Sexagesimal number system
Sistema numérico sexagesimal
- Date
- c. 3000 BCE · confidence medium
- Place
- Uruk and Shuruppak, Sumer, Iraq
- Credited to
- Sumerians
- Field
- Knowledge & symbols
What it is
Base-60 numbering with sub-bases of 10, which allows easy division by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. It survives in our minutes, seconds and degrees.
The origin of base 60 (unification of base-10 and base-12 systems, or divisibility considerations) remains without consensus.
What it led to
- Manageable fractions for dividing rations, land and inheritances
- Babylonian mathematical astronomy and the division of the circle into 360 degrees
- Multiplication tables, reciprocals and square roots in scribal schools
- Calculation of areas and compound interest
Built on
- Clay accounting tokensc. 8000 BCE
- Proto-cuneiform writingc. 3300 BCE
- Accounting ledgers and balancesc. 3100 BCE
- Uruk metric systems (multiple bases per commodity)
Made possible
- Standardized weights and measuresc. 2600 BCE
- Practical geometry and land surveyingc. 2500 BCE
- Early counting board / abacusc. 2400 BCE
- Positional number notationc. 2000 BCE
- Solution of quadratic equationsc. 1800 BCE
- Pythagorean triples of Plimpton 322c. 1800 BCE
- Water clock (clepsydra)c. 1500 BCE
- Positional numeration
- Babylonian mathematical tables
- Division of the day into hours and minutes
- Babylonian astronomy