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Meton  of Athens (ca. 440 BC) noticed that 235 lunar months made up almost exactly 19 solar years. Using
modern measurements,
The near commensurability of the two periods follows from the fact that 235/19 is the 6th convergent  of the
ratio of the lunar month and solar year periods (365.2425/29.53059).
This 19-year lunar cycle became known as the Metonic cycle, and was the basis for the Greek
calendar until the Julian calendar was introduced in 46 BC. Since 12 lunar months equal 354.367 days, about 11 days
less than a solar year, an additional
 lunar months were added to synchronize the cycle. These were
added in years 3, 5, 8, 11, 13, 16, and 19 of the cycle. The Metonic cycle was extended by Callippus to
4 19-year cycles, which is known as the Callipic cycle.
 Callipic Cycle, Hipparchic Cycle
Smith, D. History of Mathematics, Vol. 2. New York: Dover.
© 1996-2007 Eric W. Weisstein
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