![]() Multiply by an appropriate integer to clear the fraction. Assuming they knew the Pythagorean relation, divide by b to getĬhoose u+ v and find u- v in the table of reciprocals.Įxample. ![]() ![]() If appears to have the left section broken away. The Plimpton 322 tablet dates from about 1700 BC. Note: was commonly used as a brief, rough and ready, approximation. Now carry out this process in sexigesimal, begining with They seemed to have an elementary knowledge of logarithms. However, they do not appear to have noticed infinite periodic expansions. The Babylonians knew some approximations of irregular fractions. They give squares of the numbers up to 59 and cubes up to 32. Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 B.C. Irregular fractions such as, etc are generally not used.Ī table of all products equal to sixty has been found. Generally the only fractions permitted were such asīecause the sexigesimal expression was known. The exact value of, to 8 decimal places is = 1.41421356.įractions. This number was found on the Old Babylonian Tablet (Yale Collection #7289) and is a very high precision estimate of. The ``gap" problem was overcome by the time of Alexander the Great, rather late in the game for the Chaldeans.
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