Shulou(Shulou.com)11/24 Report--

Today's Gregorian calendar comes from ancient Egypt. At that time, the Nile flooded about every 365 days, over and over again. So 365 days is set as a year. The moon is missing and round about every 30 days, so 30 days is set as a month. In this way, there are still five days left in 12 months of the year, and the ancient Egyptians put the extra five days at the end of the year as a holiday for everyone to celebrate the New year.

However, the cycle of flooding of the Nile is only a rough figure. It takes four days longer than 365 days for the earth to rotate around the sun and return to its original position. In this way, the time of flooding of the river has actually been pushed back by about 1x4 days a year. With the passage of time, the date of the Nile flooding is getting later and later, and the New year sometimes appears in the hot summer, sometimes in the middle of winter! About every 1460 spring and autumn, there are 1461 Egyptian years, a full year more!

In 46 BC, the legendary Roman ruler Julius Caesar (JulianCaesars, 120-44 BC) finally made up his mind to change the chaos. With the help of astronomers, he extended 46 BC to 445 days, and from 45 BC, he changed it to the solar calendar, which is still in use. This is the Julian calendar named after Caesar.

The Julian calendar uses a leap method for about 1pm and 4 days a year. That is, when you encounter a leap year, add one day each year and become 366 days. If a return year is exactly 365 and 1/4 days, then one leap every 4 years is enough! But the exact time of a return year is 365.2422 days, and each year actually has an extra 0.2422 days. In this way, 2422 days must be added every ten thousand years, with an average of 24 days per 100 years. This is the principle of "one leap in four years and one leap less in a hundred years".

However, a hundred years 24 leap, ten thousand years only add 2400 days, there are 22 days how to do? So the calendars set a rule of adding one leap every 400 years, which almost made up for the undercalculated difference of "24 leaps in a hundred years"! Of course, that's an extra three days every ten thousand years, but it's accurate enough. From Caesar to the present, there is no difference between the Julian year and the return year. Mathematicians have a different idea about the leap method, and they expand the extra days by 0.2422 into continuous fractions:

Its asymptotic score is

Each of these asymptotic scores is closer to 0.2422 than the other.

These asymptotic scores show that 4 years plus a leap is the initial best solution, but 29 years 7 leaps would be better, and 33 years 8 leaps would be better! This is equivalent to 99 years plus 24 days, and it is very close to "24 leaps in a hundred years". But the latter is obviously much easier to remember and practical, so even mathematicians will agree with the calendar's leap plan!

The same method can be applied to the leap of the Chinese lunar calendar. The lunar month is determined according to the "Shuowang moon". The so-called new moon refers to the interval from one full moon to the next. The interval is 29.5306 days to be exact. As mentioned earlier, there are 365.2422 days in a year, so the number of months in a year should have

That is, an average of a little more than 12 months. Therefore, lunar months sometimes have 12 months in a year, and sometimes 13 months in a year, which is also called a leap year in the lunar calendar. Expand the decimal part of the quotient above into a continuous fraction:

Its asymptotic score is

The nature of asymptotic scores shows that there are too many leaps in two years of the lunar calendar, too few in three years, too few in three years, too few in four years in 11 years, and so on. Once readers know the above truth, they will not be surprised by the leap of the Chinese lunar calendar.

Let's turn to another important celestial phenomenon-solar and lunar eclipses. Many readers may find this mysterious, but after reading this section, all the mystery will be eliminated, and maybe they can even be a little prophet.

Because people in ancient times did not understand the natural phenomena such as solar and lunar eclipses, they mistook them for signs of disaster. So when these phenomena appear, they show panic and panic!

According to historical records, about the 6th century BC, Greece's Lydia and Medea, two countries, war after disaster, the two sides fiercely fought for five years, the victory or defeat has not been divided. On the day of the sixth year, there was a fierce battle between the two sides. All of a sudden, the sky was dark and the night came! The soldiers thought they had offended the gods and angered the sky, so they suddenly woke up. The two sides immediately dropped their weapons and shook hands to make peace! Astronomers later helped historians determine exactly when the war took place in the afternoon of May 28, 585 BC.

Another legend is that when the navigator Columbus was in Jamaica, the local Caribbean tried to starve him and his entourage to death. Columbus told them that if they didn't give him food, he wouldn't give them moonlight that night! As a result, as soon as the eclipse began that night, the Caribbean surrendered! It has now been verified that the story took place on May 1, 1504.

In fact, solar eclipses and lunar eclipses are only the result of the movement of the sun, the moon and the earth. When the moon moves around the earth, and the earth revolves around the sun, when the moon turns between the earth and the sun, and the three celestial bodies are in a straight line, the moon blocks the sunlight, and a solar eclipse occurs. When the moon turns to the side of the earth behind the sun, and the three celestial bodies are in a straight line, the earth blocks the sunlight, and a lunar eclipse occurs, as shown in the picture.

However, since the moon's orbital plane is not on the plane in which the earth revolves around the sun, the moon has an intersection with this plane every time it passes from one side of the earth's orbital plane to the other. One of these intersections is inside the earth's orbit, which is called the inner intersection, and the other is outside the earth's orbit, called the external point, as shown in the figure. The period in which the lunar ball starts from the inner intersection and then returns to the inner intersection is called the intersection month, which is 27.2123 days.

Obviously, the occurrence of solar eclipse and lunar eclipse must have two conditions at the same time, one of which is indispensable: one is that the moon is just at the internal and external intersection, and the other is that the sun, moon and earth are collinear, that is, it must be a new moon or a full moon. The above conditions indicate that if a solar or lunar eclipse happens on a certain day, the solar and lunar eclipses will repeat after another cycle, which happens to be a multiple of the intersection moon and the lunar eclipse. In order to find the least common multiple of the new month and the intersection month, expand their ratio into a continuous fraction.

Consider asymptotic fraction

It shows that after 242 or 223 months of intersection, the sun, moon and earth have almost returned to their original relative position, which is equivalent to the same period of time.

242 × 27.2123 million 6585.3766 (days)

That's equivalent to 18 years, 11 days and 8 hours. This is the famous Saro cycle! With this cycle, readers can predict future solar and lunar eclipses based on past solar and lunar eclipses. However, there are few opportunities for solar and lunar eclipses in a year, with a maximum of 5 solar eclipses and 3 lunar eclipses, and the two can never add up to more than 7 times! The following table shows the solar eclipse (○) and lunar eclipse (●) that can be seen in China during the 12-year period from 2009 to 2020.

Source: "Mathematics Story Book for Children" author: Zhang Yuannan Zhang Chang part of the picture comes from the network copyright belongs to the original author Editor: Zhang Runxin this article comes from Wechat official account: Origin Reading (ID:tupydread), author: Zhang Yuannan Zhang Chang, Editor: Zhang Runxin

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