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Babylonian Number System


Date: 06/15/98 at 15:55:01
From: DEE CARTER
Subject: Sexergesimal

I need a copy of this number system and of the Babylonian number 
system.

Thank you very much.


Date: 06/19/98 at 15:41:03
From: Doctor Mateo
Subject: Re: Sexergesimal

Hello Dee,

The Babylonian scale of enumeration is known as the sexagesimal 
system. What that means is that the Babylonians used 60 as their base, 
much as we tend to use the decimal system (base 10) in the United 
States .

In the sexagesimal system, each time a "digit" is moved to the left 
its value increases by a factor of 60. When you represent a whole 
number in the sexagesimal system the last space "digit" is for the 
numbers from 1 to 59, the next to the last space "digit" for multiples 
of 60, then the next space "digit" for multiples of 60^2 = 3600, the 
next preceding space "digit" for multiples of 60^3 = 216,000, and so 
forth.


In other words the number system is developed by working with base 60: 

   60^0 = 1
   60^1 = 60
   60^2 = 3600
   60^3 = 216,000
   .       .
   .       .
   .       .

 The Babylonian  5  53  18 would then represent the number
      
   5*60^2 + 53*60^1 + 18*60^0 =
   5*3600 + 53*60 + 18*1 =
   18,000 + 3,180 + 18 =
   21,198 (in our enumeration system).

If you want to write out the number system, it would start out 
something like

 1, 2, 3, 4,...59, 1 0, 1 1, 1 2,...

 where 1 0 = 1*60^1 + 0*60^0 = 60 + 0 = 60,
       1 1 = 1*60^1 + 1*60^0 = 60 + 1 = 61,
       1 2 = 1*60^1 + 2*60^0 = 60 + 2 = 62, 

and so forth.

I hope this gets you started on developing the Babylonian or
sexagesimal enumeration system.

-Doctor Mateo
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Associated Topics:
High School Number Theory

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