Gillings gives the scribes calculation as follows:

The scribe writes 1 divided by 3 1/7 equals 1/22 divided by 1/7.

1/22 is doubled to 1/11, producing: 1 divided by 3 1/7 equals 1/11 divided by (1/4 plus 1/28)

1/11 is doubled to 1/6 plus 1/66, producing: 1 divided by 3 1/7 equals (1/6 plus 1/66) divided by (1/2 plus 1/14).

The scribe writes this as:

1 -------------------------- 3 1/7

------------------------------------------

1/22------------------------ 1/7
1/11------------------------ 1/4 plus 1/28
1/6 plus 1/66--------------- 1/2 plus 1/14

All of the fractions from the right hand side of the last three rows add up to one. Gillings points out elsewhere in the RMP an awareness of 1/7 plus 1/14 plus 1/28 equals 1/4, so here, 1/2 plus 1/4 plus 1/4 equals one. (By our reckoning, 1/7 doubled is 2/7 and 2/7 doubled is 4/7. 1/7 plus 2/7 plus 4/7 = 7/7 = 1).

All of the fractions on the left hand side of the bottom three rows add up to 7/22.

Beginning with the equality of 1:3/17 = 1/22:1/7, and then doubling 1/7 to reach unity on the right hand side, results in the given solution of 1/6 plus 1/11 plus 1/22 plus 1/66.

Ro is another measurement unit of volume equal to 1/320th of a hekat. Gillings says that this is between a dessertspoon and a tablespoon full of grain.

In his concluding remark regarding RMP # 38 Gillings says:

"The proof that follows (not given by Gillings) is also not simple, and when the whole is repeated in Horus-eye fractions and ro, the solution to problem 38 appears as a rather long and involved calculation, when in fact it could have been a simple one if the scribe had taken care to use his more efficient methods."



Edited 1 time(s). Last edit at 07/30/2007 07:00PM by Jim Alison.