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Re: Egyptian fraction math only used quotient and remainder statements
Posted:
Jan 19, 2012 12:04 PM
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RMP 47 scaled 100 hekat to 6400/64 and multiplied
6400/64 by
1. 1/10 = 10 hekat
2. 1/20 = 5 hekat
3. 1/30 = 213/64 hekat + (5/5)(1/192) (modern arithmetic)
= (192 + 16 + 4 + 1) + (5/3)ro (scribal notation)
= (3 + 1/4 + 1/16 + 1/64) hekat + (1 + 2/3)ro
4. 1/40 = (2 1/2) hekat
5. 1/50 = 2 hekat
6. 1/60 = 106/64 hekat + (5/5)(2/192) (modern arithmetic)
= (64 + 32 + 8 + 2)/64 hekat + (10/3)ro (scribal notation)
(1 1/2 1/8 1/32) hekat + (3 1/3) ro
7. 1/70 = 91/64 hekat + (5/5)(30/448) (modern arithmetic)
(scribal notation)
= (64 + 16 + 4 + 2 + 1)/64)hekat + (150/70)ro
Ahmes scaled 1/7 by 6/6 = 6/42 = (3 + 2 + 1)/42 = 1/14 + 1/21 + 1/42) for fun
=(1 1/4 1/8 1/32 1/64) hekat + (2 1/14 1/21 1/42) ro
8. 1/80 = 1 1/4 hekat
9. 1/90 = 71/64 hekat + (5/5)(1/64)(1/9) (modern arithmetic)
= (64 + 4 + 2 + 1)/64 + 5/9 ro (scribal arithmetic)
1 1/16 1/32 1/64 hekat + (1/2 1/18)ro
10. 1/100 = 1 hekat
There are quadruple hekat scaled issues done in Ahmes' HEAD that are connected to this problem, a translation issue that will be discussed later.
CONCLUSION The main translation point is that Ahmes scales 100 hekat to 6400/64 hekat and divided by 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 by multiplying 6400/64 hekat by 1/10, 1/20, 1/30, 1/40. 1/50, 1/60, 1/70, 1/80, 1/90 and 1/100 by extending the rules set down in the Akhmim Wooden Tablet 250 years earlier.
Q.E.D.
Best Regards,
Milo Gardner
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