#### The Sacred Triangle of Egypt

One of the most interesting cultures in the world is that of Egypt since it was one of the first modern civilizations with social systems and large cities.

Egyptian numbering has many features in common with the current numbering system we use. It was based on a decimal system, in which numbers were divided into groups of ten. In a nutshell, the Egyptian number system was a base 10 system.

In this article we will first tell you about the Egyptian numbering system, and what happened to zero, so that later you can better understand everything about the sacred triangle of Egypt. The modern name was given to a right triangle used to find right angles.

#### How did the Egyptian system work?

The Egyptian numerical system was expressed with 7 symbols and was based on multiples of 10. They were represented as follows: vertical bar (units), inverted U (represented tens), and coiled string (hundreds).

Being an addition system, more symbols could be added regardless of their position, and they can be read from left to right or backward, from bottom to top, or top to bottom.

Their symbols were always accompanied by figures of people, animals, or vessels to describe their operational area. Another of the most common characteristics of the Egyptians is that they used foot glyphs in the same direction as their writing to show subtraction and addition in the opposite position.

On the other hand, the hieratic system arose thanks to the development of Egyptian writing, where different symbols were used from 1 to 10, which changed to tens, hundreds, and so on.

#### What Happened to the Zero in the Egyptian Numerals?

Formerly zero was not known, not even by the Chinese, Babylonians, Egyptians, Greeks, or Romans who used other types of numbering systems. As a concept, zero does not represent anything, however, on some occasions, it can be a factor to change the value of other numbers. For example, a 14 represents fourteen objects, but if we add a zero it becomes 140.

The main function of zero in Egyptian numeration was in architecture, especially for construction. The symbol that represents zero was the same that was used to represent the word beauty.

#### Representation of Fractions

The Egyptian number system also allowed fractions to be represented. However, the system was limited to fractions with a numerator equal to one. That is, all fractions had the form 1/x.

There were also three exceptional hieroglyphic combinations to represent the fractions 1/2, 2/3, and 3/4.

#### The Sacred Triangle of Egypt

Triangles with lengths of 3, 4, and 5 are known as Sacred Triangles. Their measurements comply with the Pythagorean Theorem as 52=32+42, so they are considered right triangles.

Its interior angles are 90°, 36°, 52’ 12’’ and 53° 07’ 48’’.

That is why any triangle that has these characteristics is a Sacred Triangle. For example, if we want to know if the construction of a pyramid is based on a right triangle, all we have to do is look at the angle of inclination of its faces.

#### How else can it be calculated?

There are other formulas to calculate the sacred triangle of Egypt, all can be done easily and quickly.

One of them is: c= 2(a-b) = (a+a)-(b+b) where the larger leg is equal to twice the difference of the hypotenuse with the smaller leg.

Where c= 2(5-3) = (10)-(6) =4

Or there is also the following: a = 2c-b = c+c-b, where the hypotenuse is equal to the difference between the double of the larger leg and the smaller leg.

That is, a = 2c-b = 8-3 =5

In this way, the Sacred Triangle can be solved with addition or subtraction, which is not so easy to calculate in other right triangles.

If you want to calculate a sacred triangle knowing only one of its sides, you can use the following formula: b/c = ¾ which would be summarized as: b = c ¾

All you have to do is multiply the known leg by 3/4. Once we know the two legs we can calculate the hypotenuse by any of the two previous formulas.

#### What Else Was the Sacred Triangle Used For?

Sacred Triangles were also used to construct right angles since the ratio of 3-4-5 makes a right triangle. By having these measurements, the pyramids have 4 triangles in their structure, which are formed by the apothem, the base, and the height.

We know that the apothem of a pyramid that is built with sacred triangles is equal to the half sum of the side and the height of the pyramid. Remember that it is calculated by applying the Pythagorean theorem.

The first pyramid that was built and based on the sacred triangle was the pyramid of Khafre.

Other pyramids that initially can also be considered as built on the basis of sacred triangles, since they have an inclination angle of 531 07′ 48″, are the following:

• Khaefre (Kephren) in Giza. IV Dynasty.
• Userkaf in Sakkara. V Dynasty.
• Nefierekare in Abusir. V Dynasty.
• Djedkare (Izezi) in Sakkara. V Dynasty.
• Teti in Sakkara. VI Dynasty.
• Pepi I in Sakkara. VI Dynasty.
• Merenre in Sakkara. VI Dynasty.
• Pepi II in Sakkara. VI Dynasty.

Even though the Egyptians had a number system, they still did not have a specific use for the number zero. It is for this reason that in the Egyptian culture they were considered to not have zero.

```Sources
http://www.uco.es/users/ma1fegan/Comunes/recursos-matematicos/ Sistemas-numeracion/Sistema-de-numeracion-Egipto.pdf

https://www.cultura10 .org/egipcia/numeros/1-al-100/

https://www.monogra fias .com/trabajos88/numeros-egipto-y-renacimiento/numeros-egipto-y-renacimiento.shtml

Números egipcios: El sistema de numeración egipcio

https://es.wikipedia.org/wiki/Numeraci%C3%B3n_egipcia

http://www.icarito.cl/2010/03/103-879-9-2-los-numeros-y-las-civilizaciones.shtml/

Sistema de numeración egipcio

https://sobrehistoria .com/numeracion-egipcia-y-numeros-egipcios/

https://es.wikipedia.org/wiki/Matem%C3%A1tica_egipcia

https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_papyri/

1. Dani says:
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