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大家知道，农历每11年设置4个闰年。公历每四年一闰，一百年少一闰，四百年又多一闰。农历去年闰十月，公历去年闰2月。农历闰年加一个月，公历闰年加一天。我国通用的这两种历法，按上述办法设置闰年，固然有天文学上的原因，但也有其数学道理。地球绕太阳公转一周的时间是365天5小时48分46秒，合365.2422天，而月亮绕地球一周（农历的一个朔望月）的时间是29天12小时44分2.9秒，合29.5306天，于是用辗转相除法，将一年中含有的月数365.2422/29.5306化为连分数得：
As we all know, the lunar calendar sets 4 leap years every 11 years. The Gregorian calendar is every four years, one hundred years, and four hundred years. The lunar calendar last October, the Gregorian calendar last February. Lunar New Year plus one month, Gregorian calendar year plus one day. The two general calendars used in our country set the leap year according to the above methods. Although there are astronomy reasons, there are mathematical reasons. The time for the Earth to orbit the Sun is 365 days, 5 hours, 48 minutes, 46 seconds, 36,422,422 days, and the moon’s orbit around the earth (a lunar month of the lunar calendar) is 29 days, 12 hours, 44 minutes, 2.9 seconds, and 29.5,306 days. Transferring the phase division method, the number of months contained in the year 365.2422/29.5306 is converted into a consecutive fraction: