# Value of π and precession of equinoxes in the pyramids of Teotihuacán and Giza

## The architects who built the Pyramid of the Sun (Teotihuacán) and the Pyramid of Cheops (Giza) knew the concepts of the number π (3.14...) and the precession of the equinoxes hundreds of years before Archimedes and Hipparchus of Nicaea.

The Teotihuacán archaeological complex is located approximately 40 kilometers northeast of Mexico City. “Academic” archaeologists maintain that the entire city and the pyramids of the Sun and the Moon were built starting in the Christian era.

The Pyramid of the Sun, although it is not the largest ancient construction in the New World (it is the pyramid of Cholula, with 3.3 million cubic meters of volume) and neither is it the tallest (it is the pyramid of La Danta, 72 meters), is certainly the most mysterious. One of the most intriguing features of the Pyramid of the Sun is the fact that, dividing the side of its base (which is square) by the height, we obtain the value of the number π, corresponding to 3.14…

The perimeter of the pyramid base is equal to 893.91 meters (side of 223.47 m) and the height is 71.17 meters.

We obtain: 893.91=71.17 x 4 x 3.14

Or better: 223.47 x 4=71.17 x 4 x 3.14

And, simplifying, we obtain: 223.47/71.17= 3 .14

From this it follows that the ancient builders of the Pyramid of the Sun wanted to introduce the number 3.14 into their construction.

They could very easily have used a different ratio, building a pyramid whose sides were more (or less) inclined, but they wanted to include the number 3.14 in their project. Why?

According to official history, the value of the number 3.14 was discovered in Greece, in the 3^{rd} century BC, by Archimedes. How was it possible that the ancient Teotihuacanos used it precisely in their most important construction? It is evident that they had very advanced knowledge of mathematics and geometry, although in other fields, such as iron metallurgy, they had not achieved such brilliant results.

Let us now move eastwards, imaginarily crossing the Atlantic Ocean and the Mediterranean. The archaeological complex of the Giza plateau, with the three majestic pyramids, better known by the name of the three pharaohs Cheops, Khafre and Mycerinus, continues, after hundreds of years of studies, to raise interesting questions.

First of all, let's analyze the Great Pyramid of Cheops: in this case, dividing twice the side of its base (also square) by its original height, we again obtain 3.14.

Indeed, the perimeter of the base is 921.45 meters (side 230.36 m) and the original height was 146.72 meters.

We obtain: 921.45=146.72 x 2 x 3.14

or better: 230.36 x 4=146.72 x 2 x 3.14

And simplifying 230.36 x 2=146.72 x 3.14

therefore: 460.72/146.72= 3.14

Also in this case, then, the builders of the pyramid of Cheops, which according to official history dates back to 2560 BC, included the number π in the fundamental geometric ratio between the perimeter of the base and the height of its construction. Why?

And why did they do it only in the pyramid of Cheops? In that of Khafre, for example, the geometric ratio between twice the side and the height is equal to 3:

215.25 x 2 /143.5=3

From all this it follows that the number 3.14 was surely known in the New World and in Egypt (in Egypt at least 2300 years before Archimedes). For now we are unable to provide a valid explanation as to why the ancient architects of the two pyramids wanted to include the number 3.14 in their creations. Perhaps by introducing the concept of the number 3.14 in their constructions, the ancients wanted to symbolize the perfect sphere which they worshiped, or the Sun?

The pyramids of the Sun (Teotihuacán) and Cheops (Giza) contain many other mysteries, one of which is related to the values of the astronomical phenomenon known as the “precession of the equinoxes.” To understand this concept, let's imagine that our Earth is a sailing ship. Let's imagine that the yard of our boat is inclined 23.5º with respect to the horizon.

The Earth's axis, in fact, is inclined 23.5º with respect to the “plane of the ecliptic”, or the geometric plane on which the Earth's orbit lies. This inclination is beneficial because it is the implicit cause of the change of seasons in the temperate zones of the Earth, without which our planet would be uninhabitable.

Our sailing vessel, however, rocks slowly over the ocean, so that the yard, with the passage of time, forms a different angle with respect to the horizon.

Likewise, the Earth's axis changes its inclination in a cycle of 41,000 years, during which it goes from 22.1º to 24.5º on the plane of the ecliptic, while the direction of the inclination varies with a cycle of 25,920 years ^{(1)}. From this it follows that if today the Earth's axis points north in the direction of the North Star, 13 millennia ago north was indicated by the star Vega, located in a different part of the celestial sphere. The result of all this is the precession of the equinoxes: the Sun, during the spring and autumn equinoxes, rises indicating one of the 12 constellations. Currently, the Sun rises between the constellation of Pisces and Aquarius. The slow “sway” of the Earth's axis causes the Sun, during the equinoxes, to emerge with a different constellation in its background, every 2160 years.

In effect: 25920/12=2160

The values of the wonderful cosmic “engine” that causes precession are, therefore:

- The 12 constellations of the zodiac, each of which occupies 30º of the celestial equator (1/12 of 360º).
- The 36 or 72 years that it takes the equinoctial Sun to travel, respectively, half or one degree of the celestial equator.
- The 2160 years that it takes the Sun to travel 30 degrees from the celestial equator, or to emerge (always during the two days of the equinox), having a successive constellation in its background.
- The 4320 years that it takes the Sun to travel 60 degrees from the celestial equator, or to emerge (always during the two days of the equinox), having two successive constellations in its background.
- The 25,920 years that it takes the Sun to travel 360 degrees of the celestial equator, or to complete a complete cycle.

Now let's go back to analyze the Pyramid of the Sun (Teotihuacán). It can be seen that the precession values were used in its construction.

If you multiply the height by **30** (1/12 of the celestial constellation) you obtain the value of 2135 (which is close to the value of 2160): 71.17 x 30=2135

If the value of the complete cycle is divided by the height, the value of 364.198 is obtained (number of days in the ancient Mesoamerican calendar, in addition to the biblical antediluvian one): **25920** / 71.17=364.198

If you divide the value of the perimeter by **30** (1/2 of the celestial constellation) you obtain the value of 29.79 (the days of the lunar calendar): 893.91 / 30=29.79

Analyzing, on the other hand, the pyramid of Cheops, here we can also verify that the numbers of the precession were used in its construction:

If the height is multiplied by a multiple of 4320, the value of 6338.476 is obtained (almost equal to the exact value of the Earth's polar radius):

146.72 x 43200 ^{(2)}=6338.476 (while the exact value is 6353.941 km)

If the perimeter is multiplied by the same multiple of 4320, the value of 39807 is obtained (almost equal to the exact value of the Earth's circumference at the equator):

921.45 x 43200=39807 ^{(3)} (while the exact value is 40075 km)

Also analyzing the pyramid of Khafre, an extraordinary value is obtained:

Dividing the value of the complete precession cycle by the height, we obtain 180 (the 180º of the celestial equator, occupied by 6 constellations): 25920 / 143.5=180

What can be concluded from all this?

First of all, it is evident that the precession of the equinoxes, officially discovered in the 2^{nd} century BC by the Greek Hipparchus of Nicaea, was actually known both in the New World and in Egypt (in Egypt, at least 2400 years before Hipparchus).

Assuming, then, that the ancients had a very advanced knowledge of geometry and celestial phenomena, it remains to be clarified why they gave so much importance to the number 3.14 and the precession of the equinoxes, enough to include these values in their architectural creations.

It is famous among several researchers that the ancients introduced precession values into their pyramids because they had recognized the enormous importance of the inclination of the Earth's axis. However, why spend so much time and energy on exactly matching various mathematical equations and eternalizing them in such imposing constructions?

Maybe they wanted to leave us a message? Perhaps they wanted to warn posterity of the possible relationship between the precession of the equinoxes and the alternation of glacial phases on the planet? Or perhaps they wanted to indicate that the precession cycle was, according to their legacy, the appearance of catastrophic phenomena such as the so-called “universal flood”?

By further analyzing the great pyramid of Cheops, other interesting data emerge, such as the place where it was built, at the 30º parallel; or the perimeter, which calculated in Egyptian inches, gives exactly the value of the solar year (365.24); or the perfect orientation of the 4 sides towards the cardinal points; or the incredible fact that twice the perimeter is equal to 1/60 of a degree at the equator: 921.45 x 2=1842.92 (1/60 of an equatorial degree).

Not counting the wonders of its interior, such as the queen's and king's rooms, which branch off into narrow passages that, according to some researchers, were used for the observation and worship of certain stars (respectively Sirius and Zeta Orionis).

It is obvious that these pyramids were not only tombs (in the Egyptian case) or ceremonial altars (in the Mexican case) but scale models of the dimensions of the Earth and its complex movements in celestial space, as well as astronomical observatories.

The secret of the pyramids has not yet been completely revealed. There are still hundreds of little-studied pyramids, especially in the New World, such as those of the Mayans. It is our task to try to understand the message of our ancestors.

YURI LEVERATTO

## Note

- In some scientific sources the value of 25776 years is found. The basic concept does not change: the ancients calculated the value of 25,920 years and used the numbers derived from that value to build their pyramids.
- The number 432,000 also appears in the “History of Babylon” by Berossus (3
^{rd}century BC). According to the Chaldean writer, the antediluvian kings reigned in Mesopotamia for 432,000 years. - The value of the length of the Earth's circumference (39,807 km), calculated by the builders of the pyramid of Cheops, was, in any case, more accurate than that calculated by the Greek Eratosthenes (39,375 km), in the 2
^{nd}century BC.