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
Intercalary month (Egypt) Intercalary month (Egypt) The intercalary month or epagomenal days of the Egyptian, Coptic, and Ethiopian calendars are a period of five days in common years and six days in leap years in addition to those calendars' 12 standard months, sometimes reckoned as their thirteenth month. They originated as a periodic measure to ensure that the heliacal rising of Sirius would occur in the 12th month of the Egyptian lunar calendar but became a regular feature of the civil calendar and its descendants. Egyptian and Ethiopian leap days occur in the year preceding Gregorian leap years. The English names "intercalary month"