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Secondary sourceBook3rd century AD commentary on an earlier text

Zhoubi Suanjing

Zhao Shuang · 3rd century AD commentary on an earlier text

An ancient Chinese mathematical and astronomical text containing an independent proof of the right-triangle relation known in the West as the Pythagorean theorem.

Shows that the theorem associated with Pythagoras's name was proven independently in ancient China.

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Woodblock-style diagram from the Zhoubi Suanjing: a tilted square on a grid with labeled areas 朱冪 (red power) and a caption in vertical Chinese characters reading 勾股冪合以成弦冪, illustrating the Pythagorean relation.
Zhao Shuang, commentary diagram on the Zhoubi Suanjing, 3rd century AD.

About this source

What it is

The Zhoubi Suanjing is an ancient Chinese treatise on mathematics and astronomy. Its final form dates from around the Eastern Han period, though it claims older origins. In the 3rd century, the scholar Zhao Shuang added a commentary with a diagram proving the 'gougu' theorem, the Chinese version of the right-triangle relation, for a 3-4-5 triangle.

Why it matters

This text shows that the mathematical relationship associated with Pythagoras's name was discovered and proven independently in China, by scholars such as Zhao Shuang, separately from the Greek tradition. It reminds students that important ideas are often found in more than one culture.

Look closer

  • Why might two different cultures discover the same mathematical relationship without contact?
  • What does the diagram's method of proof tell you about how ancient Chinese mathematicians thought about shapes and space?
  • Why do we call this the 'Pythagorean theorem' in the West, even though it was known elsewhere too?

This book is part of the curated material that grounds the AI version of Pythagoras on Humy.ai — when students ask about related events, the AI can quote it and cite it.

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