Ancient African Mathematics: Fractions, Algebra and Geometry

Continued from

Ancient African Mathematics: Measuring and Counting

“Moscow” Papyrus (2000 BC):

A copy of the "Moscow" papyrus in "hieratic" text with a clearer rendering below in "hieroglyphs"

A copy of the “Moscow” papyrus in “hieratic” text with a clearer rendering below in “hieroglyphs”

Housed in Moscow’s Pushkin State Museum of Fine Arts, the so- called “Moscow” papyrus, was purchased by Vladimir Golenishchev sometime in the 1890s. Written in hieratic from perhaps the 13th dynasty in Kemet, the papyrus is one of the world’s oldest examples of use of geometry and algebra. The document contains approximately 25 mathematical problems, including how to calculate the length of a ship’s rudder, the surface area of a basket, the volume of a frustum (a truncated pyramid), and various ways of solving for unknowns.

“Rhind” Mathematical Papyrus (1650 BC):

A page from the "Rhind" Mathematical Papyrus in "Hieratic" text.

A page from the “Rhind” Mathematical Papyrus in “Hieratic” text.

Purchased by Alexander Rhind in 1858 AD, the so-called “Rhind” Mathematical Papyrus (shown below) dates to approximately 1650 BC and is presently housed in the British Museum. Although some Egyptologists link this to the foreign Hyksos, this text was found during excavations at the Ramesseum in Waset (Thebes) in Southern Egypt, which never came under Hyksos’ rule. Written by the scribe, Ahmose, in the “Hieratic” script, the text reads as follows: “Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries…all secrets… This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy…” The first page contains 20 arithmetic problems, including addition and multiplication of fractions, and 20 algebraic problems, including linear equations. The second page shows how to calculate the volume of rectangular and cylindrical granaries, with pi (Π) estimated at 3.1605. Tere are also calculations for the area of triangles (slopes of a pyramid) and an octagon. The third page continues with 24 problems, including the multiplication of algebraic fractions, among others.

Timbuktu Mathematical Manuscripts (1200s AD):

A Mathematical manuscript from Medieval Timbuktu.

A Mathematical manuscript from Medieval Timbuktu.

Timbuktu in Mali is home to one of the world’s oldest universities, Sankore, which had libraries full of manuscripts mainly written in Ajami (African languages, such as Hausa in this case, written in a script similar to “Arabic”) in the 1200s AD. When Europeans and Western Asians began visiting and colonizing Mali from 1300s-1800s AD, Malians began to hide the manuscripts in basements, attics and underground, fearing destruction or theft by foreigners. This was certainly a good idea, given Europeans’ history of stealing and/or destroying texts in Kemet and other areas of the continent. Many of the scripts, such as the one shown below, were mathematical and astronomical in nature. In recent years, as many as 700,000 scripts have been rediscovered and attest to the continuous knowledge of advanced mathematics and science in Africa well before European colonization.

By: Ta Neter.org

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