Which mathematicians have made important contributions to the exploration of pi

The Chinese mathematician Liu Hui used only the approximation of the circle with a regular polygon in the annotation of the Nine Chapters of Arithmetic (263), and also obtained a value accurate to two decimal places, and his method was later called circumcision. He used circumcision until the circle was inscribed with a regular 192 polygonal shape, and obtained the root number 10 (approx. Zu Chongzhi, a famous mathematician in the Northern and Southern Dynasties, further obtained a value accurate to 7 decimal places (about the second half of the 5th century), gave an under-approximation and an excess approximation, and also obtained two approximate fractional values, a dense ratio of 355 113 and an approximate rate of 22 7.

His brilliant achievements predate Europe by at least 1,000 years. The density rate was not obtained by the German Otto until 1573 in the West, and it was published in the work of the Dutch engineer Antonis in 1625. At the beginning of the 15th century, the Arab mathematician Qasi obtained the exact decimal value of 17 digits of pi, breaking the record held by Zu Chongzhi for nearly a thousand years.

The German mathematician Curran calculated the value to 20 decimal places in 1596 and devoted his life to the last 35 decimal places in 1610, which was called the Rudolf number after him. Various value expressions, such as infinite product formulas, infinite continuous fractions, and infinite series, have appeared, and the accuracy of value calculation has also increased rapidly. In 1706, the English mathematician Machin broke the 100-decimal place mark in his calculations.

In 1873, another British mathematician, Jeanccos, calculated the value to 707 decimal places, but unfortunately his result was wrong from 528 places. By 1948, Ferguson of the United Kingdom and Lench of the United States jointly published the 808-digit decimal value, which became the highest record for manual calculation of pi value.

Archimedes, Zu Chongzhi, Rudolph.

In ancient and modern times, many people have devoted themselves to the study and calculation of pi. In order to calculate an increasingly good approximation of pi, generations of mathematicians have devoted countless hours and efforts to this mysterious number.

Before the 19th century, the calculation of pi progressed quite slowly, and after the 19th century, world records for calculating pi were frequently updated. The entire nineteenth century can be said to be the century with the greatest amount of manual calculations of pi.

In the twentieth century, with the invention of the computer, the calculation of pi advanced by leaps and bounds. With the help of supercomputers, people have obtained an accuracy of 206.1 billion bits of pi.

One of the most marathon calculations in history was Ludolph van Ceulen in Germany, who spent almost his entire life calculating the inscribed regular 262 sides of a circle, and obtained a 35-bit precision value of pi in 1609, so much so that pi is called Ludolph number in Germany; The second was William Shanks of England, who spent 15 years calculating 707 decimal places of pi in 1874. Unfortunately, later generations found out that he was wrong from the 528th place.

It doesn't really make much sense to calculate the value of pi so precisely. The value of pi used in the field of modern science and technology, a dozen digits is sufficient. If you use Rudolph's 35-bit precision pi value to calculate the circumference of a circle that encloses the solar system, the error is less than one millionth of the diameter of a proton.

In the past, people calculated pi to ** whether pi is a cyclic decimal. The mystery of pi has been unveiled since Lambert proved that pi is an irrational number in 1761 and Lindemann in 1882 to prove that pi is a transcendent number.

Nowadays, people calculate pi, mostly to verify the computing power of computers, and also, for interest.

Zu Chongzhi was taught in books.

The most now,

Mathematicians who have contributed to the circumference of a circle are:

LudolphZu ChongzhiCantor, a German historian of mathematicsArchimedesIndian mathematicians Bhashgaro, Wallis, Liu Hui, Kassi, Curran, Burn Stool, Mechinnapai, Shankos, Pi Brigade Ferguson Lench.

Liu Hui of the Three Kingdoms founded the circumcision, the judgment or Zu Chongzhi of the northern and southern forelimb dynasties, and accurately calculated pi to seven decimal places. , 7, they are Liu Hui and Zu Chongzhi respectively.

The approximation calculated by Liu Hui is.

Zu Chongzhi is, 2, Liu Hui and Zu Chonghui Chongshi, 1,

Through the famous mathematician Chern's prompt "true and false mathematics" theory.

The first to propose the correct calculation method of pi was not a mathematician, but a writer Liu Xin 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. The ratio is (6+2 3) 3 or pi).

And Archimedes, Liu Hui, Zu Chongzhi. The ratio of the circumference of a regular 6x2 polygon to the diagonal crossing the center point should be called a positive 6x2 marginal ratio.

The monument of ancient Chinese science - the sum of pi of Zu Chongzhi.

Zu Chongzhi was a mathematician during the Northern and Southern Dynasties, and his most important contribution was the precise calculation of pi.

Pi is the proportional number of the circumference and diameter of a circle. In the past, this number had been calculated inaccurately, and Zu Chongzhi was determined to overcome this difficulty. At that time, there were no modern computers, and calculations were made with chips (small bamboo sticks).

Zu Chongzhi often got up before dawn and moved his chips over and over again until late at night. He calculated more than 10,000 times and finally calculated that pi was between 3 1415926 and 3 1415927.

Zu Chongzhi (429 A.D. 500 A.D.) was an outstanding mathematician, astronomer, writer, geologist, geographer and scientist in China. During the Northern and Southern Dynasties, the Qi people, Han nationality, the word Wenyuan, was born in the sixth year of Emperor Yuanjia of Song Wen, and died in the second year of Yongyuan, Hou Yongyuan. His ancestral home was Fanyang County, Laishui County, Hebei Province, and in order to avoid war, Zu Chongzhi's grandfather Zuchang moved from Hebei to Jiangnan.

Zu Chang once served as Liu Song's "Great Craftsman", in charge of civil engineering, and Zu Chongzhi's father was also an official in the court. Influenced by the family since childhood.

Zu Chongzhi, for the first time in the history of world mathematics, calculated the value of pi ( ) to seven decimal places, that is, to. He proposed the approximate rate of 22 7 and the density rate of 355 113, which was the earliest in the world, and this achievement was nearly a thousand years ahead of the world, so some people advocated calling it the "ancestral rate", that is, the ancestor of pi. 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.

After many years of calculation, he also compiled a new calendar, the "Great Ming Calendar". It was the most advanced calendar in the world at the time. For the first time, the "Great Ming Calendar" introduced "precession" into the calendar.

It is proposed to set 144 leap 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 the long-lost guide car, the thousand-mile ship, and the water mill.

In addition, he also has research on **. But it has long been lost.

His works include "Commentary", "Interpretation of the Book of Filial Piety", "Yiyi", "Laoziyi", "Zhuangziyi" and "Narrative Differences".

Zu Chongzhi There is also a crater on the moon named after him.

1, this person is Zu Chongzhi, of course, Liu Hui has also made a certain contribution;

2. For a detailed explanation, please refer to:

The book "Fixation" written by him was included in the famous "Ten Books of Calculation" as a textbook for the supervision of Guozi in the Tang Dynasty, but unfortunately it was later lost. The Book of Sui and the Chronicles of the Law left a short record of pi ( ), and Zu Chongzhi calculated the true value between and , which was equivalent to the 7th decimal place, which was simplified into the most advanced achievement in the world at that time. Zu Chongzhi was selected as the first scientist in the world to calculate the value of pi to the 7th decimal place in the World Records Association, creating the world's largest in the China Discipline Association.

This record was not broken until the 15th century by the Arab mathematician Al-Qasi.

Zu Chongzhi also gave two forms of fractions: 22 7 (approximate rate) and 355 113 (dense rate), of which the dense rate is accurate to the 7th decimal place, which was not rediscovered in the West until the 16th century by the Dutch mathematician Otto. Zu Chongzhi and his son Zu Yuzhi also successfully used the Mouhe square cover to solve the calculation problem of the ball volume and get the correct ball volume formula.

Zu Chongzhi calculated pi to 7 decimal places for the first time, nearly a thousand years ahead of Europe.