Why was the sexagesimal system used and why does it still persist today?

 

Without going into further research, I remember learning about how ancient cultures based their calculations on their observations of nature, specifically the sky and the cycles around the sun and the moon. I understand that the 60 comes from fractions of a cycle of 360 days around the sun (that was adjusted in some moment to our 365 days), which also matches the 360 degrees of the circumference path.

EDIT-EXPANDING :

The Sexagesimal System: Origin and Persistence

Three main reasons :

1. The Mathematical meaning of 60

    The primary reason the number 60 was chosen is its unique status as a highly composite number, which means it has more divisors than any smaller positive integer.

Factors of 60:	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

    The fact that 60 is divisible by the first six counting numbers (1, 2, 3, 4, 5, 6) and by 10, 12, 15, 20, and 30 made calculating fractions simple and accurate.

• In a base-10 system, dividing 1 by 3 results in a repeating decimal (0.3333).

• In the sexagesimal system, dividing 1 by 3 is exactly 20.

This ease of division was crucial for the Babylonians' trade and land division.

2. The Cultural and Historical Trascendance

• Geometry and Astronomy: The Greek astronomer Hipparchus (2nd century BC) and Ptolemy (2nd century AD) adopted the sexagesimal system for their astronomical tables and geometric works. They used it to divide the circle into 360 degrees and further subdivide the degrees into minutes and seconds. This practice was inherited from Babylonian positional astronomy, which connected the approximated 360-day year to the circle's rotation.

• Timekeeping: Through the works of Greek, Indian, and particularly Islamic scholars, the system was integrated into the measurement of time. The division of the hour into 60 minutes and the minute into 60 seconds is a legacy of this transmission, establishing the sexagesimal system as the standard for timekeeping worldwide.

3. Why It Still Persists Today? 

The sexagesimal system has survived because it was integrated into standardized measurements that are difficult to change:

• Time: The structure of time (60 seconds, 60 minutes) is universally recognized and built into every clock and calendar system.

• Angles and Navigation: All international standards for geometry, cartography, and navigation rely on the 360-degree circle and its sexagesimal subdivisions (degrees, minutes, and seconds of arc, or D-M-S).

In conclusion, the sexagesimal system was chosen by the Babylonians for its divisibility, and it persists today not only because of a direct connection to nature, but because Greek and later civilizations adopted it for astronomy and geometry, solidifying its use in the standards of time and angle measurement.