Ancient Egyptian mathematics is mathematics developed and used in Ancient Egypt from about 3000 to 300 BC, from the Kingdom of Ancient Egypt to roughly the beginning of Hellenistic Egypt. The ancient Egyptians used a number system to count and solve written mathematical problems, often involving multiplication and fractions. Evidence of Egyptian mathematics is limited to the few surviving sources written on papyrus. It is known from these texts that the ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes, useful for architectural engineering, and algebraic concepts such as the fixed-intersect method (Latin: regula falsi, English: false position method) and quadratic equations.
Written evidence of the use of mathematics with ivory labels found at Tomb U-j in Abydos dates back to at least 3200 BC. These tags seem to have been used as tags for grave goods, and some were inscribed with numbers. Further evidence of the use of the numeral system can be found at Narmer Macehead, which shows the submission of 400.000 oxen, 1.422.000 goats and 120.000 prisoners.
Drawings at Narmer Macehead
Evidence for the use of mathematics in the Old Kingdom (2690-2180 BC) is scarce, but some conclusions can be drawn from inscriptions on the wall near a mastaba at Meidum, which give directions for the inclination of the mastaba. The lines in the diagram are spaced one cubit and show the use of this unit of measure.
Use of Papyrus
The earliest true mathematical documents are from the 12th Dynasty (circa 1990-1800 BC). The Moscow Papyrus, the Egyptian Mathematical Leather Roll, the Lahun Mathematical Papyrus, which are a much larger part of the Kahun Papyrus and the Berlin Papyrus 6619 collection, date to this period. Dating to the Second Intermediate Period (1650 BC), the Rhind Papyrus is said to be based on a mathematical text older than the 12th dynasty.
The Moscow Mathematical Papyrus and the Rhind Papyrus are referred to as mathematical problem texts. They consist of a set of problems with solutions. These texts may have been written by a teacher or a student engaged in solving typical math problems.
An interesting feature of ancient Egyptian mathematics is the use of unit fractions.
The Egyptians used some special notations for fractions, such as 1/2 , 1/3 and 2/3, and in some texts for 3/4, but other fractions are all written as unit fractions of the 1/n form or sums of such unit fractions.
Writers used tables to help them work with these fractions. For example, the Egyptian Mathematical Leather Roll is a table of unit fractions expressed as the sum of other unit fractions. The Rhind Papyrus and some other texts include 2/n tables. These tables allowed the authors to rewrite any part of the 1/n form as the sum of unit fractions.
Mathematical problems of the New Kingdom (ca. 1550–1070 BC) are mentioned in the literary Papyrus Anastasi I, and land measurements are recorded in the Papyrus Wilbour from the time of Ramses III. In the workers' village of Deir el-Medina, several ostraca (a piece of pottery used as a writing surface) were found, in which a record amount of mud was transported when the tombs were quarried.