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Babylonian Table of Squares

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Babylonian Years
Senkareh Table of Squares (Plate 18)

Senkareh Table of Squares (Plate 18)

http://www.gutenberg.org/files/16161/16161-h/16161-h.htm - The Seven Great Monarchies, G. Rawlinson
In "Homage to Babylonia" [The Mathematical Gazette, Vol. 76, No. 475, "The Use of the History of Mathematics in the Teaching of Mathematics" (Mar., 1992), pp. 158-178], writer-teacher Nick Mackinnon says he uses Babylonian mathematics to teach 13-year-olds about bases other than 10. The Babylonian system uses base-60, meaning that instead of being decimal, it's sexagesimal.

You can think of Babylonian mathematics as a puzzle -- one you can solve with a bit of patience. Here is an example of Babylonian mathematics, written in cuneiform, that shows how they created a table of squares. Not only will this provide insight into the way the Babylonians did their calculations, but it will also show you base 60 put into practice.

We talk about periods of years using decimal quantities. We have a decade for 10 years, a century for 100 years (10 decades) or 10X10=10 years squared, and a millennium for 1000 years (10 centuries) or 10X100=10 years cubed. I don't know of any higher term than that, but those are not the units the Babylonians used. Nick Mackinnon refers to a tablet from Senkareh (Larsa) from Sir Henry Rawlinson (1810-1895)* for the units the Babylonians used:

  1. soss
  2. ner
  3. sar.
A soss refers to a period of 60 years. The ner is a unit of 600 years, or one soss times 10 [while the Babylonian system is described as sexagesimal, it is also partly decimal] and the sar, a unit of 3600 years -- a soss squared.
All photos come from this online scanned version of a 19th century edition of George Rawlinson's The Seven Great Monarchies Of The Ancient Eastern World.
*George Rawlinson (1812-1902), Henry's brother, shows a simplified transcribed table of squares in The Seven Great Monarchies of the Ancient Eastern World. The table appears to be astronomical, based on the categories of Babylonian years.

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