"Every four years, not a hundred years, then four hundred years." This is a popular saying. I have many questions about this proverb: What is a leap year? Why will there be a leap year in four years? Why is there no leap year after 100? These questions have been lingering in my mind. To this end, I have done the following research.
Second, the study of the problem.
1, what is a leap year?
The establishment of leap year is to make up for the time difference between the number of days in a year and the actual period of revolution of the earth caused by man-made calendar regulations. The year to make up for the time difference is leap year. The popular explanation is that how many days, hours and minutes there are in a year, rounding to 365 is redundant. When the cumulative amount reaches 24 hours a day, an extra day is a leap year.
The most fundamental reason for the extra day is that the cycle of the earth's orbit around the sun is 365 days, 5 hours, 48 minutes and 46 seconds (365.245438+09 days), which is the tropic year, while the average year in the Gregorian calendar is only 365 days, which is about 0.24 19 days shorter than the tropic year and 0.2438+09× 4 = 0. This is what we call a four-year leap.
In the leap year algorithm, there is another saying that a year that is a multiple of 100 (not a multiple of 400) is not a leap year. Because it takes 0.242 19 days a year,100× 0.24219 = 24.219 ≈100 takes 24 days. But if you press "leap every four years", you actually make up 100/4 = 25 days, so you make up one more day.
In the leap year algorithm, the last sentence is called "leap again in 400 years", that is, years with multiples of 400 are leap years. 400×0.242 19=96.876≈97 days need to be supplemented within 400 years. If you press "leap every four years, 100 years does not leap", only 400/ 100× 24 = 96 days will be added, which is actually one day less.
2. Practical application
Once, my father tested me with a math problem: New Year's Day in 20 18 is Monday, so what day is New Year's Day in 20 19? What day is New Year's Day in 202 1 year? I didn't have a clue when I heard this question, but now, I can do it right. 20 18 New Year's Day is Monday, and I judge 20 18 as a normal year, so 365/7 = 52... 1, which means it takes 52 weeks 1 from 20 18 to 20 19. That is to say, 52 weeks and 2 days passed from New Year's Day in 2020 to New Year's Day in 2002 1, and 52 weeks1day passed from 20 19 to 2020, so 202 1.
Third, the extension of the class
1, the chronological method of China people.
In addition to the Gregorian calendar, China also uses the calendar year of trunk and branch in many occasions. For example, in 2007, the calendar year of trunk and branch was Dinghai, 20 18, and the calendar year of trunk and branch was 1898.
The chronology of trunk branches is divided into heavenly stems and earthly branches.
Tianganyou 10: methyl, ethyl, propyl, butyl, pentyl, hexyl, octyl, nonyl (rén) decyl (guǐ).
Underground branch 12: zi chouyin (yín) Mao (mo) Tatsumi (s) noon (yǒu) noon (hài).
Arrange the heavenly 10 Chinese characters and the earthly 12 Chinese characters into the following two lines:
Ah, b, d, e, g, n, N …
Mao Yinchen's ugly son didn't come to apply at noon, Mao Yinchen's ugly son didn't come to apply at noon …
The two words corresponding to the top and bottom of the same column are a year number of the main branch. In this way, pairings can form 60 different year numbers (that is, the least common multiple of 12 and 10).
2. Wenzhou mathematician short story
Su Zai 1983, a famous mathematician in China, told a story that a person who studies literature and history should also learn some mathematics: "I have a student who studies classical literature and sent me some collections of Su Dongpo. I looked through a poem "Fu on the Red Wall". When did Su Dongpo write it? This book is printed 1080. Su Dongpo was born in 1037 and lived for 64 years. The first few words of "Red Cliff Fu" are autumn, looking forward to July. As we all know, 1982 is the year of the main branch. When I saw Su Dongpo writing "Red Cliff Fu" at 1080, I knew it must be wrong. " Sue's judgment is right. 1080 Su Dongpo did not write Ode to the Red Wall. So, what year did he write it?
We can infer that. 1982 is the year of Ren Xu, so if 1080 is the year of Ren Xu, and the year of trunk and branch is a 60-year cycle, then their difference should also be a multiple of 60.
Then continue to infer what year Su Dongpo wrote "Red Cliff Fu". Su Dongpo's writing time range is1037 ~110/year. So 1037
Four. Research conclusion
The algorithm of leap year is: leap every four years, not leap in a hundred years, and leap again in four hundred years.
Common sense: Because the number of days that the earth rotates every year is about 365 and 1/4 days, 2008 is divided into leap year and peace year. 365 days in normal year: 52 weeks is 1 day, and 366 days in leap year: 52 weeks is 2 days.
Chronology of trunk and branch: divided into ten-day trunk and twelve-day branch.
Xungan: a, b, d, e, g, n, n, n.
Twelve earthly branches: ugly Mao Yinchen has asked for an audience at noon.
Every 60 years is a cycle, and 4 years is the year of Jiazi.
Research opinions on verbs (abbreviation of verb)
In our life, mathematical knowledge is everywhere. As long as we explore carefully, we will find the mystery and gain a lot of fun and knowledge. Mathematics is like a mountain peak, soaring into the sky. I felt relaxed at first, but the higher I climbed, the steeper the peak became, which made people feel scared. At this time, only those who really love mathematics will have the courage to continue climbing. Therefore, people who stand at the peak of mathematics all like mathematics from the heart. People who stand at the foot of the peak will never see the peak. Only by discovering and feeling mathematics in life can we broaden our horizons!