Metaphysical Geometry and the Golden Ratio

All the ancient cultures patiently arranged a correspondence between the heavens - especially the sun's orbit and the zodiac, with the settled land - and especially with the holy buildings and important cities, and with people - especially the religious and governmental elite.

Various researchers present enormous astrological diagrams in the Mediterranean basin. The zodiac stretched across the land and the sea, and passed through many centers of pilgrimage in ancient times. The architects of these huge earthly zodiac signs turned their country into a living image of the sky.

Other sacred geographies have a whole base that comes from geodesy, the branch of mathematics and applied geometry, which deals with measurements and distances on Earth, and the location of points on the surface. These special measurements evolved into geometric paintings over vast expanses of triangles, squares, and circles, and more complicated geometric forms and connections. Ancient builders erected temples in the landscape, which were placed exactly according to the knowledge of sacred geometry.

The ancient Egyptians ruled this science. The main line of ancient Egypt was determined to cross the country in half. Cities and ceremonial centers were deliberately built at distances measured precisely from this sacred longitude. Even in ancient Greece, religious centers were all separated from each other by precise distances.

We find evidence of ancient landscape geometries in France, Germany and England. Researchers have found extensive evidence in these countries for a linear arrangement of ancient sacred sites over long distances. Their source is a huge system of merchant routes that were built in the Neolithic period. Archaeological findings have since confirmed the Neolithic origin, but the idea that the lines were used for transport purposes should be ruled out. The lines form a straight arrow on the ground, making them impractical for useful transportation. These are energy lines, and in fact there is a sense of energy or power flowing along them, felt by people with sensitivities to earth energies.

This category belongs also to straight lines created on the landscape by archaic cultures in the Western Hemisphere. Examples include the Nasca lines in Peru, similar lines across Bolivia's deserts, and many linear signs left by Indians in the Chaco Canyon area of New Mexico. These lines are also integrated into giant drawing of animals and humans in adjacent geometric shapes. These are spiritual lines - a symbol created on Earth to represent the spiritual journeys, magical flights and experiences outside the body of ancient shamans.

The Nasca lines in Peru are the most important example of huge shaped lines on the landscape. The lines were discovered in the 1920s when regular commercial flights began over the desert. The lines can be identified as meaningful shapes on when viewed from the air.

The Nasca Desert is a high, arid plateau that stretches 85 kilometers off the coast of the Pacific Ocean some 400 kilometers south of Lima, the capital of Peru. The creators of the lines belonged to the Nasca culture, which existed between 200 BC and 600 AD. The lines form hundreds of shapes, whose complexity varies from simple and straight lines of up to 20 kilometers, to triangles and trapezes, to complex and stylish forms of animals such as birds, spiders, monkeys, lizards, whales, and even human figures. The lines were formed by digging the dark gravel that covered the desert and removing it to the side, so the lighter surface was revealed. The color of the lines is yellow and beige, and their depth is no more than a few centimeters. The total area of the lines is nearly 500 square kilometers and the length of the greatest characters reaches 270 meters. The lines are preserved due to the stable weather, which is windless and very arid.

The conventional archaeological theory is that the Nasca people created the lines with meticulous planning and simple technologies, and in a relatively short period of time. The lines are the remains of 'walking temples', in which a large group of believers walked along a predetermined pattern, which was dedicated to a unique sacred entity, similar to the custom of walking through a maze. They asked the gods to ensure that the water will continue to flow to them from the Andes through the extensive underground water channels they have constructed.

In Christian and Islamic Europe, in the Middle Ages and the Renaissance, painters were known to define the initial design of their paintings according to different geometrical formulas, imitating and perfecting ancient knowledge. According to this approach, the placement of elements within the painting is as important as the theme itself. This geometry was integrated into the worldview, and in the planning and construction of temples, public buildings, and entire cities.

Particularly prominent in metaphysical geometry formulas is the 'Golden Ratio'. This is ostensibly a simple mathematical series of numbers, but it is also referred to as the 'divine proportion'.

The golden ratio is the series of numbers in which each bigger number is the sum of the two numbers before it:

Let's take the number 1 and add it to 1. To the result 2 we shall add the previous number 1 and the result is 3. To 3 we shall add the previous number 2 and the result is 5.

Here are the first numbers in the series:

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584

In this series of numbers there are many interesting mathematical phenomena. The most important is that the ratio between two consecutive numbers in a series, for example between 5 and 8 or between 21 and 34, is always about ... 1: 1.618. 

This ratio is never an integer. 

The 'Golden Section' is the name of the geometric form of the arithmetic golden ratio. The basic geometric form is that of a line divided into two according to the golden ratio: the length of the smaller part of each line relative to the larger part is like the length of the largest part relative to the entire length of the line.

When you take two consecutive lines in this sequence and form a rectangle, you get a rectangle of elegant dimensions known as the Golden Rectangle. 

This rectangle can be divided into sub-squares, smaller and smaller. If you draw an arch between two opposite edges in each inner square and connect all the arches created, you get a spectacular shape, called the Golden Spiral.

The golden section was discovered through practical experience thousands of years ago, and was used by the ancient architect, who debated what is the best point in dividing one line into two parts. The most beautiful dividing point is when the two parts of the line have the golden ratio between them.

The dimensions of the Great Pyramid in Egypt, the Parthenon in Athens and the Pantheon in Rome were designed according to the golden section. The ratio was the central visual concept and the focus of religious attraction in these temples. The ratio appears in various places in the buildings, from the general appearance to the rooms. The golden ratio is considered, since then, the most perfect form in art. The great Renaissance artists made sure to use it. It is found in Mozart's symphonies. It is also common in modern art and is used by architects, musicians, poets and designers.

The golden ratio and the golden section are also of great importance in the natural sciences because they appear in innumerable and very different natural phenomena. The organs of the human body are shaped according to the golden ratio. This fact was one of the principles of classical sculpture in the ancient world. The relationships in the human body produce the deepest effects on the human mind. The DNA form is also of two integrated gold spirals.

It is therefore possible to say that the reality in which we live is built to a large extent according to the principles of this ratio. The golden ratio has been used by builders of temples already in antiquity, whereas modern scientists have found that it is one of the basic mathematical frameworks of the universe. Its effects help shape a harmonious personal world, because it is used in nature, science, and art. This is the perfect standard. Preoccupation with it created entire worldviews, in past and present. Historians attribute great importance to the golden ratio in shaping human history and knowledge.

A 100-meter-long bird drawn across the Nasca plain in Peru

golden section

The golden ratio in a graph of rising and falling

The golden ratio in a pentagram, the most known star shape

The golden ratio in the Great Pyramid of Egypt

The golden ratio in the Parthenon of Athens

Human dimensions according to the pentagram

The golden ratio in nature

golden ratio in the human body

The golden ratio in the fingers

A golden rectangle and the golden spiral inside

A golden spiral shaped conch

The golden ratio in the DNA

The UN building is a golden rectangle

A golden rectangle in Renaissance painting

golden spiral in Botticelli's Venus painting

The golden ratio as an infinite wave