How did Zu Chongzhi discover pi?

Zu Chongzhi (429-500 AD) was a native of Laiyuan County, Hebei Province during the Northern and Southern Dynasties of China He read many books on astronomy and mathematics since he was a child, and he was diligent and studious, and practiced hard, which finally made him an outstanding mathematician and astronomer in ancient China

Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi Before the Qin and Han dynasties, people to"Trail three times a week"As pi, this is"Ancient rate"Later, it was found that the error of the paleorate was too large, and the pi should be"The circle diameter is more than three days", but how much is left, opinions differ Until the Three Kingdoms period, Liu Hui proposed a scientific method for calculating pi"Circumcision", use the circumference of the circle inscribed regular polygon to approximate the circumference of the circle Liu Hui calculates that the circle is inscribed with 96 polygons, and obtains =, and points out that the more sides of the inscribed regular polygon, the more accurate the value obtained Zu Chongzhi On the basis of the achievements of his predecessors, after hard study and repeated calculations, he found between and and obtained an approximate value in the form of fractions, which was taken as the approximate rate.

Take it as the density rate, where six decimal places are taken, it is the fraction with the numerator denominator within 1000 What method did Zu Chongzhi use to arrive at this result, there is no way to examine it now If it is assumed that he followed Liu Hui's"Circumcision"If you want to find this method, you have to calculate that the circle is connected with 16,384 polygons, which requires a lot of time and labor! It can be seen that his tenacious perseverance and intelligence in his studies are admirable Zu Chongzhi's calculation of the dense rate, foreign mathematicians obtained the same result, it is more than a thousand years later In order to commemorate Zu Chongzhi's outstanding contributions, some foreign historians of mathematics suggest that = be called"Ancestral rate"．

Zu Chongzhi read the famous classics at that time, insisted on seeking truth from facts, he compared and analyzed a large number of materials from his own measurement and calculation, found the serious errors of the past calendar, and had the courage to improve, and at the age of 33, he successfully compiled the "Ming Calendar", opening up a new era in the history of the calendar

Zu Chongzhi was an outstanding mathematician during the Northern and Southern Dynasties, how did he calculate pi?

What Zu Chongzhi discovered was not pi, but the ratio of the circumference of the regular 6x2 polygon of the approximate, approaching, approaching, or equivalent to the circle to the diagonal crossing the center point is a positive 6x2 marginal ratio.

It was not a mathematician who discovered pi in ancient and modern times, but Liu Xin, a writer in the late Western Han Dynasty in China. Liu Xin determined that pi was derived from the ratio of "the number of points on the circumference of the circle to the number of points on the diameter" 6+2 3 to 3.

And Archimedes, Liu Hui, Zu Chongzhi. and so on are all positive 6x2 marginal ratios.

Positive 6x2 edge ratio is not equal to pi.

Pi refers to the ratio of the circumference to the diameter of a circle on a plane.

Through the hard work of Zu Chongzhi, for the first time in the history of mathematics in the world, he calculated the value of the circumferential concealment rate ( ) to seven decimal places, that is, to. He proposed a rate of about 22 7 and a density rate of 355 113, which was the earliest in the world, more than a thousand years earlier than in Europe, so some people advocated calling it the "ancestral rate". He compiled the results of his mathematical research into a book called "The Art of Fixation", which was once designated as a mathematics textbook in the Tang Dynasty.

The "Da Ming Calendar" compiled by him introduced the "precession" into the source calendar for the first time. It is proposed to set 144 Yan months in 391 years. The length of a return year is calculated to be days, and the error is only about 50 seconds.

He was not only an outstanding mathematician and astronomer, but also an outstanding mechanical expert. We have recreated a variety of ingenious machines such as guide cars and thousand-mile boats that have long been lost. In addition, he also has research on **.

His works include "Commentary", "Interpretation of the Book of Filial Piety", "Yiyi", "Laoziyi", "Zhuangziyi" and "Narrative Differences", etc., all of which have long been lost.

During the Northern and Southern Dynasties, the famous mathematician Zu Chong accompanied the trouser chain to a pure beat to get a value accurate to 7 decimal places (about the second half of the 5th century), and concluded that pi should be between and .

As we all know, pi is a universal mathematical constant in mathematics and physics, which is represented by the Greek alphabet and is an irrational number, that is, an infinite non-cyclic decimal number. We use it to accurately calculate geometric problems such as the circumference of a circle, the area of a circle, and the volume of spherical permeability. But do you know how it was deduced that Cong Sakura came from?

Why some people say that it is closely related to the mysteries of the universe.

Zu Chongzhi has been fond of mathematics since he was a child, and he learned a lot of mathematics under the guidance of his father and grandfather. Once, his father brought him a copy of the Sutra of Calculations from the bookshelf, which was a famous mathematics book from the Western Han Dynasty or earlier. It is said that the circumference of a circle is three times its diameter.

So, he measured the wheel with a rope and checked it, only to find that the circumference of the wheel was a little more than three times the diameter of the wheel. He went to measure the basin again, and the result was the same. He thought that the circumference is not exactly 3 times the diameter, so how much longer is the circumference than the 3 diameters?

Before the Han Dynasty, China generally used three as the value of pi, that is, "three diameter one". This is a large error when calculating the circumference and area of a circle. On the basis of the scientific method of using "circumcision" to find pi created by Liu Hui, Zu Chongzhi used the method of opening and density, and after repeated calculations, found that pi is:

>。This was the most accurate value in the world at the time, and he became the first person in the world to calculate the exact value of the circumferential nuclear rent conversion rate to the seventh decimal place. It wasn't until more than 1,000 years later that this record was broken by the Europeans.

The calculation of pi is an outstanding contribution of Zu Chongzhi in mathematics, and some foreign historians of mathematics call it "Zu rate."