Les mathématiques de l'Égypte ancienne. Numération, métrologie, arithmétique, géométrie et autres problèmes.

Michel, Marianne [UCL]

The ancient Egyptians also contributed to build the great edifice of Mathematical Sciences but where exactly do their mathematics fit in and what are their characteristics? This thesis tries to answer these two questions. The corpus analyzed includes the major sources of the Middle Kingdom as well as more recent documents such as demotic papyri. This way, it is possible to highlight some continuities of reasoning or, conversely, some changes in procedures. The content of these documents has been subjected to a thorough study described here in a didactic way that exposes the problems discussed, their original presentation in hieratic, their transposition into hieroglyphics, their French translation. The problems have been classified and treated according to their nature: arithmetic problems, geometry problems relating to surfaces, volumes and slope calculations, problems relating to specific areas. Previous analyses have been discussed and a personal and innovative interpretation has been added on some occasions. The text is illustrated extensively and a glossary of terms used in the Egyptian mathematical corpus provides common and specific meanings to the documents studied.