Why And How Did The Ancient Egyptians Use Mathematics

golden ratio egypt

Ancient Egyptian Mathematicians used the same formulas and symbols as today to help them understand and interpret the world around them. In fact, we can see evidence of this ancient form of math, as examples of ivory labels found at Abydos. Moreover, ancient Egyptians used these pieces to describe fractions and calculate them, as we can see in the Narmer macehead. These pieces contain 84 different calculations, and the Egyptians used this method to record the value of their offerings.

There are many great things about the history of ancient Egypt, and one of these is the use of math. This math was developed and used in Ancient Egyptian society, from roughly 3000 BCE to 300 BCE, during the Old Kingdom and Hellenistic Egypt. If you’re interested in the history of mathematics, then you should know about this fascinating culture. This is the first civilization to have developed and used math. But what about the methods they used?

The Ancient Egyptians had very accurate representations of numbers, and the most ancient versions of the decimal system were written with offsets and the values of fractions. The numbers were represented by an arch, a coil of rope, a finger, or a god with raised arms. As a result, they used a ten-digit system to determine the volume of an oxen-shaped pyramid or a squat circle. Similarly, they knew that the height of the frustum of a square pyramid was equal to one-third of its circumference. They used hieroglyphics and a lotus plant to represent ten-digit numbers to get the correct fraction.

Why And How Did The Ancient Egyptians Use Mathematics 1
The system of Egyptian Numerals

Ancient Egyptian Mathematics

Ancient Egyptian mathematics was a vital part of life in ancient Egypt. The system was used and developed from 3000 BCE to roughly the beginning of Hellenistic Egypt. This is where we can see the first signs of geometrical patterns in architecture. Today, we can see a lot more advanced math in our modern world, such as the use of fractions. The development of these systems is particularly fascinating. If you’re interested in ancient Egypt, you might be interested in these tools and their applications.

Early mathematicians were familiar with the golden ratio, which is length to width. The pyramids were probably built to maximize their aesthetic value, but it is also possible that they were the first to observe it. It is also possible that the Egyptians knew how to calculate the volume of a truncated pyramid and figured out that the ratio was precisely 1:1.618. Although they may not have known about the golden number, they were undoubtedly aware of it.

golden ratio egypt
egypt pyramids and golden ratio

In addition to writing, ancient Egyptians were also adept at multiplication. Their approach to multiplying numbers relied on a repeated doubling of the multiplicand. This process, known as binary arithmetic, was connected to the Old Kingdom. 

The multiplicand was written next to a figure or number, such as one or two, and the result was a number called two. The doubling process was repeated until the multiplier reached half its value. Then, the numbers were repeatedly subtracted, and a single calculation was chosen to add to the others.

Advancements in Math and Science Made by Ancient Egyptians

There is debate about the importance of mathematics to ancient Egyptians. Egyptologists argue that it was purely practical and had only practical uses. However, Greek philosophers like Pliny and Herodotus consistently mention the Egyptians as the origin of their theoretical mathematics. 

  • They also attribute the development of geometry to the Egyptians, pointing out that circle and rectangle areas are the same.
  • The ancient Egyptians also developed a system of weights. 
  • The ancient Egyptians understood volume and geometry and created the first irrigation system. The Egyptians also cultivated crops using a plow drawn by an ox.
  • The ancient Egyptians made outstanding contributions to math and science. They developed the decimal system and used it to keep track of their business. 
  • Fun fact: The oxen were drawn in two gauges, one heavy and the other lighter and designed a system for irrigation.
  • They even figured out how to divide a circle into 360 degrees.
  • Ultimately, the ancient Egyptians understood the value of astronomy.
  • The ancient Egyptians contributed to the modern math world with their discoveries of decimals, fractions, negative numbers, and the value of Pi.
Why And How Did The Ancient Egyptians Use Mathematics 2
Pi

  • They also developed a system of weights and divided it into 360 degrees.
  • Had methods to add and subtract and understood how fractions and volumes worked.
  • They created a numbering scheme and a calendar based on lunar cycles.
  • They used a method called false position and learned to write down numbers.

The ancient Egyptians contributed to the development of modern mathematics. 

They conceived the first number system in history. In addition, they used a number system to store their knowledge. The Egyptians were also the first people to develop a numerical notation. They set the number system and created a variety of mathematical tools.

How is Egyptian Mathematics Used Today?

Egypt’s ancient mathematics is still relevant today, but how is it applied?

The term “Egyptian triangle” was given to a specific triangle with three sides, the 3-4-5 right triangle. The name derives from its functions in the construction of monuments and stonework. In addition to the geometrical shapes, the mathematical principles that Egyptian builders developed are still used today. 

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Egyptian triangle

The following are some of the most notable examples.

The first Egyptians used a binary system to multiply numbers. This is the basis for the concept of multiplication, which is still used today. The binary system has only two levels: 0 and 1.

The doubling and halving methods were both effective for this purpose. Egyptians would subtract one and halve the first number to double a number. Thus, the mathematicians of the Middle Kingdom did not use the decimal system in multiplication and division.

Ancient Egyptians also made extensive use of the concept of decimal systems. In fact, they used a decimal system with no symbol for zero, which helped them calculate quantities. Their numbers were simple, but multiplication was complex and time-consuming. For example, Egyptians were only able to add and subtract in the ancient world. 

Then, they had to double or halve numbers, which required them to use hieroglyphics.

Early Egyptians did not use decimals to calculate numbers. They could only say a third and fourth, but they did not have a fraction that allowed them to use fractions systematically. Even the simplest fractions are two-thirds, three-quarters, and a half. It’s not so difficult to figure out the remainder of any given number.

Early Egyptians often used fractions to calculate quantities in everyday life. They also knew how to divide and multiply by two. They also had a complex method of addition, which included multiplication and subtraction. But unlike today, they used a number system based on whole numbers. Using these fractions, the Egyptians would find an answer that was only a percentage of a percent. The Egyptians were obstinate, but they understood fractions and did not have any problems.

The Development of Mathematics in Egyptian Society

It is widely accepted that Egypt was the first civilization to develop a system of numbers. In fact, the oldest mathematical text from Egypt is called Moscow papyrus, which contains problems relating to distributing bread and beer as wages. It dates from around 2000 to 1800 BCE. While its use was limited, it was still an advanced form of mathematical thinking. The ancient Egyptians had a sophisticated understanding of numbers, and their earliest written language is still a testament to their knowledge of the subject.

The Egyptians developed a complex system of fractions. They developed numerals based on the symbol Eye of Horus. Each part of the Eye of Horus represented a different fraction, half of the previous one. The eye also served as the first known example of a geometric series. In fact, it is possible to trace the history of fractions back to the Middle Kingdom. Even though they did not develop a sophisticated system of mathematical notation, their mathematics was beneficial for commerce.

The effect of mathematics in Egyptian society was significant for practical purposes. 

The evolution of unit fractions on papyrus is the first known example of unit fractions. 

The Eye of Horus symbol was used to represent units on papyrus. 

Each part of the Eye of Horus represented a different fraction, half of the previous. Similarly, the Eye of Horus symbol was an example of a geometric series.

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eye of horus mathematics

The Egyptians developed a base-ten numeration system as early as 2700 BCE. The symbols were the heel-bone symbol for units, a spiraling rope for hundreds, and a lotus plant for thousands. Increasing the powers of ten and a million required more symbols, including a single character for a thousand. The knowledge of geometry helped them construct better buildings.

The development of mathematics in Egyptian society was important for trade. The knowledge of numbers helped assess taxes and teach children to count. 

Furthermore, knowledge of three dimensions was essential for constructing better buildings. Hence, the development of mathematics in Egypt was an important step toward modernizing the country. 

The ancients had a great need to learn the use of numbers

In addition to its practical applications, the development of mathematics in Egypt was also crucial for its social, economic, and cultural life. As the Egyptians used hieroglyphs to express numbers, they could control resources, manage labor and thus monetize them. However, their numerical systems were not limited only to constructing better buildings.

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