foreign country
There are records of scores and various scoring systems in ancient documents of many nationalities. As early as 2 100 BC, the ancient Babylonians (present-day Iraq) used fractions with a denominator of 60.
Fractions were also used in Egyptian mathematical literature around BC 1850, but at that time, fractions in ancient Egypt were only fractional units.
China
In the Spring and Autumn Period (770 BC-476 BC), Zuo Zhuan stipulated that the capital scale of vassals should not exceed one third of the capital of Zhou Wenwang, one fifth of the medium capital and one ninth of the small capital. The calendar of Qin Shihuang's time stipulated that the number of days in a year was 365 and a quarter days. This shows that scores appeared very early in China and were used in social production and life.
The earliest number produced in human history is a natural number (non-negative integer), but in the future measurement and averaging, it is often impossible to get accurate integer results, thus producing a fraction.
Use a standard quantity (unit of measurement) to measure another quantity, and only when the equivalent is accurately measured several times can the measurement result be expressed as an integer. If the quantity cannot be accurately measured several times, there are two situations:
For example, use b as a standard to measure a:
One case is that B is divided into n equal parts, and one of them is used as a new unit of measurement to measure A, which means that A contains m equal parts after B is divided into n equal parts. For example, divide B into four equal parts, and use one part of A to measure it exactly nine times. In this case, we can't use an integer to represent the result of measuring A with B, and we must introduce a new number-fraction to represent the measurement result.
On the other hand, no matter how many equal parts B is divided into, one of them can not be accurately measured as a new measure A (for example, the circumference of the same circle can be measured by the diameter of the circle). In this case, it is necessary to introduce a new number-irrational number. In integer division, when two numbers are divided, sometimes the integer quotient cannot be obtained. In order to make division always possible, it is also necessary to introduce a new number-fraction.
To sum up, the score is generated by actual measurement and average score.
origin
The history of scores began in Egypt more than 3000 years ago.
More than 3,000 years ago, ancient Egypt used special symbols to represent fractions with the numerator 1 in order to represent numbers that could not be divisible. China had music scores more than 2,000 years ago, but the forms of music scores in Qin and Han Dynasties were different. There is a fractional representation system in India similar to that in China. Later, Arabs invented the fractional line, and today's fractional expression also came from it.
More than 200 years ago, the Swiss mathematician Euler said in his book General Arithmetic that it is impossible to divide a 7-meter-long rope into three equal parts because there is no suitable number to represent it. If we divide it into three equal parts, each part is 7/3 meters. Like 7/3 is a new number, which we call a fraction.
name
mark
Why is it called a score? The name score shows the characteristics of this number intuitively and vividly. For example, a watermelon is divided equally among four people. Why not divide it into four equal parts? As can be seen from this example, the score is generated by the need of measurement and mathematics itself-the need of division operation.