Zhoubi Suanjing

The work's original title was simply the Zhoubi: the character 髀 is a literary term for the femur or thighbone but in context only refers to one or more gnomons, large sticks whose shadows were used for Chinese calendrical and astronomical calculations.

[1] The Zhoubi is an anonymous collection of 246 problems[dubious – discuss] encountered by the Duke of Zhou and figures in his court, including the astrologer Shang Gao.

[2] This concept of a 'canopy heaven' (蓋天, gàitiān) had earlier produced the jade bi (璧) and cong objects and myths about Gonggong, Mount Buzhou, Nüwa, and repairing the sky.

The original text being ambiguous on its own, there is disagreement as to whether this proof was established by Zhao or merely represented an illustration of a previously understood concept earlier than Pythagoras.

A translation to English was published in 1996 by Christopher Cullen, through the Cambridge University Press, entitled Astronomy and mathematics in ancient China: the Zhou bi suan jing.

[20] The work includes a preface attributed to Zhao Shuang, as well as his discussions and diagrams for the gougu theorem, the height of the sun, the seven heng and his gnomon shadow table, restored.

Title page from a Ming dynasty printed edition of the Zhoubi Suanjing
Pages of the Zhoubi Suanjing