Zhou Bi Suan Jing

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Geometric proof of the Pythagorean theorem from the Zhou Bi Suan Jing

The Zhou Bi Suan Jing, or Chou Pei Suan Ching, (周髀算經) is one of the oldest and most famous Chinese mathematical texts. The title literally means The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven.

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.

Marion Tzui Yang (1969-), a Taiwanese storyteller, has a different take on what appears to be "Chinese" Pythagorean Theorem. She follows the ancient texts closely and in one of her books about numbers, points out that this important discovery was a result of deliberate efforts from deduction of nine positive integers. It was the "Law of Numbers" in the dawn of this ancient civilization.


  • Boyer, Carl B., A History of Mathematics, John Wiley & Sons, Inc., 2nd edition, (1991). ISBN 0-471-54397-7.
  • Yang, Marion Tzui, The World of Numbers: Where Did Middle Land Come From?, CreateSpace Independent Publishing Platform (2014). ISBN 978-1500508593.

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