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Re: Who discovered irrational numbers?
Posted:
Mar 22, 2009 3:38 PM
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Dear Math forum members,
Ahmes' 2/th table member 2/97 was also calculated in RMP 31 and 33, as either a multiplication by 56/56, or a subtraction by 1/56.
As a LCM 56 multiplier, with (aliquot part) divisors 56, 28, 14, 8, 7, 4, 2, 1
2/97*(56/56) = 112/5432 = (97 + 8 + 7)/5432 = 56' 679' 776'
or, by the alternate subtraction method,
2/97 - 1/56 = (112 -97)/5432 = (8 + 7)/5432 = 679' + 776'
meant, 2/97 = 56' 679' 776'
I suspect that multiplication was the primary method, with subtraction as an available proof method.
It may be interesting to forum members that Fibonacci (in 1202 AD) exclusively used Ahmes' subtraction method, not hinting at understanding of Ahmes' LCM multiplication method.
Best Regards,
Milo Gardner
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