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These have been called "Horus-Eye fractions" after a theory (now discredited) [4] that they were based on the parts of the Eye of Horus symbol. They were used in the Middle Kingdom in conjunction with the later notation for Egyptian fractions to subdivide a hekat , the primary ancient Egyptian volume measure for grain, bread, and other small ...
The presence of various Horus eye fractions is familiar from the rest of the papyrus, and the table seems to consider feed estimates for birds, ranging from largest to smallest. The "5/3 hinu" portions at the top of the table, specifically its factor of 5/3, reminds one of the method for finding s in problem 82.
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Möller hypothesized that the Horus-eye hieroglyphs were the original hieroglyphic forms of the hieratic fraction signs, and that the inner corner of the eye stood for 1/2, the pupil for 1/4, the eyebrow for 1/8, the outer corner for 1/16, the curling line for 1/32, and the cheek mark for 1/64.
An interesting feature of ancient Egyptian mathematics is the use of unit fractions. [7] The Egyptians used some special notation for fractions such as 1 / 2 , 1 / 3 and 2 / 3 and in some texts for 3 / 4 , but other fractions were all written as unit fractions of the form 1 / n or sums of such unit ...
Pesu of 1000 loaves. Horus-eye fractions. 21 Mixing of sacrificial bread. 22 Pesus of loaves and beer. Exchange. 23 Computing the work of a cobbler. Unclear. Peet says very difficult. 24 Exchange of loaves and beer. 25 Solve the equation + =. Elementary and clear.
The use of the Horus eye fractions shows some (rudimentary) knowledge of geometrical progression. [1] One unit was written as 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64.
The answers were written in binary Eye of Horus quotients and exact Egyptian fraction remainders, scaled to a 1/320 factor named ro. The second half of the document proved the correctness of the five division answers by multiplying the two-part quotient and remainder answer by its respective (3, 7, 10, 11 and 13) dividend that returned the ab ...
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