The Rhind Mathematical Papyrus (RMP) is one of the most significant surviving records of ancient Egyptian mathematics. Dating to approximately 1550 BC during the Second Intermediate Period, the document was copied by a scribe named Ahmes from an even older text originating in the reign of Amenemhat III. The papyrus is divided into three main sections: arithmetic and algebra, geometry, and a miscellany of tables and practical problems. It serves as a primary source for understanding how ancient Egyptians handled complex calculations involving trade, construction, and resource management.

A photograph of the ancient Rhind Mathematical Papyrus showing Egyptian hieroglyphs and mathematical notations.
The Rhind Mathematical Papyrus, a primary source for understanding ancient Egyptian arithmetic and geometry.en.wikipedia.org

This image provides a visual reference for the physical document described in the opening paragraph.

One of the most distinctive features of the RMP is its use of unit fractions—fractions with a numerator of one. The document contains a famous 2/n table, which expresses the division of 2 by odd numbers ranging from 3 to 101 as sums of unit fractions. For example, the papyrus records the division of 2 by 101 as 1/101 + 1/202 + 1/303 + 1/606. Beyond these tables, the papyrus includes 'aha' problems, which are essentially linear equations. One such problem involves solving for an unknown value (x) in an equation like x + 1/3 x + 1/4 x = 2. The document also demonstrates early geometric principles, such as calculating the volume of cylindrical and rectangular granaries and approximating the area of a circle by assuming a specific ratio between a circle and its circumscribing square.

A mathematical equation showing the division of 2 by 101 as a sum of unit fractions.
An example of the unit fraction calculations found in the 2/n table of the papyrus.en.wikipedia.org

This figure illustrates the specific example of the 2/101 division mentioned in the second paragraph.

While the RMP provides a sophisticated look at mathematical theory, it also highlights the practical constraints of the era. Much of the text is dedicated to dimensional analysis, showing how to convert between various Egyptian units of volume, such as the heqat and the ro. However, the document is not without its flaws; some of the later problems in the miscellany section are noted by modern scholars to be plagued by ambiguity and inaccuracy. Furthermore, while the scribe Ahmes presented the work with grandiose claims of revealing 'all secrets,' some researchers suggest the document may have functioned more as a student's notebook for practicing application exercises under a teacher's guidance.

A complex table of mathematical calculations involving fractions and Egyptian units like heqat and ro.
A detailed table demonstrating the conversion of fractions into Egyptian units and unit fractions.en.wikipedia.org

This table illustrates the sophisticated dimensional analysis and unit conversions discussed in the final paragraph.