Remarks on the Egyptian 2/D table in favor of a global approach (D composite number)

Lionel Bréhamet (1)

1 Retired from CEA/Saclay

Egyptian decompositions of 2/D as a sum of two unit fractions are studied by means of certain divisors of D, namely r and s. Our analysis does not concern the method to find r and s, but just why the scribes have chosen a solution instead of another. A comprehensive approach, unconventional, is developed which implies having an overview of all pre-calculated alternatives. Difference s-r is the basis of the classification to be examined before taking the right decisions, step by step, if difficulties are encountered. An adequate adjustment of s-r limits the number of all alternatives to 57, what is very few. A four-component generator (2/3, 2/5, 2/7, 2/11) operates as a (hidden) mother-table. Adding few logical rules of common sense is enough to explain the reasons of the Egyptian choices. Even the singular case 2/95, which can not be decomposed into two fractions but only into three, reveals a doubly justified explanation.

Mots clés: Rhind Papyrus; 2/n table; Egyptian fractions

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Lionel Bréhamet. Remarks on the Egyptian 2/D table in favor of a global approach (D composite number). 2014. ⟨hal-00968948⟩