Mathematics in Ancient Egypt

Ancient Egypt, one of the greatest early civilizations, made significant contributions to mathematics. Unlike the Babylonians, who used a base-60 system, the Egyptians developed a decimal-based number system. Their mathematical knowledge was deeply rooted in practical applications, such as engineering, surveying, construction, and administration. Egyptian mathematics was primarily documented in papyrus scrolls, such as the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus.

The Egyptian Numeral System

The Egyptian number system was decimal and based on powers of ten. It used hieroglyphic symbols to represent numbers, with separate symbols for 1, 10, 100, 1,000, and so on.

Key Features of the Egyptian Number System:

• Additive Notation – Numbers were written by repeating symbols (e.g., 23 was written as two 10s and three 1s).
• No Place Value – Unlike the Babylonian system, Egyptian numbers had no positional value.
• Hieratic Numerals – A simplified version of hieroglyphic numbers used for administrative purposes and calculations.
• Fractions – Egyptians primarily used unit fractions (fractions with a numerator of 1) and represented other fractions as sums of unit fractions. The Rhind Mathematical Papyrus contains extensive fraction tables used for calculations.

Despite these limitations, the Egyptians developed efficient arithmetic techniques, including multiplication, division, and fractions, often using doubling methods for complex calculations.

Egyptian Mathematics in Geometry

Geometry was a crucial part of Egyptian mathematics, primarily driven by the need to survey land after the annual flooding of the Nile River. Egyptian architects and engineers used geometric principles to construct pyramids, temples, and other structures.

Contributions to Geometry:

• Area Calculations – Formulas for calculating areas of rectangles, triangles, and circles.
• Approximation of Pi (π) – The Egyptians estimated π as 3.16, which was fairly accurate for practical construction.
• The Use of Right Triangles – Evidence suggests knowledge of Pythagorean triples for ensuring right angles in construction.
• Volume Calculations – The Moscow Mathematical Papyrus contains problems related to finding the volume of truncated pyramids and cylindrical granaries.
• Surveying Techniques – The Egyptian “rope stretchers” used knotted ropes to create right angles, which was essential for building and dividing land.

The Great Pyramid of Giza is an example of Egyptian mastery of geometry, with its precise alignment and proportional structure.

Applications of Mathematics in Daily Life

Egyptian mathematics was not purely theoretical but had direct applications in daily life:

• Taxation and Accounting – Scribes used mathematical calculations for tax collection, land measurement, and inventory management.
• Construction and Architecture – Engineers applied mathematical techniques to design and construct monumental structures.
• Agricultural Planning – Farmers used mathematics to measure land plots and distribute water efficiently.
• Medicine and Healing – Some medical papyri, such as the Ebers Papyrus, included mathematical calculations for dosage and treatment measurements.
• Astronomy and Calendars – Egyptians used mathematical calculations to track celestial cycles, creating a 365-day calendar based on solar observations.

---

Mathematics in Ancient Egypt was deeply tied to practical applications. Their numeral system, geometric understanding, and administrative calculations influenced later Greek and Roman mathematics. The Egyptians demonstrated an impressive ability to solve problems related to construction, land division, and commerce, ensuring the success of their civilization for thousands of years.

In the next post, we will explore how Greek mathematicians formalized mathematical concepts into a structured discipline, paving the way for the development of deductive reasoning and formal proofs.

Stay tuned for the next post: Mathematics in Ancient Greece!