Islamic calendar lunar months begin precisely at the time of the monthly "conjunction", when the Moon is located most directly between the Earth and the Sun. The month is defined as the average duration of a revolution of the Moon around the Earth (29.53 days). By convention, months of 30 days and 29 days succeed each other, adding up over two successive months to 59 full days. This leaves only a small monthly variation of 44 minutes to account for, which adds up to a total of 24 hours (i.e., the equivalent of one full day) in 2.73 years. To settle accounts,
History of mathematics the Roman Kingdom and included 356 days plus a leap year every other year. In contrast, the lunar calendar of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the solar year, a discrepancy that was solved by adding an extra month into the calendar after the 23rd of February. This calendar was supplanted by the Julian calendar, a solar calendar organized by Julius Caesar (100–44 BC) and devised by Sosigenes of Alexandria to include a leap day every four years in a 365-day cycle. This calendar, which contained an error of 11 minutes and 14 seconds, was