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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
The Math Forum http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

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