Zu Chongzhi

Zu Chongzhi (429–500) was a Chinese mathematician and astronomer whose achievements included a highly accurate approximation of pi and calendar reform.

Pi: Pi is the ratio of a circle’s circumference to its diameter, an irrational constant used throughout mathematics. Zu Chongzhi’s best-known numerical result was an unusually precise bound on this constant.
Chinese remainder theorem: The Chinese remainder theorem describes how to solve systems of congruences with pairwise coprime moduli. Modular arithmetic offers a mathematical framework for reconciling recurring cycles in calendar computation.
Liu Hui: Liu Hui was a third-century Chinese mathematician known for influential commentaries and methods in geometry. His polygon-based approach to estimating pi preceded and informed the mathematical tradition Zu Chongzhi extended.
Daming calendar: The Daming calendar was a Chinese calendar system associated with Zu Chongzhi and introduced in 510, after his death. It carried forward his calculations for coordinating lunar months and the solar year.
Calendar: A calendar is a system for organizing days into periods that track astronomical cycles or social conventions. His calendar work addressed the challenge of aligning counted days with celestial cycles.
Astronomical observation: Astronomical observation is the systematic measurement of celestial objects and events. Calendar parameters depend on observations of the Sun, Moon, and planetary motions.
Three Kingdoms period: The Three Kingdoms period was an era of division in China from 220 to 280 CE. Liu Hui’s mathematical work emerged in this earlier period of Chinese history.
355/113: The fraction 355/113 is a rational approximation to pi accurate to about six decimal places. This approximation, attributed to Zu Chongzhi, remained a benchmark for precision for centuries.
Chinese calendar: The Chinese calendar is a lunisolar calendar system that coordinates lunar months with the solar year. The Daming calendar he helped develop belonged to this long-running calendrical tradition.
Solar year: A solar year is the time Earth takes to complete one cycle of seasons, measured relative to the Sun. Estimating the year’s length was essential to the accuracy of Zu Chongzhi’s calendar.

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Chinese mathematicsBroader topic: His approximation of pi exemplifies advanced computation in early imperial China.