Scientists / Mathematics
祖沖之
CN 0429-01-01 ~ 0501-01-01
Fifth-century Chinese mathematician and astronomer
Calculated pi to seven decimal places, a record unbroken for nearly a thousand years
Combined pure mathematics with calendar reform and mechanical invention
Chinese mathematician and astronomer born in 429 AD who calculated pi to seven decimal places, a precision unmatched for nearly a thousand years. He also reformed the calendar and invented mechanical devices.
What You Can Learn
Zu Chongzhi's pi calculation demonstrates that extraordinary results can emerge from patient, methodical work, a lesson for any data-intensive project. His practical ratio 355/113, still used in engineering, shows the value of elegant approximations that balance accuracy and simplicity. And his combination of pure mathematics with practical inventions models the integration of research and development.
Words That Resonate
To pursue the task of measuring heaven and earth, probing the minute and contemplating the marvelous.
当量天地之功を追い、窮微考妙す。
Personally measuring instruments and closely examining water clocks.
親量圭尺、躬察儀漏。
The ratio of the circumference of a circle to its diameter lies between 3.1415926 and 3.1415927.
Life & Legacy
Zu Chongzhi achieved the most accurate approximation of pi in the ancient world, pinning it between 3.1415926 and 3.1415927. This precision was not surpassed for nearly a millennium, and the fraction he derived, 355/113, remains one of the best rational approximations of pi.
Born in 429 during the Liu Song dynasty of southern China, he came from a family of astronomers and engineers. He served as a government official while pursuing mathematics and astronomy.
His calculation of pi used Liu Hui's method of inscribed polygons, extended to a 24,576-sided polygon. The computation required extraordinary patience and precision in manual arithmetic. He also derived the approximation 22/7 (which he called the 'rough ratio') and 355/113 (the 'precise ratio').
In astronomy, Zu Chongzhi reformed the calendar, creating the Daming Calendar, which more accurately predicted solstices and equinoxes. He calculated the length of the year as 365.24281481 days, remarkably close to the modern value.
He also built a south-pointing chariot, a mechanical compass vehicle, and water-driven mills. His son Zu Geng continued his mathematical work, calculating the volume of a sphere using a method similar to Cavalieri's principle, discovered independently in Europe over a thousand years later.
Zu Chongzhi died around 500 AD. A crater on the Moon is named in his honor, and his pi approximation remained the world's best until the work of Jamshid al-Kashi in the fifteenth century.
Zu Chongzhi's calendar reform faced political opposition from conservative officials who resisted change, yet his astronomical predictions proved more accurate than those of the incumbent calendar. The episode illustrates a recurring pattern in the history of science: established interests resist innovation even when evidence clearly favors the new approach. His son Zu Geng's calculation of the sphere's volume, using a principle independently discovered by Cavalieri in Europe over a millennium later, further attests to the family's mathematical stature.
Expert Perspective
Among scientists, Zu Chongzhi represents the peak of ancient Chinese mathematics. His pi approximation stood as the world record for a millennium. His calendar reform and mechanical inventions show the breadth of Chinese scientific achievement during the Southern Dynasties. His son's volume calculation independently prefigured Cavalieri's principle.