Lunar calendar or crescent moons and others employing detailed calculations. Since each lunation is approximately days (29 days, 12 hours, 44 minutes, 3 seconds, or days), it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of twelve such lunations, a lunar year, is only 354 days, 8 hours, 48 minutes, 34 seconds ( days), purely lunar calendars lose around 11 days per year relative to the Gregorian calendar. In purely lunar calendars like the Islamic calendar, the lack of intercalation causes the lunar months to cycle through all the seasons of
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