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To: James C. Bennett; pillut48

Decimal (base 10) of course is a better way to manipulate numbers, but didn’t the Babylonians use the sexigesimal (base 60) system? How easily do the operations flow in that numeric system?


10 posted on 11/27/2010 4:51:29 PM PST by tarheelswamprat
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To: tarheelswamprat

My understanding is very easily. I also think that their base 60 system gave us our time measurements, IIRC.


20 posted on 11/27/2010 7:53:49 PM PST by 1010RD (First Do No Harm)
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To: tarheelswamprat
Aaboe suggests that Babylonian numbers were quite well suited for arithmetic because 60 is a highly composite number. Multiplication was reduced to successive multiplication by the prime factors of the multiplier and Babylonian scribes were well versed in multiplication tables. The place were base 60 shone was in division, which is a much harder problem than multiplication. Since 60 has so many multipliers, many division problems reduced to multiplication and division by sixty. By analogy, in base 10, division by 5 reduces to multiplication by 2 followed, trivially, by division by 10. One of the mathematical tablets found from Babylonia was a four Sexagesimal place table of reciprocals of 7, for all integers from 1 to 59. This would be equivalent to a six decimal place table of reciprocals of 7 for integers 1-9 in base 10. (142857, 285712, 428571, 57142, 714285, 1000000, 1142857 1285712... division of result by a 10^6 implied.) Clearly such tables were NOT ephemera, as implied by the article, but were standard reference works like tables of trigonometric functions and logarithms were up to around 1980.

Ptolemy also recommends and teaches Babylonia arithmetic in the Almagest because of its superiority for computation.

26 posted on 11/28/2010 1:14:09 PM PST by Lonesome in Massachussets (Socialists are to economics what circle squarers are to math; undaunted by reason or derision.)
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