## The Golden Mean Spiral/Golden Rectangle/Golden Ratio/ **Divine Proportion**/**Divine Section/Phi Ratio has many names.**

The Golden Mean Spiral can wear many hats in its function and relationship to Creation. It is my personal opinion that the Golden Mean Spiral represents the purest form of the feminine aspect of Creation. Considering that all lines curved are feminine in nature and all lines that are straight are male in the study of sacred geometry. The Golden Mean is the measuring stick of Creation and can be found in many forms outside of the spiral. While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind. It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names. Uses in architecture date to the ancient Egyptians and Greeks It appears that the Egyptians may have used both pi and phi in the design of the Great Pyramids. The Greeks based the design of the Parthenon on this proportion.

Phidias (500 BC - 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon.

Plato (circa 428 BC - 347 BC), in his views on natural science and cosmology presented in his "Timaeus," considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos.

Euclid (365 BC - 300 BC), in "Elements," referred to dividing a line at the 0.6180399... point as "dividing a line in the extreme and mean ratio." This later gave rise to the use of the term mean in the golden mean. He also linked this number to the construction of a pentagram.

The Fibonacci Series was discovered around 1200 AD Leonardo Fibonacci, an Italian born in 1175 AD (2) discovered the unusual properties of the numerical series that now bears his name, but it's not certain that he even realized its connection to phi and the Golden Mean. His most notable contribution to mathematics was a work known as Liber Abaci, which became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. (3)

It was first called the "Divine Proportion" in the 1500's Da Vinci provided illustrations for a dissertation published by Luca Pacioli in 1509 entitled "De Divina Proportione" (1), perhaps the earliest reference in literature to another of its names, the "Divine Proportion." This book contains drawings made by Leonardo da Vinci of the five Platonic solids. It was probably da Vinci who first called it the "sectio aurea," which is Latin for golden section.

The Renaissance artists used the Golden Mean extensively in their paintings and sculptures to achieve balance and beauty. Leonardo Da Vinci, for instance, used it to define all the fundamental proportions of his painting of "The Last Supper," from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background.

Johannes Kepler (1571-1630), discoverer of the elliptical nature of the orbits of the planets around the sun, also made mention of the "Divine Proportion," saying this about it:

"Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

The term "Phi" was not used until the 1900's It wasn't until the 1900's that American mathematician Mark Barr used the Greek letter phi to designate this proportion. By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion. Phi is the first letter of Phidias (1), who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter "F," the first letter of Fibonacci. Phi is also the 21st letter of the Greek alphabet, and 21 is one of numbers in the Fibonacci series. The character for phi also has some interesting theological implications.

Recent appearances of Phi in math and physics Phi continues to open new doors in our understanding of life and the universe. It appeared in Roger Penrose's discovery in the 1970's of "Penrose Tiles," which first allowed surfaces to be tiled in five-fold symmetry. It appeared again in the 1980's in quasi-crystals, a newly discovered form of matter.

Phi as a door to understanding life The description of this proportion as Golden and Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That's an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the universe at large. lets take a look at some great examples of the spiral in the natural world around us.

Phidias (500 BC - 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon.

Plato (circa 428 BC - 347 BC), in his views on natural science and cosmology presented in his "Timaeus," considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos.

Euclid (365 BC - 300 BC), in "Elements," referred to dividing a line at the 0.6180399... point as "dividing a line in the extreme and mean ratio." This later gave rise to the use of the term mean in the golden mean. He also linked this number to the construction of a pentagram.

The Fibonacci Series was discovered around 1200 AD Leonardo Fibonacci, an Italian born in 1175 AD (2) discovered the unusual properties of the numerical series that now bears his name, but it's not certain that he even realized its connection to phi and the Golden Mean. His most notable contribution to mathematics was a work known as Liber Abaci, which became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. (3)

It was first called the "Divine Proportion" in the 1500's Da Vinci provided illustrations for a dissertation published by Luca Pacioli in 1509 entitled "De Divina Proportione" (1), perhaps the earliest reference in literature to another of its names, the "Divine Proportion." This book contains drawings made by Leonardo da Vinci of the five Platonic solids. It was probably da Vinci who first called it the "sectio aurea," which is Latin for golden section.

The Renaissance artists used the Golden Mean extensively in their paintings and sculptures to achieve balance and beauty. Leonardo Da Vinci, for instance, used it to define all the fundamental proportions of his painting of "The Last Supper," from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background.

Johannes Kepler (1571-1630), discoverer of the elliptical nature of the orbits of the planets around the sun, also made mention of the "Divine Proportion," saying this about it:

"Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."

The term "Phi" was not used until the 1900's It wasn't until the 1900's that American mathematician Mark Barr used the Greek letter phi to designate this proportion. By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion. Phi is the first letter of Phidias (1), who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter "F," the first letter of Fibonacci. Phi is also the 21st letter of the Greek alphabet, and 21 is one of numbers in the Fibonacci series. The character for phi also has some interesting theological implications.

Recent appearances of Phi in math and physics Phi continues to open new doors in our understanding of life and the universe. It appeared in Roger Penrose's discovery in the 1970's of "Penrose Tiles," which first allowed surfaces to be tiled in five-fold symmetry. It appeared again in the 1980's in quasi-crystals, a newly discovered form of matter.

Phi as a door to understanding life The description of this proportion as Golden and Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That's an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the universe at large. lets take a look at some great examples of the spiral in the natural world around us.

The Golden Mean Spiral perceived from different angles of reality.

## The Golden Mean Rectangle and Phi Ratio

__I want to talk about
vortex energy here, because we need this information in order to
understand the energies that exist around the world's Sacred Sites.

In this discussion, I will not try to interpret the underlying meaning of this energy. My purpose is only to bring your attention to the fact that these energies exist around Sacred Sites, and to make you aware of their complexity. Then, when you read someone's idea about Sacred Sites and vortexes, you will realize that you have to ''see'' from where they are before you will be able to make up your own mind as to what it all means.

What follows is a layman's summary of the way the energy in a vortex moves, its possible nature, and what personal meaning it may have for you.

Vortexes: Energy In Motion

The simplest vortex is a circle, where the beginning meets the end. Moving matter — in the form of water, wind or dust, any form of energy such as electricity through a wire, or even magnetic fields — can move in circles. But when the movement of the energy begins to spiral, a special vortex is formed — a hurricane is a good example of this and the nature of a spiral vortex is determined by the way it moves.

At first, we might think that a spiral is a spiral is a spiral. But on closer examination, we can see that a spiral may be more complex than we had thought. For example, a spiral moving toward the center is different from one that is expanding, or moving away from center. And further, the direction that the spiral is moving — clockwise or counterclockwise — is an important factor. Some scientists see vortexes as either male or female, depending on which direction they are rotating. Generally, clockwise is seen as ''female,'' and counterclockwise as ''male.''

But is it really that straightforward? For is it not true that the direction a vortex is rotating depends on where you are located relative to it? When we look from the North Pole, the Earth appears to be moving from East to West, and would thus be ''male.'' But viewed from the South Pole, the Earth appears to be moving from West to East, and would be ''female.'' So which is it? Perhaps what you see is what you get.

Again, I'm not here to interpret, only to point the way for your own experiences.

Here are more thoughts: If you are positioned above a sprinkler like a ''Rainbird,'' which rotates to make the water move in a vortex — two directions are taking place at once. The water may appear to be moving, say, clockwise. But if you look only at the object that is rotating and creating the vortex, you will see that it is rotating in the opposite direction. Think about it.

To me, what this means is that if a vortex appears to be moving in a certain direction, the force that created it will be moving in the opposite direction. Very often, vortex researchers forget this idea, and so mix up the idea of male and female when they describe a specific vortex. But a problem arises in comparing one vortex to another unless both researchers use the same system to identify them. For example, the Japanese see the ''North'' pole of a magnet in the exact opposite way that Americans do. We see it as the ''South'' pole.

Endless versus Finite Energy Motion

Vortexes also follow certain mathematical laws as they move. Two such examples are the Golden Mean vortex and the Fibonacci vortex. They appear almost the same, but they are extremely different in their natures.

The Golden Mean vortex will rotate toward or away from center forever — never reaching the center and never ending its outer expression. And the Fibonacci vortex also rotates forever outward from the center. But the Fibonacci vortex is absolutely finite in its inner quest to reach the center. It eventually comes to its beginning, and there must either stop or reverse direction. If it reverses direction, a Fibonacci spiral will appear to create a completely new, outwardly-moving vortex — of the opposite spin!

Another vortex type, the toroidal vortex, also reverses its spin as it enters exact center. And this type of vortex actually moves in three dimensions, following the contours of the torus shape.

So if someone describes how a vortex is moving, or says it is female or male, we must realize not only that where we are located relative to the vortex determines its nature, but that nothing is as simple as it may seem.

In this discussion, I will not try to interpret the underlying meaning of this energy. My purpose is only to bring your attention to the fact that these energies exist around Sacred Sites, and to make you aware of their complexity. Then, when you read someone's idea about Sacred Sites and vortexes, you will realize that you have to ''see'' from where they are before you will be able to make up your own mind as to what it all means.

What follows is a layman's summary of the way the energy in a vortex moves, its possible nature, and what personal meaning it may have for you.

Vortexes: Energy In Motion

The simplest vortex is a circle, where the beginning meets the end. Moving matter — in the form of water, wind or dust, any form of energy such as electricity through a wire, or even magnetic fields — can move in circles. But when the movement of the energy begins to spiral, a special vortex is formed — a hurricane is a good example of this and the nature of a spiral vortex is determined by the way it moves.

At first, we might think that a spiral is a spiral is a spiral. But on closer examination, we can see that a spiral may be more complex than we had thought. For example, a spiral moving toward the center is different from one that is expanding, or moving away from center. And further, the direction that the spiral is moving — clockwise or counterclockwise — is an important factor. Some scientists see vortexes as either male or female, depending on which direction they are rotating. Generally, clockwise is seen as ''female,'' and counterclockwise as ''male.''

But is it really that straightforward? For is it not true that the direction a vortex is rotating depends on where you are located relative to it? When we look from the North Pole, the Earth appears to be moving from East to West, and would thus be ''male.'' But viewed from the South Pole, the Earth appears to be moving from West to East, and would be ''female.'' So which is it? Perhaps what you see is what you get.

Again, I'm not here to interpret, only to point the way for your own experiences.

Here are more thoughts: If you are positioned above a sprinkler like a ''Rainbird,'' which rotates to make the water move in a vortex — two directions are taking place at once. The water may appear to be moving, say, clockwise. But if you look only at the object that is rotating and creating the vortex, you will see that it is rotating in the opposite direction. Think about it.

To me, what this means is that if a vortex appears to be moving in a certain direction, the force that created it will be moving in the opposite direction. Very often, vortex researchers forget this idea, and so mix up the idea of male and female when they describe a specific vortex. But a problem arises in comparing one vortex to another unless both researchers use the same system to identify them. For example, the Japanese see the ''North'' pole of a magnet in the exact opposite way that Americans do. We see it as the ''South'' pole.

Endless versus Finite Energy Motion

Vortexes also follow certain mathematical laws as they move. Two such examples are the Golden Mean vortex and the Fibonacci vortex. They appear almost the same, but they are extremely different in their natures.

The Golden Mean vortex will rotate toward or away from center forever — never reaching the center and never ending its outer expression. And the Fibonacci vortex also rotates forever outward from the center. But the Fibonacci vortex is absolutely finite in its inner quest to reach the center. It eventually comes to its beginning, and there must either stop or reverse direction. If it reverses direction, a Fibonacci spiral will appear to create a completely new, outwardly-moving vortex — of the opposite spin!

Another vortex type, the toroidal vortex, also reverses its spin as it enters exact center. And this type of vortex actually moves in three dimensions, following the contours of the torus shape.

So if someone describes how a vortex is moving, or says it is female or male, we must realize not only that where we are located relative to the vortex determines its nature, but that nothing is as simple as it may seem.