Chapter 6 Decimal and Sexagesimal Systems

readx;? -- "If you haven't gone anywhere, why are you hanging out? Go to school and stand in front of your teacher to memorize your homework." Pen, fun, pavilion www. biquge。 infoOpen your schoolbag and let your 'big brother' tell you new knowledge. Come back to me when you're done and report to your class leader, and don't wander the streets. Hey, do you understand?" After the nagging, the father began to reprimand his son harshly, saying that he was "against his heart" and frustrated with the young man's complaining nature. "Your whining has killed me, you have annoyed me".

Usually when students come to school, they first review the clay tablet material they have learned the day before, and then the "elder brother" prepares a new clay tablet material, and the student copies and learns according to it. Finally, "Big Brother" and "Father of the School" check the clay tablets copied by the students for errors. At the same time, teachers and "elder brothers" will also make some academic reports to increase students' knowledge.

Sumerian teaching did not have any of the characteristics of progressive education. The school discipline is very strict, and although teachers also use encouragement and praise to teach students to study hard, corporal punishment is mainly used to make students correct their mistakes, and there are many examples of this. A clay tablet of a student's school life records the corporal punishment that a student receives during the course of a day.

"My headmaster read my clay tablets and said, 'A few characters are missing here,' and whipped me with a rattan. The cleaning officer said, 'You're wandering the streets, you're not tidying up your clothes,' and whipped me with a rattan. The person in charge of the quiet of the class said, 'Why didn't you speak without permission,' and whipped me with a rattan. The person in charge of the student assembly said, 'Why did you stand up without permission,' and whipped me with a rattan. The officer in charge of the students entering and leaving the school said, 'Why did you go out of the school gate without permission,' and whipped me with a rattan stick. The teacher who taught Sumerian said, 'Why don't you speak Sumerian,' and whipped me with a rattan. My teacher said, 'Your homework is unsatisfactory,' and whipped me with a rattan. "Corporal punishment in schools is very harsh, but there are ways for students to deflect the anger of teachers. One graduate recalled that in order to win the favor of one of the teachers, he begged his father to invite the teacher to his home in order to soften him with a good meal and "a little extra respect (money)". It seems that the flattery tactics have worked. Before leaving that night, the teacher praised the student for his diligence and hoped that he would be a role model for the rest of his classmates.

The earliest division of 12 units and 60 units came from the Sumerians. Dividing the whole into 12 units (12 months of the year, the concept of "a dozen") and 60 units of measurement (minute hand), the unit of length is 12 inches, the unit of weight is 12 ounces, the unit of weight is 12 ounces, the shilling is equal to 12 pence, and even the imperial length of a penalty kick in football is 12 yards. Textimal source: Legend has it that it is ten fingers plus two feet. This was stipulated in the past. A dozen 12 is a form of decimal system. Now the common timekeeping method in all countries in the world, that is, 60 minutes per hour, 24 hours a day, the scale on the clock is 12 hours, and the "beat" with 12 as the basic unit of measurement, are all developed on the basis of the base of the 60 system, and the use of the base 60 system is also passed down by the Sumerians through the Babylonians.

The astronomical surveying activities of the ancients contributed to the development of geometry, and in this process they often needed to divide angles, bisects, thirds, quarters... Of course, they have to solve the problem of a small number of equal divisions first, from two, three, four, five. Initially, if the base 60 is used, since 60 is the common divisor of 2, 3, 4, 5, 6, these angles can be divided equally, while if the base 100 is used, the third and sixth divisions cannot be realized.

The reason why the ancients set the angle as the base 60 system is very simple, that is, for the convenience of measurement and drawing, make a measuring ruler, and you can divide the angle into many parts according to the reading. The corresponding dozen-12 as a unit of measurement is also for the same reason---- in order to make it easy to divide equally, it can be divided into 2, 3, 4 equal parts. Comparing decimal and decimal as a commonly used decimal system, decimal is good, and there are more cases where it needs to be divided into 2, 3, 4, and 6 than in 2, 5, so the decimal system is used.

They were the earliest known documentaries of astronomical phenomena, created the earliest astrological astronomy, and believed in superstitious divination. In the texts and patterns left by the Sumerians, the images of the Sumerian gods recorded are related to the stars in the sky, none of these gods have a human form, each god represents a star, and each star is surrounded by a number of different planets, large and small, and the whole astrological map is almost exactly the same as that surveyed by modern people through telescopes.

The Sumerians, who were almost 1,000 years later than the Shennongs, established the Taiyin (moon) calendar, the difference being suitable for agricultural production in the region. In a situation as in Mesopotamia, when it was so warm and humid that floods of the two rivers were frequent, it was essential to know the punctuality of sowing and harvesting, and it was necessary to find some kind of time itinerary to determine a reliable way to repeat the cycle. The easiest way to do this is to take advantage of the moon's waxing and waning cycle. Since it takes 29 and a half days for the moon to travel from the first Emei month to the next first Emei month, one can consider such a cycle as a basic unit of time (we call it a month), and then after the moon has traveled 12 such time units (6 is 29 days, 6 is 30 days), a "year" has passed, and it is time to start again: sowing.

Unfortunately, they don't know that a year is actually the time it takes for the Earth to revolve around the Sun, and that the 12 cycles or 12 months of the Moon are 11 days less than a solar year. It wasn't until around 3000 BC, 900 years after the creation of the lunar calendar, that the Sumerians learned that every few years they had to add a leap month to their calendar in order to accurately predict the cycle of the seasons.

The Sumerians' use of numbers can be said to have reached an unattainable level: on a clay tablet found near the pyramid, there is a problem of multiplying two numbers, the final product of which is expressed in Arabic numerals, and the result is a fifteen-digit number 195,955,200,000,000,000, which is the level of mathematical knowledge reached by the Sumerians 6,000 years ago. Explain that addition, subtraction, multiplication and division are no longer a problem for them. And in order to solve everyday problems, simple algebra and geometry are not difficult for them.

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