What are Zu Chongzhi s research results on pi?

By the 5th century AD, pi.

There has been a big leap forward in the calculation of the exact value of . The world has given birth to a famous mathematical superstar and outstanding Chinese mathematician Zu Chongzhi.

Born in 429 AD, Zu Chongzhi was one of the most famous scientists of the Northern and Southern Dynasties in ancient China, and made outstanding contributions to mathematics, astronomy, and mechanical engineering. Zu Chongzhi once recorded the research results of his life's mathematics and astronomy in his masterpiece "Fixation".

in the book. However, it is very regrettable for future generations that this precious treasure book has been lost after countless wars. However, according to some other literature works at that time, later generations can understand that Zu Chongzhi once calculated pi to 6 decimal places, that is:

Liu Hui's "circumcision."

to achieve this result. If Zu Chongzhi really used the "circumcision technique", he would have to go through 11 times of doubling the process before finally finding the area of the circle with a regular 12288 side and an inner positive 24576 side, and for each time he doubled the process, he had to perform a sum of 9 to 18 digits of four rules and square operations.

Needless to say, it was a calculation at that time, and even now it is a relatively heavy task to calculate with a computer. In particular, it is worth mentioning that the "approximate rate" and "density rate" invented by Zu Chongzhi are not only simple and practical in practical life, but also the best fraction of pi. The approximate rate is the best approximation of all approximate scores with a denominator up to the hundreds; The density is also the best approximation among all approximate fractions with a denominator up to the thousands.

China's most - the world's first person to calculate the value of pi to seven decimal places: Zu Chongzhi.

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

Zu Chongzhi, Liu Hui, Cassie, Archimedes.

Archimedes. The great Greek mathematician Archimedes (287 212 BC) pioneered the theoretical calculation of pi as a precedent in human history.

Liu Hui. In 263 AD, the Chinese mathematician Liu Hui used the "circumcision" to calculate pi, he first connected the regular hexagon from the circle, and then divided it one by one until the circle was connected with a regular 192 sides.

Aye Bodo. Around 530 A.D., the Indian mathematician Ayebodo calculated that pi was about. Brahmagupta used another method to deduce the arithmetic square root of pi equal to 10.

Kathy. 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 Rudolf van Koylen 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.

Zu Chongzhi was the first to accurately reduce pi to the seventh decimal place.

Zu Chong studied natural sciences all his life, and his main contributions were mathematics, astronomical calendars, and mechanical engineering. On the basis of the precise method of exploring pi pioneered by Liu Hui, he actuarially calculated "pi" to the seventh decimal place for the first time.

That is, between and , the "ancestral rate" proposed by him has made a significant contribution to the study of mathematics. It wasn't until the 16th century that the Arab mathematician Al Qasi broke this record.

Zu Chongzhi's main contribution to pi:

The study of pi has positive practical significance, and his research adapts to the needs of production practice at that time. He personally studied weights and measures, and used the latest results of pi to correct the calculations of the volume of ancient measuring vessels.

In ancient times, there was a measuring instrument called "kettle", which was generally one foot deep and cylindrical in shape.

He also recalculated the "Lijia Quantity" created by Liu Xin in the Han Dynasty, and corrected the value with the "ancestral rate". Later, when people made measuring instruments, they used Zu Chongzhi's "ancestral rate" value.

1. Zu Chongzhi calculated pi to the seventh place. Zu Chongzhi first actuarially calculated "pi" to the seventh decimal place, that is, between and , the "ancestral rate" he proposed made a significant contribution to the study of mathematics.

2. During the Northern and Southern Dynasties, Zu Chongzhi calculated the approximate value of pi between and proposed, and proposed that the approximate rate of pi was 22 7, and the density rate was 355 113. Zu Chongzhi was the first to mention the upper and lower limits, and set pi between this boundary. And his exact value of pi was far ahead of the world at that time, and it was not until 1000 years later that the Arab mathematician Alqassic surpassed him.

Therefore, it has been proposed in the international community to name the "circumferential orange rate" as the "ancestral rate".

Zu Chongzhi's knowledge of pi is that Zu Chongzhi calculated that the true value of pi is between and is equivalent to the 7th decimal place.

1. On the basis of his predecessors, Zu Chongzhi calculated pi to 7 decimal places (i.e., between and) after hard study and repeated calculations, and obtained an approximate value in the form of pi fractions.

2. Zu Chongzhi calculated pi accurate to the 7th place in the number of small slag shelters, simplified into, 3. And used the latest pi results to correct the calculation of the volume of the ancient measuring instrument. In ancient times, there was a measuring instrument called a kettle, which was generally one foot deep and cylindrical in shape, and Zu Chongzhi used his pi research to find the exact value.

4. Zu Chongzhi also recalculated the amount of law made by Liu Xin in the Han Dynasty, and corrected the value by using the ancestral rate. Later, when people made measuring instruments, they used Zu Chongzhi's "ancestral rate" value.

Zu Chongzhi introduced:

1. Zu Chongzhi was born in Jiankang, his ancestral home is Fanyang County, Luoxian County (now Laishui County, Hebei), and he was an outstanding mathematician and astronomer during the Northern and Southern Dynasties of China. He devoted his life to the natural sciences, and his main contributions were mathematics, astronomical calendars, and mechanical engineering.

2. Zu Chongzhi also observed and calculated the orbits of the five planets in the sky and the time required to orbit for one week, and gave a more accurate five-star conjunction period.

3. Zu Chongzhi re-measured and came to the conclusion that Jupiter is supercelerated once every 84 years, that is, Jupiter's orbital period is determined to be years (now measured as years).

4. For example, Pizhou Zu Chongzhi designed and manufactured guide cars, thousand-mile boats, timers, etc., which have been driven by water mills and copper parts. In ancient China, the name of the guide car has been around for a long time, but its mechanism and structure have not been circulated.

Circumcision. Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, used circumcision to further obtain a value accurate to 7 decimal places (466 AD), gave an under-approximation and an excess approximation, and also obtained two approximate fractional values, a density rate of 355 113 and an approximate rate of 22 7, a record that has been maintained in the world for a thousand years.

In order to commemorate Zu Chongzhi's contribution to the development of pi in China, this estimated value was named "Zu Chongzhi's Pi", referred to as "Zu Chongzhi's Pi".

The answer is: Zu Chongzhi.

Zu Chongzhi (429 A.D. 500 A.D.) was an outstanding mathematician and scientist in China. During the Northern and Southern Dynasties, the Han people, the characters were far away. He was born in the sixth year of Emperor Yuanjia of Song Wen and died in the second year of Yongyuan, Marquis of Qi.

His ancestral home is Fanyang County, Laishui County (now Laishui County, Hebei). In order to avoid the war, Zu Chongzhi's grandfather Zu Chang moved from Hebei to Jiangnan. Zu Chang once served as Liu Song's "master craftsman", in charge of civil engineering; Zu Chongzhi's father was also an official in the court.

Zu Chongzhi received scientific knowledge from his family since he was a child. When he was young, he entered Hualin University and engaged in academic activities. In his lifetime, he successively served in the history of Southern Xuzhou (now Zhenjiang City), the government to join the army, the order of Louxian County (now the northeast of Kunshan City), the servant of the confessor, and the captain of Changshui.

His main contributions are in mathematics, astronomical calendars, and mechanics.

Zu Chongzhi's main contributions were mathematics, astronomical calendars, and mechanics. In addition, history records that Zu Chongzhi is proficient in music and rhythm, good at playing chess, and also wrote ** "Narrative Differences". Zu Chongzhi's writings are many, but most of them have been lost.

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 also worked with his son Zu Xuan to successfully use the Mouhe square cover to solve the problem of calculating the volume of the sphere and obtain the correct formula for the volume of the sphere.