Lunar calendar average length of the synodic month is days. Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively “"hollow"” and “"full"”). The distribution of "hollow" and "full" months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed: These fractions can be used to construct a lunar calendar, or in combination with a solar calendar
Lunar month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions, one for each day of the month, identified by the prominent star(s) in them. The synodic month (, "synodikós", meaning "pertaining to a synod, i.e., a meeting"; in this case, of the Sun and the Moon) is the average period of the Moon's orbit with respect to the line joining the Sun and Earth. This is the period of the lunar phases, because the Moon's appearance depends on the position of the Moon with