Golden ratio
The golden ratio, otherwise known as the Divine Proportion or Phi, is a mathematical ratio with special properties and aesthetic significance. An enormous number of things in the universe are engineered around the ratio, ranging from the human body to the ark of the covenant to snail shells to the orbits of the planets. Some argue that the prevalence of the Golden Ratio is positive evidence of a common design plan uniting a wide variety of phenomena which share only their creator in common.
Calculating
Phi is derived by dividing a line segment into two parts in such a way that the ratio of the smaller segment to the larger segment is the same as the ratio of the large segment to the whole.
The number is irrational, meaning it never ends or repeats in a decimal system. To the first ten decimals, it is 1.6180339887 ...
A golden rectangle is one in which the ratio of length to height is 1:phi.
The divine ratio also makes an appearance in the Fibonacci sequence. The fibonacci sequence is derived by starting with 0 and 1, and then calculating the next number in the sequence by adding the last two together. Thus the sequence is 0, 1, 1 (0+1), 2(1+1), 3(1+2), 5(2+3), 8(3+5) and so on. The ratio of a number to the previous number in the sequence approximates the golden ratio, and comes to approximate it more closely as the values increase. Thus:
8/5 = 1.6
144/89 = 1.6179775280
10946/6765 = 1.6180339985
Examples
Because Phi is irrational, it is impossible for anything to measure at "precisely" the golden ratio. However, a large number of things approximate the golden ratio to a startling degree.
Architecture
The divine ratio and golden rectangles appear throughout ancient architecture and art. It was believed to be the most aesthetically pleasing and harmonious means of design. Statistical analysis seems to indicate that "people involuntarily give preference to proportions that approximate to the Golden Section." The Oxford Companion to Art, Ed. Harold Osbome, First Edition, Oxford University Press, Oxford, 1978, p.489.
- Egyptian pyramids were designed with reference to the golden ratio. Slant height / distance from center to perimeter = Phi;
- Greek Parthenon designed and constructed out of golden rectangles;
- Modern credit cards are golden rectangles;
- The painting, The Last Supper, is based on the golden ratio;
- The Notre Dame cathedral in Paris is based on the golden ratio;
In Genesis 6:15, God commanded Noah to build an ark saying, "And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits." The end of the ark is thus in a ratio of 5:3. Both are fibonacci numbers, thereby approximating phi at 1.667, so close as to be indistinguishable to the eye.
In Exodus 25:10, God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying, "Have them make a chest of acacia wood- two and a half cubits long, a cubit and a half wide, and a cubit and a half high." 2.5/1.5 or 5/3 (a fibonacci relationship) = 1.667, again approximating Phi so closely as to be indistinguishable to the eye.
Biology
Humans
- The human head forms a golden rectangle;.
- The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin.
- Whole body height / head to fingertips = Phi;
- Top of head to fingertips / head to navel and elbows = Phi;
- Top of head to navel and elbows / head to pectorals and inside top of arms = Phi;
- Top of head to navel and elbows / width of shoulders = Phi;
- Top of head to navel and elbows / length of forearm = Phi;
- Top of head to navel and elbows / length of shinbone = Phi;
- Top of head to pectorals / top of head to base of skull = Phi;
- Top of head to pectorals / width of abdomen = Phi;
- Length of Forearm / length of hand = Phi;
DNA
Each cycle of the DNA molecule measures 34 angstoms long by 21 angstroms wide. 34 and 21 are fibonacci numbers, as noted above. 34/21 is 1.619, approximating phi. Jean-claude Perez suggests there is a strong link between DNA and golden ratio in 1991, then again in 1997 in his book l'ADN décrypté. In this work, he shows that relative proportions of nucleotides within coding DNA sequences like genes or RNA strings are governed by specific Fibonacci and Lucas numbers sets. This discovery was validated particularly on all known HIV and SIV (Simian Immunodeficiency Virus) retroviruses whole genomes with Professor Luc Montagnier (the discoverer of HIV virus) which called the discovery a "DNA supracode" .
DNA supracode is revealed by computing sets called "resonances" within any DNA sequence: specific nucleotides clusters like FFF (Fibonacci Fibonacci Fibonacci), LLL (Lucas Lucas Lucas), FFL (Fibonacci Fibonacci Lucas) or LFF (Lucas Fibonacci Fibonacci). An example of elementary FFF resonance: 144 contiguous TCAG bases contain exactly 55 bases T and 89 bases A or C or G. This kind of screening is processed along the DNA sequence, for all possible Fibonacci/Lucas combinations, and for all possible values (example here 144 89 and 55 are 3 consecutive Fibonacci numbers). Then there appear lots of "resonances". For example, in HIV whole genome, long of about 9000 bases, there are more than 50000 significant Fibonacci/Lucas resonances. The longer resonances (several hundred resonances) are overlapping about 2/3 of the whole HIV genome (6765 bases which is a Fibonacci number).
Then, to explore both aesthetics and Ethics dimensions of this discovery, Perez published in 1994 an audio CD entitled "the first music of genes" - SACEM GEN0694 - (a subset of supracode for the oncogene KIRAS involved in cancers)...
And also in 1995 sone thinkings related to Ethics of a discovery .
In 2008 Jean-claude Perez is publishing proofs on evidence of Golden ratio based rules at all levels of Life information: bioatoms, DNA, RNA amino acids or whole genomes
Particularly he will publish a central book entitled " CODEX BIOGENESIS: les 13 CODES de l'ADN " (spring 2009) .
Human Genome
The book CODEX BIOGENESIS show that the whole Human Genome is controled by two BINARY CODES ATTRACTORS which provide a kind of self-organized bistable binary code like in computers.[1]
With the central following difference - the binary code within computers was invented artificially by humans and yet the binary code of Life has either “emerged” spontaneously perhaps by self-organization or was the intentional act of divine creation.
The ratio between both bistable states is exactly equal to “2” (the space between two consecutives octaves in Music...)
- The Top state is exactly matching with a GOLDEN RATIO...
- The Bottom state is also exactly related to Golden Ratio...
- “Top” level = = 1 / Phi
- “Bottom” level = 1 / 2 Phi
- Top / Bottom = 2
Where Phi is the "Golden Ratio"
In 2009 new proofs were provided on the human Fractal Genomephysical and logical structure.
Other life
- The bodies of dolphins are defined by the golden ratio
- The bodies of ants are defined by the golden ratio
- Snail shells and many seashells are golden spirals, that is, a spiral formed by making successively smaller golden rectangles.
- In plants, petals, leaves, sections, and seeds, pinecones, pineapples and sunflowers all exhibit fibonacci numbers;
- Fruit seeds form in golden spirals.
Astronomy
- Golden ratio in the planets: The orbital periods, mean distances, and orbital velocities of the planets in the solar system are all related by phi to a statistical significance of over 99%.
- The rings of Saturn form two golden sections, divided by the Cassini division.
