part II from “Music of the Spiral”
Sacred Geometry, The Spiral, Fibonacci & The Golden Mean
The Golden Mean, or The Golden Section is perhaps best known from the image drawn by Leonardo DaVinci called The Vitruvian Man. Drawn around 1487. It depicts a male figure with two superimposed images with arms and legs apart, within a square and a circle. It is sometimes called the “Canon of Proportions” and is based on the geometry of proportions described by Roman architect Vitruvius.
Da Vinci considered the human body as a microcosm of the functioning of the universe, so that the proportions of man, would also be found in nature. Man’s body contains exact proportions of one part of anatomy to another.
The Golden Mean, also known as the Golden Ratio, or Phi, is a ratio of two objects whose total 1.1618.
For example, in this image, the ratio of A to B is the same as B to C.
This can only happen when the larger measurement is 1.1618 times the smaller. In a series of numbers of this ratio, adding two numbers together, gives the next number as the total. This also works when multiplying two numbers together.
These are the same ratio of proportions in the human body, the pyramids in Egypt, ancient architecture, much modern architecture. It is taught in art classes, since this proportion is considered the most attractive proportions (Gustav Theodor Fechner, 1860’s; Chris McManus 1980; Eric Haseltine 2002. The Parthenon in Greece, Notre Dame in Paris, the painting of the Mona Lisa are examples of art with these).
Certain triangles are also based on this ratio, such as the Pythagorean Theorum and finding the hypotenuse in a right-angled triangle.
This type of triangle is also found in the Sri Yantra symbol, used in Hindu/Vedic meditation, and has existed for thousands of years. Its central triangles are based on the Golden Ratio.
The Sri Yantra symbol is produced by the sound vibrations of the word “AUM”.
This is the shape from saying ‘AUM’
into electronic transmitter , as demonstrated by Ajit Mookerjee.
Relationship to Fibonacci sequence and the Spiral
The mathematics of the Golden Ratio and of the Fibonacci sequence are intimately interconnected.
The Fibonacci sequence is: 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ….
Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates phi; e.g., 987/610 ≈ 1.6180327868852. The numbers known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … are of the same proportions, where the sum of two numbers gives the next number.
As it expands, or multiplies it gets greater by 1.618 but it is still in proportion, and on and on it goes. When we draw a square within a Golden Ratio rectangle, the rectangular shape that is left over is also of Golden Ratio proportions.
This remaining rectangular shape is approximately 1.618 times smaller than the previous Golden Ratio rectangle it sits within.
When we draw a spiral based on Golden Ratio rectangles repeated within larger Golden Ratio rectangles, we find that the shape of this spiral is that often seen in the natural world, in a sea shell or a flower.
With a phi spiral, every 45 degrees the spiral gets a distance of 1.272 times as far from the central vortex point. For every 90 degrees, it becomes 1.1618 times as wide as the previous radius.
It can also be observed, that both the solar system and the Milky Way Galaxy are Golden Spirals.
The diameters of the Earth and the Moon also relate in the same manner.
The planets are in elliptical orbits using their mean distances from the Sun, we find that the Sun to each planet in millions of miles, followed by their distance ratios is …..
Mercury 35.5 .382
Venus 55 .618
Earth 93 1.000
Mars 149 2.618
The Universe is a Golden Spiral
In 2003, NASA’s Wilkinson Microwave Anisotropy Probe (WMAP), obtained data which lead to a new hypothesis about the structure of the Universe; that the geometry of the Universe is similar in shape to a horn or a pipe with an extended bell.
By plotting the data, these graphs were formed:
and when plotted in three dimensions, they produce what is called The Golden Shofar.
The Golden Shofar is another new model of the golden hyperbolic world. The article “The Hyperbolic Universes with a Horned Topology and the CMB Anisotropy” proved a great surprise to the authors because it showed that the geometry of the Universe is quite possibly is “shofarable” by its structure.
In other words, the universe, itself, if a Golden Shofar, structured in the fundamental mathematics of The Golden Spiral 20 mg prednisone.