
Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Jan 3, 2012 1:55 PM


Scribes in RMP 41, 42, 43, MMP 10 and the Kahun Papyrus used of four area (A) and volume (V) formulas that replaced radius (R) by diameter (D/2) and pi by 256/81 in the area of circle formula allowing
A = (256/81)(D/2)(D/2) = (64/81)(D)(D), and adding height (H) four formula were written as:
a. A = (8/9)(8/9)(D)(D) cubits (MMP 10, and RMP 41)
b. V = (H)(8/9)(8/9)(D)(D) cubits (RMP 42)
c. V = (3/2)(H)(8/9)(8/9)(D)(D) khar (RMP 42)
d. V = (2/3)(H)((4/3)(4/3)(D)(D) khar (RMP 43 and the Kahun Papyrus)
e.In RMP 44 1500 khar times (1/20) = (75) 400hekat, was not (75) '100quadruple hekat' The correct 400hekat point was a point that was true for RMP 41, 42 and 43 by: "... I refer you again to Spalinger's SAK 17 article and his discussions of RMP Book II (pp. 320323), and to Griffith's writings on the RMP (as referenced by Spalinger) in PSBA 1316, and to Griffith again in PSBA 14. As Griffith says in the latter (p. 429) in regard to whether single, double or quadruple hekats are intended: "the meaning is implied by context", and he adds in regard to hundreds of quadruple hekats that: "I conclude, therefore, that the scribe uses a rather inaccurate but perfectly intelligible abbreviation of language, in saying that '75 is the number of quadruple hekt' when (in may not be the truth) that 75 is the number of complete squares (of 100 each) of the quadruple hekt" (p. 430) ...".
RMP 43 4096/9 x 1/20 = (22 + 1/2 + 1/4 + 1/180) 100 hekat was listed on line 5 as:
*f. 1/180 400 hekat =
4 x [100/180 = (5/9)x (64/64) = 320/576 = (288 + 18 + 9)/576 + 5/576 = 1/2 + 1/32 + 1/64 + (25/9)ro] =
4 x (100/180) = (5/9) x 4 x (64/64) = 4 x 320/576 = 4x (288 + 18 + 9)/576 + 5/576 = 1/2 + 1/32 + 1/64 + (25/9)4ro]
with (25/9)4ro = (2) 4ro + (7/9)4ro = (2) 4ro + (28/36)4ro =
(2) 4ro + (18 + 9 + 1)/36 4ro = (2) 4 ro + (1/2 + 1/4 + 1/36) 4ro
1 cubitcubitcubit = (3/2)khar =30 hekat (reported in RMP 41, 42, and 43),
(2/3)cubitcubitcubit = 1 khar = 20 hekat (reported in RMP 41, 42 and 43),
(2/15) cubitcubitcubit = (1/5)khar = 4 hekat (reported in RMP 41, 42 and 43)

