# Definition:Sexagesimal Notation

## Definition

**Sexagesimal notation** is the technique of expressing numbers in base $60$.

## Also known as

The **sexagesimal notation** system can also be seen referred to as **logistic arithmetic** or **logistic notation**.

## Examples

### Example: $6, 30$

- $6, 30$ in sexagesimal is $6 \frac 1 2$ expressed as a mixed fraction.

### Example: $11, 22, 30$

- $11, 22, 30$ in sexagesimal is $11 \frac 3 8$ expressed as a mixed fraction.

## Also see

- Results about
**sexagesimal notation**can be found**here**.

## Historical Note

From as early as $3500$ BCE, the Sumerians were using a sexagesimal system for certain purposes, based on divisions of $10$ and $6$:

- $1, 10, 60, 600, 3600, 36 \, 000, \ldots$

For conventional business purposes, they used a decimal system.

Their $60$-based system was adopted by the Babylonians, who used it for mathematical and astronomical purposes.

As $60 = 5 \times 12 = 6 \times 10$, it has the advantages of both the decimal (base $10$) and duodecimal (base $12$) systems.

In particular, the ancient division of the sky into the $12$ signs of the zodiac fits the sexagesimal system far better than a decimal system.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $12$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**logistic**:**2.** - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $12$