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Analysis by Milo Gardner: The Achmim Wooden Tablets (C.G. 25.367 and C.G. 25.368)
			LAST MODIFIED: 3/9/05
	Middle Kingdom texts exactly computed a hekat, a unit of grain, written  partly in the
`	Horus-Eye system and also partly in the Hieratic  system. The myth of Anubis, "monitor of
	the scales of truth" suggests that this modular arithmetic system may date to the Old
	Kingdom, Saqqara. There was a gate** at Saqqara that metaphorically solved the Horus-Eye
	balance beam problem. Today this means that there was a literal  scaling of Horus Eye
	binary fractions by a substitution process, that mathematicans may title as parametrics.
	Modular arithmetic statements of radix (quotients) and remainders were written out in
	the Middle Kingdom and later times, following an exact system that may not have been
	mathematically altered after its birth. Names within the exact 1/n divisor system of volume
	measurement may have changed over 2,000 years or more of Egyptian history, however,
	the modular arithmetic that began by replacing 1/64 with 5/320 in the remainder term, did not.
	Radix 10 (Q)	Remainder (R)
				with ro = 1/320, after 1/64 replaced by 5/320
	Q	5*R
(64/64)/n =	---------------	+ ----------  * ro		and (5*R)/n being written as exact Egyptian fractions
	64	n		series, as noted below, maybe for the first time.
Historical Sources:
AWT: The Achmim Wooden Tablets
	(C.G. 25.367 and C.G. 25.368) Two plastered wood planks inscribed in Hieratic. 12th Dynasty
RMP: The Rhind Mathematical Papyrus
	(BM 10057 and 10058) Hieratic papyrus originally connected, now torn in two with small fragments in NY
**Gate at Saqqara: Text reference; gate location
		Unity means that 1 = 64/64 in the hekat case
									remainder divisor
Source &	hin  unit  size	Hekat	divisor		Horus-Eye	quasi ro units	quasi ro units	remainder units	was an LCM = (n*320) before the ro factoring		actual ro units
Problem #		Unity	(n)	quotient	factors	(Q)	(R)	(R)
implied	10 hin	64/64		64	64					1 hekat	320
RMP #81	8.75	64/64	1 1/7	56	32+ 16 + 8	320	0	0	365.7143	0.875	280
RMP #81	8.125	64/64	1  3/13	52	32+ 16 + 4	320	0	0	393.8462	0.8125	260
RMP #81	7.8125	64/64	1  7/25	50	32+ 16 + 2	320	0	0	409.6	0.78125	250
RMP #81	7.65625	64/64	1 15/49	49	32+ 16 + 1	320	0	0	417.9592	0.765625	245
RMP #81	7.5	64/64	1 1/3	48	32 + 16	320	0	0	426.6667	0.75	240
RMP #81	6 hin	64/64	1 3/5	40	32 + 8	320	0	0	512	2/3 hekat	200
RMP #81	5.625	64/64	1 7/9	36	32 + 4	320	0	0	568.8889	0.5625	180
RMP #81	5.3125	64/64	1 15/17	34	32 + 2	320	0	0	602.3529	0.53125	170
RMP #81	5.15625	64/64	1 31/33	33	32 + 1	320	0	0	620.6061	0.515625	165
RMP #81	5 hin	64/64	2	32	32	320	0	0	640	0.5	160
RMP #81	5.15625	64/64	2 2/3	24	16 + 8	320	0	0	853.3333	0.515625	165
AWT #3	3 hin	64/64	3	21	16 + 4 + 1	315	5	1	960	0.375	120
RMP #81	3.125	64/64	3 1/5	20	16 + 4	320	0	0	1024	0.3125	100
RMP #81	2.8125	64/64	3 4/9	18	16 + 2	320	0	0	1102.222	0.28125	90
RMP #81	2.65625	64/64	3 13/17	17	16 + 1	320	0	0	1204.706	0.265625	85
RMP #81	2 hin	64/64	4	16	16	320	0	0	1280	1/4 hekat	80
RMP #81	2 hin	64/64	5	12	12	300	20	4	1600	1/5 hekat	64
RMP #81	1.5 hin	64/64	6	10	10	300	20	4	1920	1/6 hekat	53.33333
AWT #7		64/64	7	9	6 + 2	315	5	1	2240	1/7 hekat	45.71429
RMP #81	1.2 hin	64/64	8	8	8	320	0	0	2560	1/8 hekat	40
AWT #10	1 hin	64/64	10	6	6	300	20	4	3200	1/10 hekat	32
AWT #11	0.909090909	64/64	11	5	4 + 1	275	45	9	3520	0.090909	29.09091
RMP #81	0.769230769	64/64	13	4	4	260	60	12	4160	0.076923	24.61538
RMP #81	2/3 hin	64/64	15	3	2 + 1	255	65	13	4800	0.066667	21.33333
RMP #81	5/8 hin	64/64	16	3	2 + 1	300	20	4	5120	0.0625	20
RMP #81	1/2 hin	64/64	20	2	2	230	90	18	6400	0.05	16
RMP #81	1/3 hin	64/64	30	2	2	300	20	4	9600	0.033333	10.66667
RMP #81	5/16 hin	64/64	32	2	2	310	10	2	10240	0.03125	10
RMP #81	1/4 hin	64/64	40	1	1	185	135	27	12800	0.025	8
RMP #81	1/6 hin	64/64	60	1	1	205	115	23	19200	0.016667	5.333333
RMP #81	9/32 hin	64/64	64	1	1	225	95	19	20480	0.015625	5
RMP #47	0.142857143	6400/64	70	91	64+16+8+2+1	170	150	30	22400	0.014286	4.571429
implied	0.03125	64/320	320	0	0	319	1	1/5	102400	0.003125	1
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