One thing I found really interesting was that the complete eye represented 1, but the sum of the fractions that the individual parts represented was only 63/64, which was rounded to 1. If the Egyptians had added more details, and assigned them fractional values, they would have gotten a closer approximation. I thought that there was an interesting parallel between the level of detail of the drawing and the nearness of the approximation - a perfectly detailed drawing would involve an infinite number of components, which would give an infinite geometric series with sum 1! This could be an interesting way of introducing infinite geometric series to students.
However, according to Jim Ritter, were not associated with the Eye of Horus by the ancient Egyptians. He believes that this association was constructed by Egyptologists in the 20th century - in particular, Georg Möller was the first to claim the Eye of Horus as the origin of the symbols for these fractions, and his claims were repeated in academia without much scrutiny. Ritter shows that there is not sufficient evidence for Möller's claim, and that the Eye of Horus and the symbols for these fractions actually had independent origins.
(Ritter, Jim (2002). "Closing the Eye of Horus: the Rise and Fall of 'Horus-Eye Fractions'". In Steele, J.; Imhausen, A. (eds.). Under One Sky: Astronomy and Mathematics in the ancient Near East. Münster: Ugarit-Verlag. pp. 297–323.)
Zach, I appreciate your inclusion of Ritter's work on the Eye of Horus. This is a great example of the importance of revisiting and challenging historical claims.
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