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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 ...
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.
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.
The table consisted of 26 unit fraction series of the form 1/n written as sums of other rational numbers. [9] The Akhmim wooden tablet wrote difficult fractions of the form 1/n (specifically, 1/3, 1/7, 1/10, 1/11 and 1/13) in terms of Eye of Horus fractions which were fractions of the form 1 / 2 k and remainders expressed in terms of a ...
The mathematical writings show that the scribes used (least) common multiples to turn problems with fractions into problems using integers. In this connection red auxiliary numbers are written next to the fractions. [8] The use of the Horus eye fractions shows some (rudimentary) knowledge of geometrical progression.
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 ...
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 binary quotient used Eye of Horus numbers. The remainder scaled Egyptian fractions to 1/320 units named ro. Quotients and unscaled remainders were obtained for the dja, ro and other units when the divisor n was greater than 64. For example, one the 1/320 ro unit was written by Ahmes by solving 320/n ro. Gillings cites 29 examples of two ...