This entry is missing Overview , add relevant content to make the entry more complete, and it can also be upgraded quickly. Hurry up edit Come on! Zu Gui [g è ng] (456-536), a masterpiece of Zu Guizhi, with the word Jingshuo, Fan Yang Qiu County (today Hebei Laishui ）People. China Southern and Northern Dynasties Time mathematicians and astronomers, Zu Chongzhi Son of. The problem of calculating the sphere area with his father Chongzhi. Using the method of "Mou He Fang Gai" by the sage Liu Hui, the volume of the ball can be calculated by "the same power potential leads to the same product". "Nine Chapters of Arithmetic · Shaoguang" chapter "The technique of opening a circle": place the number of square feet and multiply it by sixteen, nine to one, and divide the square obtained by opening it, that is, to establish a circle. However, the income is not refined. [2] Liu Hui created the three-dimensional figure "Mouhe square cover", and the ratio of the volume of the ball to the volume of the Mouhe square cover is π to 4. [3] Zu Xuan then calculated the volume of the sphere by "the same power potential leads to the same product". [4]
Zu Chongzhi's father and son wrote the book "Conjugation" and "Sui Shu · Lvli Zhi", which said that "no scholar can study its profundity, so it is abandoned and ignored". [5]
- Chinese name
- Zu
- Alias
- Zu Jingshuo 、 Zu Youzhi
- Ethnic groups
- Chinese
- Occupation
- Mathematician
- Key achievements
- Put forward the "Zu principle"
Zudang [g è ng], also known as Zudangzhi, with the word Jingshuo, was a mathematician and scientist in the Southern Dynasty during the Southern and Northern Dynasties Zu Chongzhi 's son. [1] 
Zu Zu Chongzhi After his death, he wrote three letters in the third, eighth and ninth year of the reign of Emperor Tianjian of the Liang Dynasty (504 A.D.), suggesting that his father《 Daming Calendar 》, finally making his father's last wish come true. Zu Xuan's main job is to repair and edit his father's mathematical works《 Conjugation 》。 He used Zuo principle And created by him Openning roundness , developed his father's research results and skillfully proved that Volume formula 。 He worked out the formula Italy mathematician Cavalieri (Bonaventura Cavalieri, 1589-1647) at least 1100 years earlier. 
Zu Due to his family background, Zu Xuan also studied mathematics when he was young. Zu Xuanzhi had a wonderful idea. When he read and thought, he was very single-minded. Even if there was thunder, he could not hear it. Once, while walking, he thought about mathematical problems. As he walked, he unexpectedly bumped into a gunshot coming from the opposite side Xu Mian 。 "Bu She" is a very high official. Xu Mian is an important person in the Imperial Court, but he was touched by this young boy Be full of difficulties , can't help shouting. Only then did Zu Guizhi wake up. Liang Dynasty He fought with the Northern Wei Dynasty and failed. Zu Xuanzhi was detained by the Wei side and arranged to live in the post station. He was well treated. Zu Xuan also met an astronomy enthusiast Xindufang The two people often discuss astronomy and mathematics together, and they are very congenial. Zu Xuanzhi taught Xin Dufang his knowledge unreservedly, which made him make great progress. Zu Xuanzhi also made great achievements in science《 Daming Calendar 》It was his suggestion that Liang Chao adopted it. Some records say that《 Conjugation 》There are his research results. He first came up with a formula for calculating the volume of a sphere, although Archimedes It is nearly a thousand years late, but it is also a crystallization of wisdom because it was obtained by using the original method with his father Chongzhi. He also developed Tongrigui Clepsydra And other precision observation instruments. Zu Yuzhi's son Zu Hao He continued his family studies and later became a mathematician. Zu Xuan passed on his mathematical knowledge to Xin Dufang, Mao Qicheng and his son Zu Hao, who later became mathematicians.
Zu Liu Hui When commenting on "Nine Chapters of Arithmetic", point out that the ball and Circumscribe “ Steinmetz solid ”The volume ratio of is a: 4, but he was unable to find the volume of the Mouhefang cover. Zu Chongzhi Father and son adopted the principle of "if the power potential is the same, the product cannot be different" (two equal height solids, such as Cross-sectional area The principle of constant equality, then equal volume) solves this problem and gives the correct formula of spherical volume. This principle is later called“ Zuo principle ”In the West, it was not until the 17th century that Italian mathematicians Cavalieri Rediscover. In astronomy, Zu Xuan wrote three times in 504, 509 and 510 to suggest the adoption of Zu Chongzhi's《 Daming Calendar 》, finally realized his father's last wish, and the "Daming Calendar" was Emperor Liang Wu Celestial supervisor It was issued in. He also personally supervised the construction of an eight foot copper watch, measured the length of the shadow, and found that Polaris There was more than one time difference from the fixed position of the North Celestial Pole, which was improved at that time timer ——Leaky kettle. His works include "The Lost Classics", "The Astronomical Record", etc., but the former is lost, while the latter has only a remnant. Zuo principle That is, "equal product principle" It was founded by the outstanding mathematicians of the Southern and Northern Dynasties Zu Chongzhi It was first proposed by Zu Xuan, the son of. The content of Zuo's principle is that two geometries sandwiched between two parallel planes are cut by planes parallel to these two parallel planes. If the area of the two sections is equal, then the two Geometry The volume of is equal. The discovery of equal product principle originated from《 Chapter Nine Arithmetic 》The answer in is wrong. The hard way he proposed was to take one inch on each side cube Eight pieces of chess, put together a square with a side length of 2 inches, and draw inside the square Inscribed cylinder , and then draw the same inscribed cylinder in the transverse direction. The three-dimensional common part contained by the two columns is like two umbrellas symmetrical up and down, Liu Hui Name it“ Steinmetz solid ”。 (In ancient times, the umbrella was called "cover", and "Mou" is the same as Mou, which means the same.) According to the calculation, the volume of the ball is three quarters of the volume of the Mou He square cover, but the cylinder is larger than the Mou He square cover. However, according to the Nine Chapters of Arithmetic, the volume of the ball is three quarters of the volume of the cylinder. Obviously, the volume of the ball in the Nine Chapters of Arithmetic Calculation formula Is wrong. Liu Hui believes that the volume of the ball can be calculated as long as the volume of the Mouhe square cover is calculated. However, it is impossible to find a way to find out the volume of Muhe Fang. More than 200 years later, Zu Xuan appeared, and he deduced the famous“ Zuo principle ”According to this principle Steinmetz solid And then derive the volume of the ball. This principle is mainly used to calculate some complex Geometry Above the volume. In the West, it was not until the 17th century that it was discovered by Italian mathematician Cavallieri. The principle of equal product was put forward in Continuous Individually Geometry published in 1635, so Westerners called it Cavallieri principle. In fact, his discovery was more than 1100 years later than that of our ancestors. The principle of "g è ng" refers to all equal heights Cross sectional area The theorem that the volume of two equal solids of the same height must be equal. This principle is easy to understand. Take a stack of books or papers and stack them on the horizontal desktop, and then push them to change their shape. At this time, the height has not changed, and the area of each page has not changed, so the volume of the stack of books or papers is equal to that before deformation. Zu Xuan not only put forward this principle explicitly for the first time, but also successfully applied it to the calculation of spherical volume. with Box Based on the volume formula and Zuo principle, the volume of column, cone, platform, sphere, etc. can be calculated. Zu Xuan's "Conjugation" said: "Since the edge power potential is the same, the product cannot be different." Zu Chongzhi Using this principle, father and son calculated the volume of the Muhe square cover, and then calculated the volume of the ball. Italian mathematicians in Europe in the 17th century Cavalieri The same theorem is also found, so the principle is generally called Principle of Cavalieri 。 In modern analytic geometry And measurement applications, Zuo principle yes Fubini theorem A special case of. Kavarelli did not have a rigorous proof of this article, but only published it in the GeometrieIndividibilibu 'in 1635 and the ExercisionsGeometrica' in 1647 to prove his MethoderIndividibili '. In this way, the volume of some solids can be calculated, even exceeding Archimedes And Kepler's achievements. This theorem led to the method of calculating volume by area and became an important step in the development of integration. If the vertical shaft is cut cylinder , set as radius, we can get Cross section Circle with area. according to Zuo principle ， Volume of cylinder Equal to square area Equal to Circular area Of Cube 。 From one layer to the height perpendicular to the surface Crosscutting Hemisphere with radius according to Pythagorean theorem , find the radius, horizontal section the measure of area. The contrast solid is the same as the hemisphere Surface area And tall solid, with one in the middle cone Body. The circular section of high contrast stereo has inner circumference and outer circumference, so both stereo meet Zuo principle And they have the same volume. The volume of the contrast solid is the difference between the volume of the cylinder and the volume of the cone. Therefore, the volume of the hemisphere was successfully calculated using this famous equation, and the formula for the volume of the sphere was derived. Zu Zuo principle The concept behind it often appears in Calculus Medium. As an example of dimension, the area between two intersection points of the two equations can be obtained by using the following equation:: Essentially, it means that the area between the function graph and is the same as that under the function graph, and the intersection distance of the latter is the same as that of the former. because modern mathematics The correlation between the integral and the area in the, and the volume can be calculated by differential, so that Zuo principle becomes less used.
