Highlights of Chinese Culture and History

Zu's Ratio - The World First

On the evening of September 15, 459, guests and friends gathered in the brightly and colorfully decorated house of Dai Faxing, captain of the palace guard of the Southern Song dynasty, to celebrate his birthday.

When all the guests had arrived and the banquet was about to begin, a bodyguard rushed in in a flurry, apparently out of breath. "Ma.. Master, there's trou...trouble outside. There is a bulletin saying...that the heaven.. heavenly dog is going to eat up the moon tonight." at this, a hush fell over the crowded hall, and the atmosphere grew tense and solemn. Presently, people were heard murmuring. In those days, they believed that a lunar eclipse occurred when "the heavenly dog was eating up the moon." This, they thought, was an ominous sign of impending disaster.

Boiling with anger, Dai Faxing swore aloud, "damn it! Who was it that put up the bulletin?" Though he was not a high-ranking official, Dai was a favorite of the emperor, and people all took care not to offend him. Pointing at the bright moon high up in the sky, some said ingratiatingly, "Your Honor, the moon is so full and bright, how can it be eaten up by the heavenly dog? That's sheer nonsense. There is no doubt that someone is trying to damage Your Honor's reputation. We must find out who that bastard is and teach him a lesson."

That day, Zu Chongzhi, a member of the Hualin Academy, was also present at the celebration. Though only about 30, he was already well versed in astronomy, and had long predicted, through an analysis and study of the laws of revolution of the sun, the moon, and the earth, that there would be a lunar eclipse that night. He was hoping to make use of this occasion to provide the people with a scientific explanation of why a lunar eclipse occurred, so as to help disabuse them of superstitious beliefs. Therefore, he put up the bulletin just before the came to the banquet.

When he saw Dai Faxing letting himself go like that, Zu stood up, calm and unruffled. "There is no need to make such a fuss. The bulletin was put up by me.I am quite sure that there will be a lunar eclipse tonight. As a matter of fact, the occurrence of a lunar eclipse is subject to its own laws. It has absolutely nothing to do with human weal or woe." This said, he took up several pieces of fruit from the table and, using them as the sun, the moon and the earth,illustrated the occurrence of a lunar eclipse. There were some who nodded approvingly.

Hardly had Zu finished his explanation when the moon started tarnish. Then suddenly a voice rang out loud in alarm. "The heavenly dog is eating the moon! Hurry! Let's drive it away! Don't let it eat up the moon!" Instantly, some people fell prostrate on the floor, while others began beating bronze trays in an attempt to scare away  the heavenly dog. Some guards in the courtyard even shot arrows skywards, saying that they were killing the heavenly dog in order to rescuer the moon. Zu Chongzhi found the chaotic scene both annoying and amusing, but he congratulated himself secretly on the fulfillment of his prediction.

With the help of his friends, Zu compiled a new calendar called the "Daming Calendar", which was based on his long astronomical observation and earnest study of the experiences of his predecessors. Owing to the obstruction of Dai Faxing and his like,Emperor Xiao Wu of Song did not approve of its adoption.

Zu was also well versed in mathematical science. In the course of studying mathematics, he found that the calculation of the circumference, area and volume of a circle must needs involve the use of the ration of circumference to diameter, but the figure 3.14 arrived at by people before him was not accurate enough. So he determined to carry on the computations done by his predecessors. He drew on the floor of his study a big circle with a diameter of ten Chinese feet and worked on all fours from morning to night dividing this great circle with small bamboo sticks into a polygon of 12 slides, 24 sides, 96 sides and so on, until he succeeded in having it divided into 12,888 sides. Then by making out the length of each side and the aggregate length of all the sides, he worked out the ration to seven decimal places, which made it somewhere between 3.1415926 and 3.1415927.This was the most accurate ration in the world so far, and the record was not broken until more than a thousand years later. In the history of mathematics, people used to dub the ratio of circumference to diameter the "Antonitz ratio," because a Dutch man named Antonitz was thought to be the first man to do it. Later,when people learned that Zu Chongzhi had long before arrived at a satisfactory answer, they suggested that it should be changed to "Zu's ratio."

Under the primitive conditions of his day, what great courage and stamina were needed for Zu to work out an unprecedentedly accurate ratio with only a number of small bamboo sticks. It was said that when he finally succeeded in making his calculations, those bamboo sticks were all red and shiny with constant handling.

By applying mathematical principles, Zu also invented a kind of water mill to pound rice and mill flour, built a fast sailing ship that could go over a hundred li a day,and made innovations with the design of the compass-guided vehicle to increase its accuracy. His son Zu Xuan, who carried on his career, was also accredited with many inventions in the history of Chinese science and technology.

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