An Annotated Translation of the Zhou Bi Suan Jing

The Zhou Bi Suan Jing is the earliest mathematical classic in Chinese history. Zhou means circle, while bi means thigh. The book records a conversation between the Duke of Zhou and Shang Gao, including the earliest written record of the Pythagorean theorem: “three for the short side, four for the long side, and five for the hypotenuse.” It is also known as Shang Gao’s theorem. Using the simplest practical methods, the book determines astronomical calendars and reveals the patterns of the sun, moon, and stars. It covers the changing seasons and climate, as well as the principles behind the poles in the north and south and the alternation of day and night, providing later generations with a reliable guide to daily life. Ever since, mathematicians throughout the ages have drawn on the Zhou Bi Suan Jing, continually innovating and building upon it. The book embodies the diligence and wisdom of the Chinese people and stands as an enduring monument to the science and technology of the ancient world. This edition not only collates the original text but also provides detailed annotations for its worked examples and other content. It is the first complete translation with full annotations.