Contains the idea of seeking the limit. Liu Hui gave an approximate value of pi =3. 14 1024. After getting pi = 3. 14, Liu Hui checked this value with the diameter and volume of copper standard for volume measurement, and found that the value of 3. 14 was still small. Then continue to cut the circle into 1536 polygon, find out the area of 3072 polygon, and get a satisfactory pi.
Around 480 A.D., Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, further got the result accurate to seven decimal places, gave the insufficient approximation of 3. 14 15926 and the excessive approximation of 3. 14 15927, and also got two approximate fractional values, namely density ratio, shrinkage ratio and density.
Extended data feature
It is of little practical significance to calculate the value of pi so accurately. A dozen pi values used in modern science and technology are enough. If the value of pi with 39-bit precision is used to calculate the size of the universe, the error is less than the volume of an atom. In the past, people calculated pi to explore whether pi circulated decimals. Since Lambert proved that pi is irrational in 176 1 and Lin Deman proved that pi is transcendental in 1882, the mystery of pi has been uncovered.
π plays a very important role in many fields of mathematics.
algebra
π is an irrational number, that is, it cannot be expressed as the ratio of two integers, which was proved by Swiss scientist johann heinrich lambert in 176 1. In 1882, Lin Deman proved that π is a transcendental number, that is, π cannot be the root of any integer coefficient polynomial.
The transcendence of pi denies the possibility of turning a circle into a square, because all rulers can only draw algebraic numbers, and transcendental numbers are not algebraic numbers.
References:
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