Date: Aug 14, 2012 2:30 PM
Author: Milo Gardner
Subject: Kahun Papyrus
A bird valuation method was reported for a commodity purpose. Scaled hekat bird-feeding rates were used by 200 year older Kahun Papyrus

http://planetmath.org/encyclopedia/KahunPapyrusAndArithmeticProgressions.html (KP).

The KP raw data considered relative values of 12 fowls in terms of a set-ducks:

a. 3 re-geese unit value 8 set-ducks = 24

b. 3 terp-geese unit value 4 set-ducks = 12

c. 3 Dj. Cranes unit value 2 set-ducks = 6

d. 3 set-duck unit value 1 set-duck = 3

total value 45 set-ducks.

The data meant that 30 day feeding of grain valued each fowl.

The KP began with a short 2/n table. A longer 2/n table was reported in the Rhind Mathematical Papyrus:

http://rmprectotable.blogspot.com/

After the 2/n table RMP 83, one of 87 problems, discussed the bird-feeding scaled hekat method another way:

http://planetmath.org/encyclopedia/AhmesBirdFeedingRateMethod.html

Note that the KP and RMP required 2/n table rational numbers that were scaled to a hekat volume unit and 1/320 of a hekat reminders named ro. The same class of scaled hekat and ro remainders were written down in the older Akhmim Wooden Tablet:

http://en.wikipedia.org/wiki/Akhmim_wooden_tablets

facts that show Middle Kingdom scribe made minor modification to the system. One exception was discussed in RMP 47. Likely 4-ro remainders were implied by an unsolved aspect that mixed two 400-hekat multiplications (by 1/10 and 1/20) found (10) 4-hekat and (5) 4-hekat, respectively, with eight 100-hekat multiplications (by 1/30, 1/40, 1/50, 1/60, 1/70, 1/80, 1/90 and 1/100) found 1-hekat quotients and 1-ro remainders. The scribal method followed the AWT two-part number pattern, and two 400-hekat multiplications (by 1/10 and 1/20) found 4-hekat quotients (4-ro remainders were not cited, but would have been required if 1/30 was the multiplier).