle Clothing blog, we'll discuss how DNA conforms to Sacred Geometry principles.

 

DNA: The Essential Molecule of Life

DNA

Human beings carry a self-replicating hereditary material called deoxyribonucleic acid, or DNA. This long molecule has key information about every person's unique genome. According to the National Institutes of Health, nearly every cell in a person's body has the same DNA.

DNA was first identified in 1869. Some people mistakenly believe Cambridge University researchers James D. Watson and Francis H.C. Crick discovered the DNA molecule during the 1950s. This honor actually belongs to Swiss chemist Johannes Friedrich Miescher.

Miescher studied white blood cells and their function. These immune cells defend our bodies from invading bacteria and viruses. The researcher obtained samples from pus-covered bandages at a nearby hospital. The chemist used a salt solution to analyze their cellular components. Miescher added acid to the cell cultures. He noticed that a substance separated in the acidic solution. When Miescher added an alkaline solution to the cell samples, the substance dissolved again.

The substance's properties differed from other proteins. Miescher called it "nuclein." He believed the material came from the cell's nucleus. Miescher didn't realize that he discovered the basis of all life: DNA. The chemist published results from his experiment in 1874. The scientific community didn't appreciate his discovery until years later.

DNA resides in the nucleus of eukaryotic cells. Since cells are small, DNA is packaged tightly in the form of chromosomes.  Scientists call the DNA found in a cell's nucleus, "nuclear DNA." An organism's complete set of nuclear DNA is its genome. You can also find DNA inside mitochondria. These organelles provide energy to our bodies. Researchers call the chromosomal material, "mitochondrial DNA," or "mtDNA."

 

What is DNA Made From?

Chromatogram

Nature uses DNA's genetic information to construct, maintain, and reproduce living organisms. DNA also provides instructions about making proteins and amino acids in our bodies. Each species has a unique set of biological instructions. For example, a tiger only produces cubs, a cat always gives birth to kittens, and a human's progeny are babies. Adults pass genetic information to their offspring during the reproductive process.

German biochemist Albrecht Kossel discovered five nitrogenous bases. They are the building blocks of nucleic acids like DNA and RNA (a polymeric molecule involved in gene regulation and expression). These molecules also use chemical bases to encode genetic information. They are:

  • Adenine (A)
  • Cytosine (C)
  • Guanine (G)
  • Thymine (T)
  • Uracil (U)

Adenine, cytosine, guanine, and uracil form the structure of RNA. DNA encodes genetic information about the body's growth and processes using four chemical bases: adenine (A), guanine (G) cytosine (C), and thymine (T). Adenine only pairs with thymine; cytosine always unites with guanine. Scientists call these unions, "base pairs." Each one has a phosphate molecule and sugar molecule attached to it. Scientists call this three-part structure a "nucleotide."

The order, or sequence of bases, has instructions to produce proteins called genes. It determines what biological instructions a DNA strand produces. For example, ATCGTT gene sequence could give someone blue eyes; ATCGCT may instruct DNA to create brown eyes. In humans, gene size varies from 1,000 to one million bases. According to the National Human Genome Research Institute, genes comprise one percent of the DNA sequence. 

 

How DNA Encodes Genetic Information

DNA

DNA's attributes operate in ways similar to a language. DNA sequences use a two-step process to create proteins. First, enzymes read the instructions, or three-letter words formed by the chemical bases, on the DNA molecule. Scientists call these "words," "codons." They transfer the information to an intermediary molecule called messenger ribonucleic acid, or mRNA. This molecule directs protein synthesis.

The mRNA molecule translates the instructions into the amino acid's language. Amino acids are the building blocks of proteins. These communications tell the cell's protein makers the correct order to join amino acids to create a specific protein. There are 20 types of amino acids in the human body that can be arranged in different orders to form a variety of proteins.

 

The Discovery of DNA's Double Helix Structure

Double Helix

Researchers discovered the role DNA played in genetic inheritance around 1943. Scientists James D. Watson, Francis H.C. Crick, Rosalind Franklin, and Maurice Wilkins researched the molecule's structure. They used X-ray diffraction patterns and building models. On February 28, 1953, scientists discovered DNA has a three-dimensional, double helix shape.

DNA's chemical structure resembles a ladder. Both sides have alternating sugar and phosphate groups. The molecule's strands stretch in opposite directions. Nitrogen bases(A, C, G, and T) make up the ladder's rungs. Hydrogen bonds the pairs together. Again, A must join with T, G always connects with C. Base pairs are complementary: if A and T unite on one strand, the opposite one will contain C and G, and vice versa.

DNA's unique structure allows it to replicate itself during cell division. The molecule copies itself by unzipping down the middle to become two strands. These isolated strands serve as a template to build a new DNA double-helix structure.

Additionally, when living organisms produce proteins, DNA unzips. It allows a single strand to serve as a template for the protein. The strand translates its information to mRNA. This molecule delivers instructions to the cell's protein-making factory.

The term "double helix" entered popular culture with the publication of James Watson's book, "The Double Helix: A Personal Account of the Discovery of the Structure of DNA" in 1968.

 

DNA, Phi, and the Golden Ratio

DNA Human Body

The DNA double helix molecule conforms to the Golden Ratio. The Golden Ratio (also known as the Golden Section) is a mathematical ratio commonly found in nature. It occurs when a line is divided into two parts. The longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which equals 1.618.

The Fibonacci sequence is related to the Golden Ratio, or Phi. Its value approximately equals 1.618. Mathematicians call Phi an irrational number since it doesn't precisely equal to 1.618. This term means its digits carry on forever without repeating a pattern. The Greek symbol (Φ) symbolizes Phi.

Fibonacci Equation:

  • F0=0.
  • F1=1
  • Fn = Fn-1 + Fn-2, for n>1. (Binet's formula)

Binet's formula expresses the "nth" Fibonacci number in terms of "n" and the Golden Ratio. It implies that the ratio of two consecutive Fibonacci numbers approximately equals the Golden Ratio as "n" increases. This formula shows their ratio 1.6190476 almost coincides with the Golden Ratio (Φ) = 1.6180339.

Fibonacci Sequence:

  • (0,) 1,1,2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

The most common form of DNA is B-DNA found in cell nuclei. The double helix structure of B-DNA is right-handed with 10 to 10.5 base turns. The double helix structure contains a major and minor groove. In B-DNA, the major groove is wider than the minor one.

Many proteins bind to this structure. The major groove's proportion to the minor one is 21 angstroms to 13 angstroms. Additionally, these are two sequential numbers in the Fibonacci Sequence.

Scientists believe the cross-section of DNA forms a decagon (two pentagons rotated by 36 degrees from one another). The ratio of a pentagon is Phi to 1. Research hasn't verified this hypothesis, yet.

The mathematical sequence shows each number is the sum of the two preceding it, starting from 0. DNA's diameter is 21 angstroms wide. Its base height is 3.4. (the helix extension is 34 angstroms long). Twenty-one and 34 are consecutive numbers in the Fibonacci series. Their 1.6190476 closely approximates phi, 1.6180339.

The most common form of DNA is B-DNA found in cell nuclei. The double helix structure of B-DNA is right-handed with 10 to 10.5 base turns. The double helix structure contains a major and minor groove. In B-DNA, the major groove is wider than the minor one.

Many proteins bind to this structure. The major groove's proportion to the minor one is 21 angstroms to 13 angstroms. Additionally, these are two sequential numbers in the Fibonacci Sequence. Scientists believe the cross-section of DNA forms a decagon (two pentagons rotated by 36 degrees from one another). The ratio of a pentagon is Phi to 1. Research hasn't verified this hypothesis, yet.

 

 

The DNA Model and Geometrical Flaws

Artist Mark E. Curtis analyzed DNA's geometric construction in 1995. The illustrator produced a series of drawings and paintings based on DNA's double-helix structure. Italian artist and mathematician Paolo Uccello inspired Curtis' series. The fifteenth-century painter explored visual perspectives. Curtis believed the DNA drawings could help him depict spatial dimensions.

The artist embarked on a series of scale drawings using standard textbook dimensions that he derived from x-ray diffraction data. Curtis began to notice discrepancies in his recreations of DNA using Watson and Crick's data. It revealed their structure does not conform to geometric principles.

Nature can construct a helix from any series of polygons, but there is only one polygonal form that would fit DNA's structure. They are ten regular pentagons oriented around a decagon.  In 3D models, these pentagons become prisms with equal length.

Curtis constructed a DNA replica using the exact dimensions suggested by Watson an Crick's X-ray diffraction data. He used single pentagon prisms to illustrate the 3-D helix. The artist discovered geometric flaws in the proposed model. Watson and Crick's model didn't adhere to geometric principles.

Without compromising the essence of their structure, Curtis proposed a resolution of the geometric inconsistencies. He suggested a small change between the alignment of the purines and pyrimidines that adheres to geometric principles.

Curtis learned through his research that:

  • Geometric equations predict DNA's structural dimensions.
  • Pentagonal geometry predicts the helical dimensions and demonstrates its principle causation.
  • Pentagonal geometry provides dynamics essential to construct a uniform and stable helical structure, and why there should be ten bases contained in a single turn of DNA's helix.
  • Although sugar-phosphate columns provide stability to the helical structure of DNA, the geometry of the base-pairs are responsible for the helix formation.

  

DNA, the Golden Ratio, and the Universal Fractal Genome Code Law.

Jean-Claude Perez is a French interdisciplinary scientist that conducted bioinformatics research. Perez's bridged genomics and mathematics.

He researched the strong connection between fractals and the Fibonacci sequence (based on the Golden Ratio). The scientist demonstrated that DNA coding for genes is based on proportions related to Fibonacci numbers.

Perez presents his theories in the research article, "Codon Populations in Single-Stranded Whole Human Genome DNA are Fractal and Fine-Tuned by the Golden Ratio 1.618." The National Institutes of Health published his peer-reviewed research article.

Perez proposed a universal "Fractal Genome Code Law." He said places in the Universal Genetic Code Table governs the frequency of 64 codons within the human genome. The researcher analyzed each codon's frequency of usage within single strands of DNA sequences. He demonstrated that the entire human genome uses the Universal Genetic Code Table as a macro-structural model. Additionally, Perez said the codon's table position determined their population numbers.

Perez concluded the Universal Genetic Code Table not only maps codons to amino acids; it serves as a "global checksum matrix."

Perez discovered:

  • The entire Human Genome Structure uses the Universal Genetic Code Table as a "tuning model."
  • The codon population's six folding steps model binary divisions in the Dragon fractal paper folding curve. Mathematicians calculate Dragon fractals using recursive methods like the Lindenmayer systems. The Dragon Curve shows evidence of two attractors.
  • This code predetermines global codons proportions and populations.
  • The Universal Code Table governs the micro and macro behavior of the genome.
  • Perez found codon frequencies in the genome clustered around two fractal-like attractors linked to the golden ratio of 1.618.

 


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