## Sumerian and Babylonian Numerals

Closely linked - treat as one civilisation.

In the original form the symbols for 1 and 60 would be distinguished

```1
60
```
With the later cuneiform numerals 1 and 60 were both represented by a simple wedge

Question - how could the Sumerians and Babylonians distinguish between 1 and 60? Sometimes from the position of the wedge and sometimes from context.

 60 10 10 10
(Sumerians wrote from left to right)

obviously first symbol is 60 because they would write largest unit first.

In later times the notation was simplified further. All powers of 60 were denoted by a single wedge and ten times a power of 60 by an L shaped wedge
Later the same symbols and were also used to denote fractions

= 1/60 or 1/ or , 60, 1
= 10/60 or 10/ or 10 x , 10 x 60, 10 had to use context to decide.

The Babylonian system of writing numbers is a place value system, value of wedge depends on its position.

Systematic use of a place value notation has great advantages in computations and the Babylonians base of 60 has special advantage because it has so many factors.

Serious drawback - no symbol for zero, to overcome this difficulty the Babylonians introduced a special symbol to indicate an empty space.

, 0, 4 = 3604
This system was used by astronomers - divided the degree into 60 minutes and minutes into 60 seconds.

The Alexandrian astronomer Ptolomy (C2 AD) used the symbol 0 for zero not only between digits but also at the end of a number. This gave the finishing touch to the sexagesimal system - the value of every written number was now completely determined.

Questions

Egyptian Numerals

History of Mathematics Module

Links to other History of Mathematics sites

These pages are maintained by M.I.Woodcock.