# Why Ancient Egyptians Preferred Some Sum-of-Inverses Representations of Fractions?

## Publication Date

11-2020

Technical Report: UTEP-CS-20-109

Published in Applied Mathematical Sciences, 2020, Vol. 14, No. 18, pp. 859-865.

## Abstract

Ancient Egyptians represented a fraction as a sum of inverses of natural numbers, with the smallest possible number of terms. In our previous paper, we explained that this representation makes sense since it leads to the optimal way of solving a problem frequently mentioned in the Egyptian papyri: dividing bread between workers. However, this does not explain why ancient Egyptians preferred some representations with the same number of terms but not others. For example, to represent 2/3, they used the sum 1/2 + 1/6 but not the sum 1/3 + 1/3 with the same number of terms. In this paper, we use a more detailed analysis of the same dividing-bread problem to explain this preference. Namely, in our previous explanation, we assumed that each cut requires the same amount of time. If we take into account that in practice, each consequent cut of the same loaf -- just like any other repetitive action -- takes a little less time, we get the desired explanation of why ancient Egyptians preferred, e.g., 1/2 + 1/6.

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