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Other historical usages

In the Chinese calendar, a system is commonly used in which days or years are named by positions in a sequence of ten stems and in another sequence of 12 branches. The same stem and branch repeat every 60 steps through this cycle.

Book VIII of Plato 's Republic involves an allegory of marriage centered on the number 60 = 12 960 000 and its divisors. This number has the particularly simple sexagesimal representation 1,0,0,0,0. Later scholars have invoked both Babylonian mathematics and music theory in an attempt to explain this passage.

Ptolemy 's Almagest, a treatise on mathematical astronomy written in the second century AD, uses base 60 to express the fractional parts of numbers. In particular, his table of chords, which was essentially the only extensive trigonometric table for more than a millennium, has fractional parts of a degree in base 60, and was practically equivalent to a modern-day table of values of the sine function.

Medieval astronomers also used sexagesimal numbers to note time. Al-Biruni first subdivided the hour sexagesimally into minutes, seconds, thirds and fourths in 1000 while discussing Jewish months. Around 1235 John of Sacrobosco continued this tradition, although Nothaft thought Sacrobosco was the first to do so. The Parisian version of the Alfonsine tables (ca. 1320) used the day as the basic unit of time, recording multiples and fractions of a day in base-60 notation.

The sexagesimal number system continued to be frequently used by European astronomers for performing calculations as late as 1671. For instance, Jost Bürgi in Fundamentum Astronomiae (presented to Emperor Rudolf II in 1592), his colleague Ursus in Fundamentum Astronomicum, and possibly also Henry Briggs, used multiplication tables based on the sexagesimal system in the late 16th century, to calculate sines.

In the late 18th and early 19th centuries, Tamil astronomers were found to make astronomical calculations, reckoning with shells using a mixture of decimal and sexagesimal notations developed by Hellenistic astronomers.

Base-60 number systems have also been used in some other cultures that are unrelated to the Sumerians, for example by the Ekari people of Western New Guinea.