Binary Numeration: From Ancient Egypt to a 19th Century French Mathematical Recreation

Abstract

This article focuses on the use of base 2 in two historical contexts: ancient Egypt during the Middle Kingdom and 19th-century France. In ancient Egypt, base 2 was central to the “duplation” algorithm to multiply two numbers. In 19th-century France, it featured in mathematical recreations by Charles-Ange Laisant and Édouard Lucas. Duplation in ancient Egypt involved doubling a number successively, leveraging the binary nature of the numbering system for rapid calculations. In France, Laisant and Lucas contributed to mathematical recreations rooted in base 2, popularizing mathematics and engaging the public. The article aims to present these historical resources, highlighting their educational potential. It suggests integrating these examples into mandatory education from age 9 onwards, offering students a practical understanding of mathematics and its history. However, specific teaching methods are left to the reader’s discretion.