sexagesimal number system
Quick Summary
The sexagesimal number system is a base-60 system, meaning it uses 60 as its base rather than the more common base-10. This system was notably used by the Babylonians around 3000–2000 BCE.1
Key characteristics include:
* Positional Notation: Similar to our modern decimal system, the position of a digit determines its value.1
* Digits 0-59: Because the base is 60, there are 60 unique digits. The Babylonians represented these using a grouping system based on 10.1
* Fractions: Sexagesimal fractions have denominators that are powers of 60, such as 1/60 or 1/3600.2
The sexagesimal system is still used today in measuring time (hours, minutes, seconds) and angles (degrees, minutes, seconds). The choice of 60 as a base may have been due to its many divisors, which would have simplified division.34
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mathematicsThe numeral system and arithmetic operations…the base of 60 (sexagesimal). The reasons for the choice of 60 are obscure, but one good mathematical reason might have been the existence of so many divisors (2, 3, 4, and 5, and some multiples) of the base, which would have greatly facilitated the operation of division. For…
Read More…the base of 60 (sexagesimal). The reasons for the choice of 60 are obscure, but one good mathematical reason might have been the existence of so many divisors (2, 3, 4, and 5, and some multiples) of the base, which would have greatly facilitated the operation of division. For…
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history of MesopotamiaThe achievements of ancient Mesopotamia…to the Babylonians—for instance, the sexagesimal system for the calculation of time and angles, which is still practical because of the multiple divisibility of the number 60; the Greek day of 12 “double-hours”; and the zodiac and its signs. In many cases, however, the origins and routes of borrowings are…
Read More…to the Babylonians—for instance, the sexagesimal system for the calculation of time and angles, which is still practical because of the multiple divisibility of the number 60; the Greek day of 12 “double-hours”; and the zodiac and its signs. In many cases, however, the origins and routes of borrowings are…
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- mathematicsGreek trigonometry and mensuration
…the Greeks adopted the Mesopotamian sexagesimal method in arithmetic, whence it survives in the standard units for angles and time employed to this day.
Read More…the Greeks adopted the Mesopotamian sexagesimal method in arithmetic, whence it survives in the standard units for angles and time employed to this day.
Read More - mathematicsMathematics in the 10th century
…second common system was the base-60 numeration inherited from the Babylonians via the Greeks and known as the arithmetic of the astronomers. Although astronomers used this system for their tables, they usually converted numbers to the decimal system for complicated calculations and then converted the answer back to sexagesimals.
Read More…second common system was the base-60 numeration inherited from the Babylonians via the Greeks and known as the arithmetic of the astronomers. Although astronomers used this system for their tables, they usually converted numbers to the decimal system for complicated calculations and then converted the answer back to sexagesimals.
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history of scienceThe Middle East…of weights and coinage, was based on 60 (it was in ancient Mesopotamia that the system of degrees, minutes, and seconds developed) and was adapted to a practical arithmetic. The heavens were the abode of the gods, and because heavenly phenomena were thought to presage terrestrial disasters, they were carefully…
Read More…of weights and coinage, was based on 60 (it was in ancient Mesopotamia that the system of degrees, minutes, and seconds developed) and was adapted to a practical arithmetic. The heavens were the abode of the gods, and because heavenly phenomena were thought to presage terrestrial disasters, they were carefully…
Read More