Reisner Papyrus

The Reisner Papyri date to the reign of Senusret I, who was king of Ancient Egypt in the 19th century BCE. The documents were discovered by Dr. G.A. Reisner during excavations in 1901-04 in Naga ed-Deir in southern Egypt. A total of four papyrusrolls were found in a wooden coffin in a tomb.

Several sections contain tables with mathematical content.

Section G consistes of 19 lines of text. In the first line the column headings are given: length (3w), width (wsx), thickness or depth (mDwt), units, product/volume (sty), and in the last column the calculations of the number of workers needed for the work of that day.

The format of the table in section H is similar to that of section G. In this document only the column heading product/volume is used however, and there is no column recording the number of workers required.

Section I closely resembles section H. Columns recording the length, width, height and product/volume are presented. In this case there are no column headings written down by the scribe. The text is damaged in places but can be reconstructed. The units are cubits except where the scribe mentions palms. The square brackets indicate added or reconstructed text.

Gillings and other scholars accepted 100-year-old views of this document, with several of the views being incomplete and misleading. Two of the documents, reported in Tables 22.2 and 22.2, a detail a division by 10 method, a method that also appears in the Rhind Mathematical Papyrus. Labor efficiencies were monitored by applying this method. For example, how deep did 10 workmen dig in one day as calculated in the Reisner Papyrus, and by Ahmes 150 years later? In addition, the methods used in the Reisner and RMP to convert vulgar fractions to unit fraction series look similar to the conversion methods used in the Egyptian Mathematical Leather Roll.

Gillings repeated a common and incomplete view of the Reisner Papyrus. He analyzed lines G10, from table 22.3B, and line 17 from Table 22.2 on page 221, in the "Mathematics in the Time of the Pharaohs", citing these Reisner Papyrus facts: divide 39 by 10 = 4, a poor approximation to the correct value, reported Gillings.

Gillings fairly reported that the scribe should have stated the problem and data as:

Yet, all other the division by 10 problems and answers were correctly stated, points that Gillings did not stress. Table 22.2 data described the work done in the Eastern Chapel. Additional raw data was listed on lines G5, G6/H32, G14, G15, G16, G17/H33 and G18/H34, as follows:

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