How it began
Sexagesimal, or base 60, originated with the ancient Sumerians of Mesopotamia, in present-day Iraq, in the 3rd millennium BCE and was passed down to the Babylonians. Proto-cuneiform signs of the 4th millennium BCE already include marks for 60, 600 and 3,600. The historian Otto Neugebauer cautioned that the origins were not simple, consistent or singular in time, and that the notation always carried a strong undercurrent of decimal counting.
How it works
The Mesopotamian system was not a pure base 60 with sixty separate digits. Each digit was built from smaller marks whose values were added together. Sixty has twelve divisors, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, and is the smallest number divisible by every number from 1 to 6, so many fractions come out evenly. There was at first no sign for zero, so the signs for 1 and 60 looked the same and a value had to be read from context. Later Babylonian texts used a placeholder in middle positions.
What changed first
The strongest driver of consistent sexagesimal use was its advantage for writing and calculating fractions, and it appears most uniformly in mathematical tables. It also helped merchants divide large quantities of goods. In the late 3rd millennium BCE, Sumerian and Akkadian weights were sexagesimal: a talent was divided into 60 minas and a mina into 60 shekels. The Babylonian tablet YBC 7289 records an approximation of the square root of 2 in sexagesimal digits.
Where it stands today
The system was carried into later astronomy, notably the work of Ptolemy, and the Parisian version of the Alfonsine tables of about 1320 recorded multiples and fractions of a day in base 60 notation. A modified form of the system is still used to measure time, angles and geographic coordinates. One hour equals 60 minutes and one minute equals 60 seconds, and an hour can be divided evenly into periods of 30, 20, 15, 12, 10, 6, 5, 4, 3, 2 and 1 minutes. Astronomical coordinates still use sexagesimal notation, now with decimal fractions added.
