“Geometry has two great treasures: the Pythagorean theorem and the division of a segment in the mean and extreme ratio. The first can be compared with a measure of gold, the second we can call a precious stone. Johannes Kepler.
Sacred geometry is the sacred geometry of forms that underlie life, the key to cognition of man and the Cosmos. "Geometry" translated from Greek means "measurement of the earth", it predetermines the shapes of molecules and crystals that make up our bodies and the Universe. In ancient mystical practices, geometry was referred to as "the first and most noble of the sciences."
Sacred geometry combines the wisdom of many mystical schools that existed long before our era, and modern ones, linking esotericism with the latest achievements of quantum physics. Sacred geometry has played and plays a major role in the art, architecture and philosophy of many cultures for thousands of years. The term sacred geometry is used by archaeologists, anthropologists, religious leaders and philosophers.
Johann Goethe said: "Numbers do not rule the world, but they show how the world is governed." Geometric shapes are a specific embodiment of numbers: the number 5 is associated with a pentagram, 4 - with a square, 3 - with a triangle, 2 - with an angle, 1 - with a point or line.
Numbers
The world is evolving according to the laws of numbers. All the knowledge of the world lies in the icons denoting numbers that we see a thousand times a day and do not even think about them. Indians invented them. The curved line symbolizes love, the horizontal line symbolizes affection, crossing them is a choice. One is the level of minerals.
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The unit rises motionless, like a monolith. She doesn't feel anything, she's just present. There are no curved or horizontal lines, no crosses. That is, there is no love, no attachment, no choice. At the level of minerals, everything is unconsciously present here and now.
Two is the plant level. Curved stem and horizontal root line. The deuce is tied to the ground. The flower cannot move. At the top is a curved line. The deuce loves the sky. The flower wants to be beautiful, it has a lot of colors and graceful veins to please the higher dimension.
Three is the level of animals. In two curved lines, above and below, she loves both heaven and earth. The three are driven by instincts. She is an eternal slave to her feelings.
Four is the stage of man. It is symbolized by the cross, the crossing of roads. The intersection is a choice. If we can make the right choice, the intersection will help us to leave the animal stage and move on to the next stage. From the animal stage of the three to the five stage. We will no longer be able to rush between fear and desires, we will be able not to experience only emotions caused by instincts. We will be able to go beyond the dilemma "love - not love" and "I am afraid - I inspire fear."
Five is the spirit stage. Evolved man. The five has a horizontal line at the top, therefore, it is tied to the sky. A curved line means that she loves what is below - the earth. Five is the exact opposite of two. The plant is riveted to the ground. A spiritual person is associated with heaven. The plant loves the sky, the spiritual person loves the earth.
This is what André Malraux had in mind in his famous saying: "The third millennium will be spiritual, or it will not be at all." The person will be a five, or he will not be at all.
Mathematical relations
There is a group of five basic mathematical relationships that can be found all over the world, from Japanese pagodas to Mayan temples in Yucatan, from Stonehenge to the Great Pyramid of Giza. Knowledge of these relationships is the basis for understanding sacred geometry. This relationship:
The number π (pi) = 3.1416 …
The number π (pi) is a mathematical constant expressing the ratio of the circumference of a circle to the length of its diameter, an irrational number, since its value cannot be accurately expressed as a fraction.
The number π (pi) can be found in any circle. In sacred geometry, the circle represents "spiritual kingdoms." One of the most famous sacred places in the shape of a circle is the labyrinth on the floor of the Cathedral in Chartres.
Square root of 2, V2 = 1.414 …
In sacred geometry, the square represents the physical world. The discovery of incommensurable segments is connected with V2, which led mathematicians to the development of the theory of irrational numbers, and ultimately to the creation of modern mathematics. Almost all known figures are associated with V2: triangle, square, hexagon.
The square was discovered in one of the most sacred places - the Temple of Solomon, which is the central symbol of Freemasonry. According to the texts of Philo of Alexandria, the Temple of Solomon was a geometrical figure designed specifically to form a "force field", a place of transition from one world to another: from the visible world to the invisible world. Isaac Newton devoted all the last years of his life to calculating the structure of the Jerusalem Temple. For him, the Temple of Solomon was a blueprint of the Universe, the bearer of all the secrets of the world, he believed that the laws of nature are encoded in its structure and proportions between its various parts.
Vesica piscis
A structure called "vesica piscis" (fish bubble) is formed when the centers of two circles with equal radii are located on each other's circles. The area bounded by intersecting arcs of circles - "vesica piscis".
This configuration is one of the predominant and most important among all the relationships in sacred geometry. Its spiritual significance was used by Renaissance artists in painting and architecture. The "Flower of Life" found in the temple of Seti I at Abydos is the "vesica piscis".
Equilateral triangle, obtained on the basis of "vesica piscis" - one of the earliest mystical symbols known to mankind. Plato pointed out: "Between the many triangles there is one, the most beautiful, for the sake of which we will leave all the others, namely the one that, in conjunction with a similar one, forms a third triangle - equilateral."
The square root of 5 = 2.236 … Double square.
The Pythagoreans revered the number 5 as sacred, it served as a symbol of their union. The diagonal of a double square refers to the smaller side in the same way as V5 to 1. The arithmetic mean of 1 and the root of 5 (1 + 2.236): 2 = 1.618 - Golden ratio - φ (phi).
The number φ (phi) - 1.618 … Golden ratio.
The Golden Ratio is considered the fundamental constant in architecture, painting and science. The definition of the golden ratio by Plato: “To combine two parts with the third in a perfect way, a proportion is needed that would hold them together into a single whole. Moreover, one part of the whole should relate to the other as the whole to the greater part."
Phi - the value of the calculus of proportions - a transcendental number, since it is expressed by an infinite decimal fraction. The name of the city of Thebes (Luxor), one of the sacred places of Ancient Egypt, begins with this sign.
The ancient mystics considered the Fibonacci number series: (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.) a universal key to explaining the laws of the universe. Finding the quotient between two adjacent numbers of this series, you can approach the number Phi - 1.618 … - Golden ratio, but never reach it. The Fibonacci sequence was well known in ancient India, where it was used in metric sciences much earlier than it became known in Europe. In the West, this sequence was explored by Leonardo of Pisa, known as Fibonacci.
Fibonacci ratios are ubiquitous in nature, this proportion has been used by many artists and sculptors since time immemorial. The Phi number is present, first of all, in a person, the "divine proportion" of the human body is displayed in the famous drawing by Leonardo da Vinci.
In the temples of the pharaohs: Seti I in Abydos, Ramses II in Luxor, the proportions of the figures correspond to the Golden Section. The Phi proportion is the basis for the design of the Great Pyramid of Giza. The ancient Greek temple of the Parthenon also has golden proportions.
Phi can be found everywhere: in flowers, plants, atoms, Egyptian hieroglyphs, architecture, in the spirals of seashells and galaxies. Plato viewed Phi as the key to understanding the physics of space.
So, there are five mystical geometric relationships: π (pi), φ (phi), V2, V5 and Vesica Piscis. They serve as the basis for all sacred geometric constructions.
Platonic Solids
The division of the sphere leads to the creation of five regular polyhedrons, the so-called "Platonic solids": tetrahedron, octahedron, cube, icosahedron and dodecahedron. The first three have been known since time immemorial, the others were described by the Pythagoreans.
All the faces of the "Platonic Solids" have the same size (the cube has a square for each of its faces, and all its faces are of the same size), all the edges have the same length (all the edges of the cube are of the same length), all internal angles between the faces have the same size (in in the case of a cube, this angle is 90 degrees).
If the "Platonic solid" is placed inside a sphere, then all its vertices will touch the surface of the sphere. In addition to a cube, only four forms correspond to such definitions, which have all these characteristics: tetrahedron (tetra means "four"), octahedron (octa means "eight"), icosahedron - has 20 faces that look like equilateral triangles with the same length of edges and angles, dodecahedron (dodeca - 12).
"Platonic solids" are the alphabet of sacred geometry. Pythagoras believed that each of these figures is a model of the corresponding element: the tetrahedron is a model of the fire element, the cube is the earth, the octahedron is air, the icosahedron is water, and the dodecahedron is ether. These elements are the “building blocks” of the universe. At the microscopic level, the dodecahedron and icosahedron are relative parameters of DNA.
Two interpenetrating tetrahedrons that fit exactly into the cube are the Mer-Ka-Ba “field of light”, which includes five “Platonic solids”, it is also called the “volumetric Star of David”. In Leonardo da Vinci's drawing "Vitruvian Man", the tetrahedron facing up to the Sun is masculine, facing down to the Earth - feminine. The male tetrahedron is called "solar", the female - "earthly." Two intersecting tetrahedrons symbolize perfectly balanced masculine and feminine energies and make up the "Star Tetrahedron" - a "vehicle" capable of moving the spirit and body from one world or dimension to another. In ancient Egypt, Mer-Ka-Ba meant - "the union of Spirit and Soul" - "the gate between dimensions."
The principles of sacred geometry, which are based on "Platonic solids", the Golden Section spiral, the Phi number, fractals are equally inherent in humans, flowers, and stars. Everything that exists in the real world is a fractal: the circulatory system, tree crowns and leaves, clouds and an oxygen molecule. Many objects and processes in the Universe have the property of "self-similarity". If we consider these objects at different scales, then the same elements are constantly found. All of them can be described in the form of mathematical equations.
The geometry of nature is fractal geometry. Nature itself takes advantage of its achievements and examples of this can be found everywhere: from the spirals of shells and daisy flowers to the symmetry of hexagonal honeycombs. "Self-similarity" can be found when examining the shapes of molecules or galaxies.
“The universe cannot be read until we learn the language and become familiar with the symbols in which it is written. It is written in the language of mathematics, and the letters of this language are triangles, circles and other geometric shapes, without which it is beyond human power to understand a single word. Galileo Galilei
Author: Valentina Zhitanskaya