How Did the Ancient Egyptians Do Math? Was It Better Than Ours?

Ancient Egyptians had a unique approach to mathematics that was practical and closely tied to their daily lives, particularly in areas like agriculture, trade, and construction. This essay provides an overview of their mathematical practices, highlighting both their practical applications and the differences with modern mathematics.

Numerical System

The Egyptians used a decimal base-10 system for counting, which is similar to our own. They represented numbers using hieroglyphs for different powers of ten, providing a fascinating window into their numerical system and the practical contexts in which it was used.

Symbols

1 - A single stroke 10 - A heel bone 100 - A coil of rope 1000 - A lotus flower 10,000 - A sequence of tortoises 100,000 - A tadpole, or frog 1,000,000 - A god with arms raised

Arithmetic

Addition and Subtraction: The Egyptians performed addition and subtraction using a method called exhaustive doubling.

Multiplication and Division: Multiplication was often done through a process of doubling and repeated addition. Division was handled through a method of figuring out how many times a number could be subtracted from another.

Fractions

Unit Fractions: The Egyptians primarily worked with unit fractions, fractions with 1 as the numerator (e.g., 1/2, 1/3). They expressed other fractions as sums of unit fractions, which was quite different from the way we use fractions today. For example, 2/5 was written as 1/3 1/15.

Geometry and Practical Applications

Geometry was essential for land surveying and construction, especially in building the pyramids. The ancient Egyptians understood basic geometric concepts and could calculate areas and volumes. Their practical methods for creating right angles were crucial for ensuring the structural integrity of their monumental constructions.

Pythagorean Theorem: Although they did not formulate the Pythagorean theorem as we know it, they had practical methods for constructing right angles, which were essential for accurate construction.

Comparison to Modern Mathematics

Efficiency and Complexity: While the ancient Egyptian system was highly effective for their needs, it lacked the abstract concepts and efficiency of modern mathematics. For instance, the use of unit fractions can make calculations more cumbersome compared to our decimal system.

Symbolism and Notation: Modern mathematics has a more systematic notation and a broader range of concepts, including algebra, calculus, and complex numbers. This allows for more advanced problem-solving and a deeper understanding of mathematical principles.

Conclusion

In summary, ancient Egyptian mathematics was highly practical and suited to the societal needs of their time. However, it was not as abstract or efficient as modern mathematics. The practical and symbolic differences between these two systems offer valuable insights into the evolution of mathematical thought and the diversity of human ingenuity.