Geometric proof of the Pythagorean theorem from the Zhoubi Suanjing
The Zhoubi Suanjing (Chinese: 周髀算經), or Chou Pei Suan Ching (周髀算经), is one of the oldest Chinese mathematical texts. "Zhou" refers to the ancient Zhou dynasty (周) c. 1046–771 BCE; "Bi" means thigh and according to the book, it refers to the gnomon of the sundial. The book is dedicated to astronomical observation and calculation. "Suan Jing" or "classic of arithmetic" were appended in later time to honor the achievement of the book in mathematics.
This book dates from the period of the Zhou dynasty (1046 BCE–256 BCE), yet its compilation and addition of materials continued into the Han dynasty (202 BCE–220 CE). It is an anonymous collection of 246 problems encountered by the Duke of Zhou and his astronomer and mathematician, Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm. This book contains one of the first recorded proofs of the Pythagorean Theorem.
Commentators such as Liu Hui (263 CE), Zu Geng (early sixth century), Li Chunfeng (602–670 CE) and Yang Hui (1270 CE) have expanded on this text.