Ancient Mathematical Texts

The Rhind Papyrus is a famous papyrus written by the scribe Ahmes (Ahmose) around 1650 BC. It was copied from a now lost text from the reign of king Amenemhat III (12th dynasty) 1500 years prior to Ahmose’s birth. His papyrus is one of the best known examples of advanced Egyptian mathematics; mathematician-priests of the Nile valley knew no peers. It was found during illegal excavations in or near the Ramesseum. It has been housed in the British Museum since 1865 along with the Egyptian Mathematical Leather Roll.

The most ancient mathematical texts available are: The Rhind Mathematical Papyrus , is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1650 BC. The British Museum, where the papyrus is now kept, acquired it in 1864 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind there are a few small fragments held by the Brooklyn Museum in New York. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus

The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt and is the best example of Egyptian mathematics. It was copied by the scribe Ahmes (i.e., Ahmose; Ahmes is an older transcription favoured by historians of mathematics), from a now-lost text from the reign of king Amenemhat III (12th dynasty). Written in the hieratic script, this Egyptian manuscript is 33 cm tall and over 5 meters long, and began to be transliterated and mathematically translated in the late 19th century.

In 2008, the mathematical translation aspect is incomplete in several respects. The document is dated to Year 33 of the Hyksos king Apophis and also contains a separate later Year 11 on its verso likely from his successor, Khamudi.

The first part of the Rhind papyrus consists of reference tables and a collection of 20 arithmetic and 20 algebraic problems. The problems start out with simple fractional expressions, followed by completion (sekhem) problems and more involved linear equations

The second part of the Rhind papyrus consists of geometry problems. Peet referred to these problems as "mensuration problems". Problems 41 – 46 show how to find the volume of both cylindrical and rectangular based granaries. In problem 41 the scribe computes the volume of a cylindrical granary. Given the diameter (d) and the height (h), the volume V is given by: V = [(1 - 1 / 9)d]2h In modern mathematical notation (and using d = 2r) this clearly equals V = (8 / 9)2d2h = 256 / 81r2h The quotient 256/81 approximates the value of p as being ca. 3.1605

The third part of the Rhind papyrus consists of a collection of 24 problems. Problem 61 consists of 2 parts. Part 1 contains multiplications of fractions. Part b gives a general expression for computing 2/3 of 1/n, where n is odd. In modern notation the formula given is 2/(3n) = 1/(2n) + 1/(6n )