Examples
The square root of 2, the length of the diagonal of a unit square, was approximated by the Babylonians of the Old Babylonian Period (1900 BC – 1650 BC) as
Because is an irrational number, it cannot be expressed exactly in sexagesimal numbers, but its sexagesimal expansion does begin 1 : 24 : 51 : 10 : 7 : 46 : 6 : 4 : 44 ...
The length of the tropical year in Neo-Babylonian astronomy (see Hipparchus), 365.24579... days, can be expressed in sexagesimal as 6:5:14:44:51 (6×60 ＋ 5 + 14/60 + 44/602 + 51/603) days. The average length of a year in the Gregorian calendar is exactly 6 : 5 : 14 : 33 in the same notation because the values 14 and 33 were the first two values for the tropical year from the Alfonsine tables, which were in sexagesimal notation.
The value of π as used by the Greek mathematician and scientist Claudius Ptolemaeus (Ptolemy) was 3.141666... ≈ 377/120 = 3:8:30 = 3 + 8/60 + 30/602. Jamshīd al-Kāshī, a 15th-century Persian mathematician, calculated π in sexagesimal numbers to an accuracy of nine sexagesimal digits.
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—Bernard Mandeville (1670–1733)
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