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Topic: Egyptian fraction math only used quotient and remainder statements
Replies: 18   Last Post: Aug 31, 2012 9:23 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Re: Egyptian fraction math only used quotient and remainder statements
Posted: Jan 19, 2012 12:04 PM

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

Date Subject Author
12/15/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/16/11 Milo Gardner
12/17/11 Milo Gardner
12/17/11 Milo Gardner
12/18/11 Milo Gardner
12/19/11 Milo Gardner
12/20/11 Milo Gardner
12/21/11 Milo Gardner
12/22/11 Milo Gardner
12/23/11 Milo Gardner
1/3/12 Milo Gardner
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1/6/12 Milo Gardner
1/9/12 Milo Gardner
1/19/12 Milo Gardner
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8/31/12 Milo Gardner