Positional number notation

What it is

Writing of numbers in which the value of each sign depends on its position (powers of 60), with only two basic signs. It is the world's first positional system, though without an explicit zero until the 4th century BCE.

The absence of a zero and of a decimal-point marker required magnitude to be inferred from context.

What it led to

• Multiplication and division of large numbers using regular algorithms
• Abstract mathematics: solving quadratic equations and calculating the square root of 2 (tablet YBC 7289)
• Precise astronomical tables that founded predictive astronomy
• A distant model for the Indian decimal positional system

Built on

• Lunar cycle tallies and earliest calendarsc. 30000 BCE
• Accounting ledgers and balancesc. 3100 BCE
• Sexagesimal number systemc. 3000 BCE
• Scribal school (edubba) and written curriculumc. 2500 BCE
• Sexagesimal system

Made possible

• Zero and positional notation in Europe (Fibonacci)1202
• Babylonian algebra
• Ephemeris tables
• Positional zero

Links