In Ancient Egyptian most fractions were written as the sum of two or more unit fractions (a fraction with 1 as the numerator), with scribes possessing tables of answers (see Rhind Mathematical Papyrus 2/n table). Thus instead of 3/4, one could write 1/2 + 1/4.
In the Ancient Egyptian measurement system, the Eye of Horus defined Old Kingdom number one (1) = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, by throwing away 1/64 for any rational number (1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 0.96875 = 31/32, 31/32 + 1/64 = 0.984375 = 63/64 ≈ 1). Eye of Horus numbers created six-term rounded-off numbers. The Old Kingdom definition has dropped a seventh term, a remainder 1/64, that was needed to report exact series. During the Middle Kingdom that included the eleventh through fourteenth dynasties, exact series definitions and applications were often written by 6-terms, or less. The Egyptian fraction notation scaled to volume unit remainders to 1/320 hekat. For example, the Egyptian Mathematical Leather Roll, the RMP 2/n table and the Akhmim Wooden Tablet wrote binary quotients and scaled remainders. The metaphorical side of this information linked Old Kingdom fractions 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64, to separate parts of the eye.
In the Middle Kingdom the 1/64 symbol denoted “rest” and “healing” as connected to the hekat, with the word dja being attached.
The “Eye of Horus” fractions were further discussed in the Egyptian Mathematical Leather Roll following elementary definitions that built the Egyptian fractionsystem. Weights and measure subunits of a hekat were also connected to Eye of Horus numbers in the quotient, and as an exact remainder, the remainder including an Egyptian fraction and a ro unit, correcting the Eye of Horus 1/64 roundoff error. The ro unit, 1/320 of a hekat, is cited in the Rhind Mathematical Papyrus and applied in the medical texts, i.e. Ebers Papyrus in two ways. The first replaced the hekat by a unity, 64/64 (in RMP 47, 82 and 83), and the second by 320 ro (in RMP 35–38). Exact divisions of 64/64 by 3, 7, 10, 11 and 13, written as 1/3, 1/17, 1/10, 1/11 and 1/13 multipliers, are also found in the Akhmim Wooden Tablet.
- weblyra likes this
- weblyra reblogged this from enjoy-the-silence
- shalia19 reblogged this from enjoy-the-silence
- shalia19 likes this
- supernalist likes this
- madamegreentea reblogged this from enjoy-the-silence
- madamegreentea likes this
- unchangedresilience reblogged this from enjoy-the-silence
- laineymariee reblogged this from enjoy-the-silence
- kurenaiwataru reblogged this from vivace-joyous
- sirlowkey reblogged this from vivace-joyous
- vivace-joyous reblogged this from enjoy-the-silence
- vivace-joyous likes this
- enjoy-the-silence posted this