Caption: Girl with Doves (c. 440--450 BCE). A artwork of ancient Greek sculpure from the lifetime of Meton of Athens (late 5th century BCE). For a better image, see girl_with_doves.html.

Meton is the eponym and possibly discoverer of the 19-year Metonic cycle which is a pretty accurate/precise way of inserting intercalary months in lunisolar calendar (see Wikipedia: Metonic cycle; Otto Neugebauer 1969, The Exact Sciences in Antiquity, p. 7; John North 1994, The Norton History of Astronomy and Cosmology, p. 65)

Explication of the 19-year Metonic cycle:

1. Consider 19 years.
2. Let 12 years consist of 12 lunar months.
3. Let 7 years consist of 13 lunar months.
4. To be precise, we will use values for J2000 epoch: solar year = 365.2421897 days (J2000), lunar month = 29.530588853 days (J2000).
5. In the 19 years counted thusly, there are 235 lunar months which equal 6939.69 days.
6. 19 solar years equal 6939.60 days.
7. Thus, there is a discrepancy of only ∼ 0.09 days. 19 years counted in lunar months by the Metonic cycle end 0.09 days after 19 solar years.
8. From time zero, it takes ∼ 219 years years of using Metonic cycle for the calendar year based on the Metonic cycle. to end about ∼ 1 day after the end of the 190th solar year also counting from time zero.

For a trivial procedure, the Metonic cycle isn't bad.

Credit/Permission: Original: Anonymous ancient Greek sculptor, c. 450 BCE--440 BCE, (uploaded to Wikimedia Commons by User:Dschwen, 2006) / CC BY-SA 3.0.
Image link: Wikimedia Commons.
Art_g file: girl_with_doves_meton.html.